The Relationship Between Anthropometry and Body Composition Assessed by Dual-energy X - R a y Absorptiometry in Women 75-80 years old: A r e N e w Skinfold Equations Needed? by Andrea Dalton H i l l B.Sc., The University o f British Columbia, 1991 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF M A S T E R OF SCIENCE in T H E F A C U L T Y OF G R A D U A T E STUDIES The Faculty of Education; School of Human Kinetics; Exercise Physiology We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y OF BRITISH C O L U M B I A August 2000 © Andrea Christine Dalton H i l l , 2000 In presenting degree freely at this the available copying of department publication of in partial fulfilment University of British Columbia, for this or thesis reference thesis by this for his and scholarly or thesis study. her for I of I further purposes gain that agree be It is shall requirements agree may representatives. financial the not that the Library permission granted by understood be allowed permission. Department of £ C { \ O O L - T h e U n i v e r s i t y of British Vancouver, Canada Date DE-6 (2/88) of- Columbia Ati^USr 23 s for -rAvMAM KtlOGTlCS an advanced shall for the that without head make it extensive of my copying or my written Abstract A link between age-related changes i n body composition (BC) and the increased prevalence o f disease and disability in old age has been w e l l established (Chumlea & Baumgartner, 1989; G o i n g et al., 1995; Shephard, 1997). Consequently, B C assessment is becoming increasingly important i n the evaluation o f the health and functional status o f the older adult. Individuals 75 years and older comprise one o f the fastest growing segments o f the population i n North America (Canada, 1999; Donatelle & Davis, 1994), yet current B C measurement techniques may not be accurate or reliable in this older age group. The intent o f this research was to develop new body fat prediction equations in elderly women based on anthropometry and the criterion method o f dual energy X-ray absorptiometry ( D E X A ) , which is considered to be more valid than conventional densitometry among the aging population (Baumgartner et al., 1995; Kohrt, 1998; Visser et al., 1998). Anthropometry, skinfold (SF) anthropometry, and D E X A (Hologic Q D R - 4 5 0 0 W ) body fat data were initially collected i n a sample o f 43 women 75-80 years old (m = 77.4yrs) as part o f a larger study investigating the effects o f strength training on strength, function, bone mineral density ( B M D ) , and B C . Eight B C prediction equations for the elderly were selected from the literature and applied to these data. The correlation, between prediction equations and D E X A ranged from 0.76-0.97. However, paired t-tests difference scores (8) showed that all but one o f the equations overestimated D E X A body fat i n these older aged women (8 ranged from - 3 . 3 k g to 4.0kg and 4.4% to 9.0%; p<0.001 in all cases). N e w equations were derived for F M , %Fat, trunk fat mass ( T F M ) and percent trunk fat (%TF) using a coffiblnation o f stepwise and all possible subsets regression procedures, as both total and regional' percent fat are important health indicators (Going et al., 1995). The following were entered as predictor variables: weight ( W T ) , height (HT), B M I , hip circumference (HC), waist circumference ( W C ) , S F ' s o f the subscapular (SS), suprailiac (SI), abdominal ( A B D ) , and midaxillary ( M A ) sites, the SS to triceps skinfold ratio (SSTRI), and the sum o f triceps, biceps, SI and SS ( S U M 4 S F ) ; except H C and S U M 4 S F were not included i n the trunk fat regressions. FM %Fat TFM %FT = = = = New Equations 0.611(WT) - .231(HT) + .143(MA) + 16.462 0.341 (WT) - .339(HT) + .285(MA) + 60.122 0.185(WT) - .008(HT) + .112(MA) + .136(WC)-2.072 0.387(MA) - .227(HT) + .356(WC) + 30.659 Adj. R 0.95 0.84 0.90 • 0.83 2 Cp 4.46 4.61 3.77 3.9 SEE 1.53kg 2.12% 1.27kg 2.76% Ultimately, the measure o f interest in body composition assessment is the value %Fat and thus supports using the %Fat equation over that for F M . Moreover, %Fat equation was associated with less error ( C . V . o = 5.9%; C . V . F M = 6.4%). The % T F equation, however, was less precise than the equation for total %Fat and therefore was not considered further in this research. Subsequent analysis showed the %Fat equation to be internally valid using the jackknife method for data splitting. Finally, %fat equations developed i n this study sample were tested i n two independent samples o f elderly women (71.1yrs and 74.5 yrs) and one sample o f younger women (33.4 yrs) shared by Baumgartner (1999) and Brodowicz (1999). Both independent studies used D E X A instruments manufactured by Lunar. N e w equations were / o F a t ii derived for this application using only the variables measured in these independent studies as the predictor variables. BROD BAUM %Fat %Fat Modified Equations = 9.819 + .162(SUM4SF) + .652(BMI) - .261(SS) = 9.198 + .696(BMI) + .295(TRI) Adj. R 0.82 0.80 2 SEE 2.21 2.37 The modified prediction equations were reasonably correlated (r = .73, .81) with %Fat from D E X A (Lunar) in the elderly women, yet paired t-tests results showed that the new equations significantly underestimated %fat by 6.6% ± 3.9 (p< 0.001)(BROD), and 5.1% ± 4.5 (p< 0 . 0 0 1 ) ( B A U M ) . A n unexpected finding was the accurate prediction o f %Fat i n the younger women (8 = -0.7% ± 5.4; p = 0.45). The correlation between predicted and measured %Fat was also stronger (r = .89). However, the two methods were not interchangeable as a trend in the residuals indicated that %Fat was underpredicted at low body fat and overpredicted at high body fat i n the younger women. A major finding o f this study was that neither existing equations nor the newly derived equations were able to accurately and reliably predict body fat i n independent samples o f elderly women. Some o f the prediction error can be attributed to inter-method differences and differences i n D E X A manufacturer, but this lack o f agreement also emphasizes the problem o f sample specificity with regression equations. Equations w i l l always perform better i n the sample from which they were derived and must be interpreted with caution when applied externally. A second major finding o f this research was that a single "best" equation did not exist for these data, but rather, several alternative models provided similar equation statistics and regression coefficients. However, the combination o f W T , H T (or B M I ) and S F ' s was better than S F ' s alone. Nonetheless, this study demonstrated that a strong relationship between anthropometry and D E X A exists among elderly women and that internally valid equations can be proposed for this population. Moreover, it is reasonable to conclude that prediction equations based on D E X A have greater face validity in elderly women than those based on densitometry, as the D E X A model is associated with fewer assumptions. Due to.the relatively small sample size, the new %Fat equation cannot be recommended at this time. However, this study shows promise for future use o f D E X A and anthropometry i n elderly women. t in Table of Contents Abstract : - ii List of Tables vi List of Figures vii Acknowledgements viii Dedication ix 1. Introduction 1 1.1 Rationale 1 1.2 Purpose 4 2. Review of the Literature 5 2.1 Health care implications o f an aging society 5 2.2 Study o f human body composition 6 2.3 Age-related changes in body composition 7 2.4 Conventional methods o f body composition assessment 9 2.5 Limitations o f conventional methods 12 2.6 Advances i n body composition technology 14 2.7 Support for D E X A as the criterion method for body composition 16 2.8 Hologic Q D R - 4 5 0 0 18 2.9 Limitations o f D E X A 19 2.10 Prediction equations 20 2.11 Development o f new prediction equations 23 2.12 Summary and study objectives 26 3. Methods 27 3.1 Subjects 27 3.2 Equipment and procedures - p 28 3.3 External databases 29 3.4 Data analysis 30 3.5 Research expectations 33 4. Results 3 iv 4 4.1 Characteristics o f study sample 34 4.2 Comparisons with existing databases 55 4.3 Performance o f previously published equations 57 4.4 Development o f new prediction equations 61 4.5 Validation o f new prediction equations 77 4.6 Performance o f modified prediction equations 78 5. Discussion 82 5.1 N e w prediction equations for women 75-80 years 82 5.2 Nature o f the sample population 84 5.3 Predictor variables 85 5.4 Criterion body fat 86 5.5 Regression procedures 89 5.6 Performance o f modified equations 90 5.7 Summary and recommendations . . . . . . . . 91 6. References / , 7. Appendices l i 93 101 Appendix I: Previously Published B o d y Composition Prediction Equations 102 Appendix II: Select Published Prediction Equations 103 Appendix III: M e d i c a l Clearance 104 Appendix I V : Informed Consent 105 Appendix V : Ethics Approval 107 Appendix V I : List o f Contact Authors 108 Appendix V I I : Letter o f Request for Data 110 Appendix XIII: Distribution o f Dependent Variables Ill Appendix DC: Distribution o f Independent Variables 112 Appendix X : Preliminary Stepwise Multiple Regression Analysis 115 Appendix X I : Stepwise Multiple Regression Analyses 119 Appendix X I I : A l l Possible Subsets Regression Analyses 137 Appendix XIII: Regressions for Final Equations 155 Appendix X I V : Descriptive Summaries for Independent Databases 159 Appendix X V : Stepwise Regression Outputs for Modified Equations 160 V L i s t o f Tables Number and Title Page Table 4.1.1: Descriptive Characteristics of the Study Sample 34 Table 4.1.2: Correlation Between Predictor Variables and Criterion Body Fat... 35 Table 4.1.3: Reliability of Skinfold Thickness Measurements 54 Table 4.1.4: Prediction of Total Body Mass from DEXA 55 Table 4.2.1: Summary of Current and Previously Published Group Descriptives 56 Table 4.2.2: Summary of Current and Previously Published Correlation Coefficients 56 Table 4.3.1: Previously Published Equations Selectedfor Analyses 57 Table 4.3.2: Prediction of FMfrom Published Equations Table 4.3.3: Prediction of%Fat from Published Equations 58 .'. 58 Table 4.3.4: Limits of Agreement for Predicted Fat and Criterion Fat 61 Table 4.4.1: New Regression Models for the Prediction of Body Fat 62 Table 4.4.2: Best New Prediction Equations for Body Fat 62 Table 4.4.3: New Skinfold Equations 62 Table 4.5.1: Jackknifed Internal Validation of New Prediction Equations 77 Table 4.5.2: Summary of Jackknifed Estimates 78 Table 4.6.1: Modified Prediction Equations 78 Table 4.6.2: Paired t-Test Comparisons for Elderly Women Table 4.6.3: Paired t-Test Comparisons for Younger Women Table 4.6.4: Limits of Agreement for Modified Equations and DEXA vi 79 79 79 L i s t of Figures Number and Title Page 4.1.1: Scatter Plots for DEXA Fat Mass and Independent Variables 35 4.1.2: Scatter Plots for DEXA %Fat and Independent Variables 42 4.1.3: Scatter Plots for DEXA Trunk Fat Mass and Independent Variables 47 4.1.4: Scatter Plots for DEXA %Trunk Fat and Independent Variables 52 4.1.5: DEXA Body Mass Regressed Against Standard Body Weight 55 4.3.1: Agreement Between Predicted and Measured Fat from Published Equations 59 4.4.1: Residual Analysis for the New Fat Mass Equation 64 4.4.2: Residual Analysis for the New %Fat Equation 67 4.4.3: Residual Analysis for the New Trunk Fat Mass Equation 70 4.4.4: Residual Analysis for the New % Trunk Fat Equation 73 4.6.1: Agreement Between Predicted and Measured Fat Mass in Independent Samples 80 vii Acknowledgements This study would not have been possible without the support and contribution from several individuals. I w i l l begin by thanking the members o f m y committee, D r . A l a n Martin, Dr. Robert Schutz and D r . Jack Taunton, for their support and guidance along the way and to the study participants who generously volunteered their time and energy. I owe an enormous "thank-you" to Deanna and Ivana for their work i n the anthropometry data collection and to Park for his assistance with statistics. I want to also extend m y gratitude to Rob L a n g i l l and D r . Rhodes from Buchanan Lab, and to Sonya Lumholst-Smith from the Changing A g i n g Program, for the use o f their equipment and facilities. Further acknowledgment goes to Dr. Gary Brodowicz and D r . Richard Baumgartner for sharing their body composition data sets. Finally, I must thank m y family and friends for their endless patience and encouragement. Vlll To my Irma Elizabeth Hamilton grandmothers, and Margaret IX Frances Dalton 1. Introduction 1.1 Rationale The health and well-being o f the rapidly expanding older adult population is becoming a major public health concern in North America as disease and disability become more prevalent with advancing age. M u c h o f the disease and disability affecting the elderly today has been linked to age-related changes i n body composition, which in turn, may largely be the result o f sedentary lifestyle practices and poor nutrition (Baumgartner, Stauber, M c H u g h , Koehler, & Garry, 1995; Chumlea & Baumgartner, 1989; Evans & Cyr-Campbell, 1997; Going, Williams, & Lohman, 1995; Shephard, 1997). Consequently, the measurement o f body composition is becoming increasingly important i n the assessment o f health, nutritional and functional status o f the older adult population and i n monitoring the effectiveness o f exercise, diet and medical interventions. W o m e n over the age o f 75 years comprise one o f the fastest growing segments o f the population (Canada, 1999; Donatelle & Davis, 1994), yet at present, no one method o f body composition assessment appears to be both accurate and convenient for use i n this more elderly population. Three major problems concern the measurement o f body composition in the elderly: 1) assumptions o f conventional criterion methods are invalid; 2) indirect methods based on conventional criterion methods w i l l retain errors associated with the criterion methods; and 3) the procedures o f conventional criterion methods may be less reliable. Hydrodensitometry, or underwater weighing ( U W W ) , has been considered the criterion method in body composition against which most indirect and more practical methods are standardized (Lukaski, 1987). Whole body density is measured and converted to percent body 1 fat using the well-known Siri's equation based on the conventional two-compartment (2C) model (Brodie, 1988a; K e y s & Brozek, 1953). The 2 C model divides the body into fat mass ( F M ) and fat-free mass ( F F M ) components and assumes a constant density o f l . l g / m l for the F F M component (Keys & Brozek, 1953; Lukaski, 1987). This model, therefore, does not hold for older adult populations whose F F M density (d ) is considerably lower and much more variable ffm due to rapid bone loss associated with aging (Baumgartner, Heymsfield, Lichtman, Wang, & Pierson, 1991; Deurenberg, Weststrate, & van der K o o y , 1989; Going et a l , 1995; Lukaski, 1987; Martin & Drinkwater, 1991). The U W W method is not convenient for field or clinical conditions, and therefore, it has been usual practice to regress more reasonable assessment methods against U W W . O f these, the most common indirect method is anthropometry, which includes the thickness o f the skinfold (SF), body girths, height and weight (Brodie, 1988a) (Durnin & Rahaman, 1967; Lohman, 1981). Since the strong correlation between anthropometry and body composition was discovered, numerous general and population specific equations have been derived to predict body composition from anthropometry (Durnin & Womersley, 1974; Martin, Ross, Drinkwater, & Clarys, 1985). Due to concerns for the aging population, several equations have been developed in the elderly over the past decade. However; many o f these equations were derived from body density measurements from U W W and w i l l thus retain errors inherent to the 2 C model (Baumgartner et al., 1991). Advances i n body composition technology now allow quantification o f previously unmeasureable fractions o f the F F M by dividing the body into either three compartments (3C) or four (4C) (Heymsfield et al., 1990; Mazess, Barden, Bisek, & Hanson, 1990). Dual-energy X ray absorptiometry ( D E X A ) has the capability o f dividing the body into 3 C : fat mass, non-bone 2 fat-free mass and bone mineral content, and therefore accounts for variation in the F F M component due to bone (Baumgartner et al., 1991). Originally developed for the assessment of bone mineral density, D E X A has demonstrated reasonable accuracy and precision in the measurement of soft-tissue components (Gotfredsen, Baeksgaard,* & Hilsted, 1997; Kelly, Berger, & Richardson, 1998b; Kelly, Shepherd, Steiger, &.Standi997; Kohrt, 1998; Mazess et al., 1990; Pritchard et a l , 1993; Svendsen, Haarbo, Hassager, & Christiansen, 1993). Fourcompartment models use a combination of hydrodensitometry, D E X A and total body water methods to assess body composition (Heymsfield et al., 1990). Although D E X A may be less accurate than the 4C methods, there is less error involved with using only one instrument (Guo, Chumlea, & Cockram, 1996). D E X A has a further advantage in that it can be used to assess regional body composition (Baumgartner et al., 1995). In the case of body fatness, excess abdominal adiposity (particularly internal fat) is more strongly linked to health risks than total body fat, and perhaps a more useful measure (Borkan et al., 1983). Like U W W , these more sophisticated 3C and 4C models are not practical for wide scale use because of equipment costs, the need for a laboratory setting, and the expense of trained technicians. Simple anthropometry equations based on 3C and 4C would be more useful and certainly more valid than 2C equations in the elderly. Research in this area has begun, but due to various limitations, none of the existing equations appear valid for women over the age of 75 (Chapman, Bannerman, Cowen, & MacLennan, 1998; Goran, Toth, & Poehlman, 1997; Svendsen, Haarbo, Heitmann, Gotfredsen, & Christiansen, 1991). 3 1.2 Purpose The primary intent o f this research was to evaluate the performance o f existing body composition prediction equations in a sample o f women ages 75 to 80 years and to propose new prediction equations based on D E X A for total and regional body fat for this population. Additionally, requests were made for independent databases o f both young and elderly women to test the performance o f the newly developed equations and confirm the need for separate assessment techniques among different age cohorts. 4 2. Review of the Literature 2.1 Health care implications of an aging society The number o f people aged 65 years and older in Canada is expected to nearly double over the next thirty years and comprise more than 20% o f the population as a result o f the aging "baby boomer" (Canada, 1999). A n even more dramatic rise is expected for people 75 years o f age and older due to increased life expectancy (Baumgartner et al., 1995; Canada, 1999; Going et al., 1995). Similar increases are predicted for the U . S . and other industrialized nations (Donatelle & Davis, 1994). A s disease and disability become more prevalent with age, the aging baby boomers w i l l no doubt place an unprecedented stress on the current health care system (Canada, 1999; Shephard, 1997). U . S . health care statistics for 1992 indicated that 36% o f all health care expenditures were spent on the elderly, who at that time comprised only 13% of the total population (Donatelle & Davis, 1994). There is increasing evidence that the maintenance o f desirable body composition in old age has important health and functional implications (Kuczmarski, 1989; Snead, Birge, & Kohrt, 1993). Information related to age-related changes in body composition and the factors influencing these changes w i l l therefore have substantial health care benefits. A s a result, the measurement o f body composition i n the elderly has become an important focus in the growing body o f literature on aging, body composition and health (Baumgartner et al., 1995; Chumlea & Baumgartner, 1989; Going et al., 1995; Visser et al., 1998; Visser, V a n D e n Heuvel, & Deurenberg, 1994). W o m e n continue to outlive their male counterparts and thus make up the majority o f seniors over the age o f 75 years (Canada, 1999; Donatelle & Davis, 1994; Shephard, 1997). 5 Consequently, the specific health care needs o f elderly women should be the focus o f future investigations. 2.2 Study of human body composition The study o f human body composition spans over 100 years and has applications in clinical research, basic science, medicine, nutrition, exercise physiology and i n the growing health and fitness industry (Heyward & Stolarczyk, 1996a; Lohman, Roche, & Martorell, 1988). Information related to body composition study can be categorized as biological or technical (Wang, Pierson, & Heymsfield, 1992). Biological research seeks to describe the changes in body components with growth, illness and aging, the factors affecting change, and the resulting effect on health and function (Roubenoff, Kehayias, Dawson-Hughes, & Heymsfield, 1993). Technical research focuses on the methodology involved arid aims to improve the assessment o f body composition and thus our understanding o f the biological information. Recent investigations on aging and body composition have been primarily technical i n nature as practical, accurate and reliable methods, requisite for epidemiological research and furthering our understanding o f the aging body and the relationship between body composition and health and function, are currently lacking for elderly women. Conventional methods do not account for the several anatomical and physiological changes i n the aging body which must be considered when developing new measurement tools for elderly women (Shephard, 1997). 6 2.3 Age-related changes in body composition Several age-related changes i n body fat, muscle, bone and water content have been documented i n the literature. Consequently, methods used to assess body composition in older adults must take these many changes into account. Furthermore, women do not age in the same way or at the same rate as men and should be considered separately in the research. Throughout the lifespan, women tend to be fatter than their male counterparts, with a preferential deposit o f adipose fat in the limbs and lower body, and more subcutaneously than internally (Vogel & Friedl, 1992). W i t h aging, numerous studies have shown a gradual increase in body fat and body weight (Going et al., 1995; Shephard, 1997). After menopause, the typical gynoid fat patterning is less apparent due to declines i n estrogen production, and fat stores tend to "migrate" to the trunk and visceral cavity (Ley, Lees, & Stevenson, 1992; V o g e l & Friedl, 1992). The redistribution o f fat appears to stabilize after age 65 (Baumgartner et al., 1995). Changes i n total body fat beyond age 60 are less clear. Conflicting reports have indicated both steady inclines (Baumgartner et al., 1995; Protho & Rosenbloom, 1995) and declines (Going et a l , 1995) for the older age groups. Excess adiposity has been long associated with an increased risk for several chronic diseases such as coronary heart disease, hypertension, hypercholesterolemia, diabetes, osteoarthritis, obesity and some cancers (Blair et a l , 1996; Chumlea & Baumgartner, 1989; Durnin & Womersley, 1974; Seidell, Deurenberg, & Hautvast, 1987; Shephard, 1997). More recently, the risk for heart disease and mortality has been more strongly linked the amount of abdominal and intra-abdominal fat (Borkan, Hults, Gerzof, R o b b i n s , & Silbert, 1983; Vogel & Friedl, 1992). In more extreme cases o f over fatness, reduced mobility levels can limit performance in daily routines and have lasting socialand emotional effects (Brodie, 1988a). 7 Extremely low body fat in older age has also been related to an increased risk for morbidity and mortality (Visser et al., 1994). Muscle, bone and water content remain relatively stable until the fifth or sixth decade i n life and then begin to decline (Going et al., 1995). Recent data from a study o f elderly people ages 65-85 years indicates that these'd'eclines continue into the ninth decade o f life and an average o f 6-7% o f these combined components may be lost over the 20 year span (Baumgartner et al., 1995). Wasting o f appendicular skeletal muscle is the primary source o f this decline, and accounts for approximately 60% o f the lean tissue lost with aging (Baumgartner et al., 1998; Kirkendall & Garrett, 1998). Significant and rapid bone mineral loss associated with postmenopause can contribute an additional 11% to this decline i n elderly women (Baumgartner et al., 1995; V o g e l & Friedl, 1992). Disability among the elderly has been linked to age-related declines in both muscle and bone. Muscle wasting has been associated with decreased muscle strength, endurance and mobility which, i n turn, can limit performance in activities o f daily living and threaten the independence o f the elderly (Evans & Cyr-Campbell, 1997). Significant bone mineral loss may result in osteoporosis and an increased susceptibility for fractures (Kelley, 1998; Kuczmarski, 1989). A dehydrating effect has also been observed with aging. Total body water ( T B W ) decreases from 50% o f total body weight in early adulthood to 4 5 % in middle age (Going.et al., 1995), and a possible total loss o f 4-6 litres by old age. A t present, it is unclear whether the aqueous fraction o f the fat-free tissue is effected by the loss in T B W . Several studies indicate no change in the water content o f fat-free tissue due to proportional losses in both water and muscle 8 (Deurenberg et al., 1989; Going et al., 1995), while others report small increases in the hydration level o f fat-free tissue with aging (Baumgartner et al., 1991). Together, these unfavourable changes in body composition greatly impact health and functioning i n old age. Although several biological and environmental factors likely interact to influence the age-related changes, current research suggests that chronic inactivity and poor nutrition play a major role (Evans & Cyr-Campbell, 1997; Going et al., 1995; Shephard, 1997). This has led scientists, health and fitness professionals to believe that the risk for disease and functional decline i n older age could be greatly reduced through regular exercise and proper nutrition. Consequently, the measurement o f body composition has become increasingly important in the assessment and management o f disease and disability among the elderly. 2.4 Conventional methods in body composition assessment The only true direct measures o f body fat or other body constituents is through cadaver analysis (Brodie, 1988a; Clarys, Martin, & Drinkwater, 1984); thus, human body composition assessment relies on methods o f indirect measure. Assessment techniques are commonly categorized as either criterion methods (which are actually indirect methods) or indirect methods (which are essentially doubly indirect). (i) densitometry Research on conventional methodology dates back to the 1940's and the lab of Albert Behnke whose primary interest was in the measurement o f body fatness (Lukaski, 1987). Early criterion methods o f densitometry were based on a two-compartment (2C) chemical model which partitions the body into fat mass ( F M ) and fat-free mass ( F F M ) , based on the premise that F M is considerably less dense than all other components o f the body (Heymsfield et al., 1989; Keys & 9 Brozek, 1953). The F M component contains all lipids in the body, both essential and nonessential, and the F F M includes everything else (mineral, protein, water, and all other body constituents other than lipid) (Going et al., 1995). A measure o f whole body density (D ) is b therefore dependent on the relative contribution o f F M and F F M , and is inversely related to percent body fat. Hydrodensitometry, or underwater weighing ( U W W ) has been considered the "gold standard" i n body composition against which most other methods are compared to (Brodie, 1988a; Clarys et al., 1984; Jebb & Elia, 1993; Lukaski, 1987). Using the principle o f Archimedes and U W W , Db can be calculated from body volume, by subtracting body weight i n water from body weight i n air, and then converted to percent body fat using Siri's equation (%Fat = 495/Db - 450) or other similar formulae (Brodie, 1988a). This model, however, relies on assumptions that the consistencies o f the F M and F F M are unchanging and are o f constant density, with values o f 0.9g/ml and l . l g / m l , respectively (Brodie, 1988a; Keys & Brozek, 1953). Other 2 C models include total body potassium and total body water ( T B W ) (Heymsfield et al., 1989). U W W is not practical for large-scale epidemiological studies or many private clinics because o f the equipment required (Brodie, 1988a; Brodie, 1988b; Guo et ah, 1996; Jebb & E l i a , 1993; Lohman, 1981; Lukaski, 1987; Shephard, 1997). Thus, extensive efforts have been made to describe body composition, particularly body fat, using simpler, yet more indirect methods. (ii) anthropometry The most common indirect method to assess body composition is anthropometry. Anthropometry includes the measurements o f the skinfold thickness (SF), body circumferences, 10 breadths, height ( H T ) , weight ( W T ) and body mass index ( B M I ) (Durnin & Rahaman, 1967; Durnin & Womersley, 1974; Heyward & Stolarczyk, 1996a; Keys & Brozek, 1953; Lohman, 1981; Martin & Drinkwater, 1991). Anthropometry methods are the most widely used because the equipment involved is relatively simple, inexpensive, highly portable and non-invasive (Lohman et al., 1988). The S F has been studied extensively i n the body composition literature because o f the strong relationship between the subcutaneous layer o f adipose tissue, body density and percent body fat (Durnin & Womersley, 1974; Lohman, 1981). Using spring-loaded calipers, the thickness o f one or several S F sites (which contains two layers o f skin as well as adipose tissue) are measured and compared to criterion body fat, usually measured by densitometry (Lohman et al., 1988). Numerous general and population specific equations have been developed to predict body fat measured by U W W from anthropometry (Lohman et al., 1988). Various regression techniques have been used to determine the best predictors o f body composition i n specific populations, and subsequently, the best equation to describe the relationship between anthropometry and criterion body fat (Guo et al., 1996). Height, W T , B M I and trunk or limb circumferences are often added i n combination with SF anthropometry i n order to improve the prediction equation (Baumgartner et al., 1991; Dupler, 1997; Goran et al., 1997; Williams, Going, M i l l i k e n , H a l l , & Lohman, 1995). Anthropometric predictors o f body fat must have strong statistical and biological support for their selection. Finally, equations specific to elderly women must reflect the uniqueness o f the aging female body i n the choice o f predictor variables. The prediction o f body composition from' SF anthropometry is also based on certain assumptions. First, a constant proportion between subcutaneous fat and internal fat deposits is 11 assumed and second, the fat content o f adipose tissue is presumed constant. Additionally, skin thickness and S F compressibility are assumed constant within and between individuals at various anatomical sites (Keys & Brozek, 1953; Martin et al., 1985). 2.5 Limitations of conventional methods W h e n U W W and anthropometry are used to measure body composition i n the elderly population, biological variations i n the assumptions o f the 2 C model, and technical error are both sources o f potential error (Going et al., 1995; Heymsfield et al., 1989; Lohman et al., 1988; Martin & Drinkwater, 1991). Densitometry and Siri's conversion to percent fat, require the density o f F F M (dff ), to be unchanging. This is true among young and middle-age adults, but m not the case for older adults whose muscle, bone and water fractions all change with aging. O f these, the density o f the bone mineral content is the greatest, and therefore, variations in this fraction w i l l have the largest impact on the measurement o f dff . Significant bone mineral m loss associated with aging lowers the overall density o f the F F M , and thus, violates the assumptions o f constant dff and value o f l . l g / m l (Going et al., 1995; Shephard, 1997). A s a m result, body fatness is overestimated i n the elderly when Siri's formula is applied (Martin & Drinkwater, 1991). This error is likely more drastic i n elderly women who experience more rapid and significant bone demineralization (Vogel & Friedl, 1992). Several researchers have accounted for this b y modifying Siri's equation (Deurenberg et al., 1989); however, others have shown this to be unacceptable (Baumgartner et al., 1991; Williams et al., 1995). Williams et al. (1995) have demonstrated that adjusted two-component models under and overestimate percentage body fat measured b y a multi-component model by 6% and 14%, respectively. 12 A n additional concern is the U W W procedure itself. The process o f maximally expelling air from the lungs and breathholding while remaining still underwater may be too stressful and difficult for elderly subjects to perform successfully, and could result i n further erroneous measurements o f total body density (Baumgartner et al., 1991; Brodie, 1988b; Jebb & Elia, 1993; Shephard, 1997). Measurement techniques and assumptions o f the S F method may introduce further error. M a n y experts have questioned the reliability o f the S F measurement i n elderly populations as several studies have demonstrated greater error, in, the prediction o f body fat from skinfold anthropometry with increasing age (Baumgartner et al., 1995; Williams et al., 1995). Others suggest that age-related changes in the hydration affect the elasticity and compressibility o f the subcutaneous adipose layer may alter the relationship between the skinfold thickness and body fat content (Chumlea & Baumgartner, 1989). Changes in the elasticity and compressibility o f the SF as a result o f dehydration and reduced muscle tone have been implicated (Chumlea & Baumgartner, 1989). Finally, the inability o f the S F to detect internal fat stores could result in an undersampling o f total body fat and thus alter the relationship between anthropometry and body composition. In the cadaver study, Martin et al. (1992) showed just as much variation in S F compressibility among and within elderly subjects as others attribute to aging. The variability i n compressibility among 13 cadaver subjects (ages 55-94 years) resulted i n a 2.4% deviation in percent body fat for both men and women when estimated by the Jackson & Pollock equation (Martin, Drinkwater, Clarys, Daniel, & Ross, 1992). This was the first investigation to examine the effect o f compressibility on body fat predictions, and as all the subjects were older in age, it 13 is difficult to say whether variations i n compressibility are age-related or due to individual differences. The effect o f skin thickness on the prediction o f body fatness was also examined in this study. It was proposed that i n lean subjects a thicker layer o f skin would lead to greater measurement error. W o m e n have larger skinfolds than men and were found to have thinner skin thickness as well. The potential problem associated with skin thickness is therefore much less i n women. Furthermore, in both men and women, the skin thickness at the subscapular site was greater than any other anatomical site and therefore may be less reliable i n the prediction o f body fat (Martin et al., 1992). Again, subjects were elderly, and hence, the independent factor o f age on skin thickness was not clear. Finally, less reliable prediction o f body fat in the elderly from anthropometric methods could be attributed to poor inter-method agreement. Measurement errors in body composition w i l l be propagated from one level o f directness to the next, and consequently, prediction equations derived from U W W w i l l retain the systematic errors inherent to the 2 C model (Baumgartner et al., 1991). (Heymsfield et al,, 1989). 2.6 Advances in body composition technology Advances i n body composition technology now allow for quantification o f previously unmeasureable tissue in vivo. W i t h the development of dual-photon absorptiometry (DP A ) , and then dual-energy X - r a y absorptiometry ( D E X A ) , bone mineral mass and density can be assessed with high precision and accuracy; thus, resolving limitations associated with densitometry and the 2 C model (Heymsfield et al., 1989; Mazess et al., 1990). 14 Both D P A and D E X A have been used i n combination with other criterion methods to measure body composition using a four-compartment model (4C). Typically densitometry, T B W and neutron activation have been among the other methods. This model separates the body into fat (F), fat-free mineral (M), fat-free protein (P), and aqueous ( A ) fractions (Heymsfield et al., 1990), and therefore, has the advantage o f being able to detect differences in hydration. This model is now considered the most valid model to assess human body composition in vivo. However, expensive instrumentation, complicated procedures, moderate levels o f radiation and time involved all limit its use to research and laboratory settings (Going et al., 1995; Goran et al., 1997; Heymsfield et al., 1990). Furthermore, the gains in accuracy may be offset by a loss in precision due to the accumulation o f error associated with the use o f multiple assessment methods (Guo et al., 1996). The most promising method to replace U W W as the gold standard is D E X A as it is based on a three-compartment model (3C) (Kohrt, 1995). Originally designed to measure bone, D E X A has the ability to accurately and precisely assess soft tissue components by dividing the body into fat mass, fat-free bone mineral content ( B M C ) , and fat-free bone-free mass (Kelly et al., 1997; Kohrt, 1998; Mazess et al., 1990). Several investigations have shown D E X A to be more accurate and precise than U W W when compared to 4 C measurements o f body composition (Prior et al., 1997; Pritchard et al., 1993). Moreover, D E X A has distinct advantages over the multi-method approach as D E X A is safe (< l r e m dose o f radiation for a whole body scan) and convenient for the subject, requires minimal time (~ 5-15 minutes for a whole body scan) and is of moderate cost (Gotfredsen et al., 1997; K e l l y et al., 1997; Mazess et al., 1990; Roubenoff et al., 1993). A more detailed discussion o f D E X A follows. 15 2.7 Support for DEXA as the criterion method for body composition assessment The principle mechanism underlying D E X A is the differential tissue attenuation o f photons from two energy levels emitted from an X-ray source (Jebb & Elia, 1993; Mazess et al., 1990; Svendsen et al., 1993; Wellens et al., 1994). Thus, D E X A can only discriminate two substances i n a given system (or pixel). First, it distinguishes bone-mineral (high attenuation) from soft-tissue (low attenuation) then energy levels are reset to allow for distinction of the F M and F F M components o f soft-tissue. The mass attenuation coefficients o f bone mineral at the two beam energies are known constants whereas the ratio o f the mass attenuation coefficient o f soft-tissue ( R ) is related to the fatty fraction and must be calculated from all the pixels that st contain soft-tissue only. Non-bone fat-free mass is the remainder (Svendsen et al., 1993). Early investigations conducted by Mazess et al. (1990) were the first to demonstrate D E X A ' s high precision i n the measurement o f percent fat (1.4%) and fat mass (1.0kg) in 12 young adult men and women. In another study using younger adults, the precision o f two different manufacturers o f D E X A (Hologic Q D R 1000W and Lunar D P X ) and the U W W method were compared (Pritchard et al., 1993). The Hologic model o f D E X A measured percentage fat with far greater precision than the Lunar model as reflected by the coefficient o f variation ( C V ) for Hologic (CV=1.3%) versus Lunar (CV=3-4%), and both were superior to UWW (CV=4.8%). A look at between-method differences showed better agreement between Hologic and U W W than with Lunar and U W W (Pritchard et a l , 1993). These results have been confirmed elsewhere (Jebb, 1997). D E X A ' s ability to assess various body constituents with high accuracy still awaits validation studies against cadavers; however, this is also true for densitometry and it has been considered the gold standard criterion method for several years now. U n t i l then, the validity o f 16 D E X A depends on its accurate measurement o f known quantities o f meat and lard, inanimate materials whose physical and chemical properties simulate that o f humans, animal carcasses and 4 C determined body composition (Gotfredsen et al., 1997; Kohrt, 1998; Prior et al., 1997; Svendsen et al., 1993; Visser et al., 1998). In vitro studies and comparisons with other methods have indicated good accuracy for D E X A measurements o f F M and F F M (Kohrt, 1998; Snead et al., 1993; V a n L o a n & M a y c l i n , 1992; Wellens et al., 1994); however, results based on these studies are limited because o f the unknown accuracy o f other reference methods. Until 1993, the validity and accuracy o f D E X A had not been examined in vivo (Svendsen et al., 1993). Svendsen and colleagues (1991) measured whole body composition i n seven adult sized pigs using the Lunar D P X version. Pigs were then killed and homogenized, then subjected to chemical analysis and compared to results obtained from D E X A . Correlation and regression analyses yielded r-values > 0.97 for all compartments assessed. Measurement error was low with values o f 2.9%, 1.9kg, and 2.7kg for the S E E o f %fat, F M , and non-bone F F M , respectively. Svendsen et al. (1993) also showed that D E X A accurately detected changes in body fat by measuring body composition before and after 8.8kg o f lard were placed on the ventral side o f the bodies o f six women, ages 24-49. The ability for D E X A to monitor change in body fat was confirmed i n 10 young adults, age 28 years, with 1.51kg packets o f lard using Hologic 1000W instrumentation (Kohrt, 1998). Several researchers have validated D E X A against 4 C models. Prior and colleagues (1983) found D E X A fat and fat measured using a 4 C model to be highly correlated (r = 0.94) and not significantly different in 172 college-aged men and women. Furthermore, D E X A demonstrated superior accuracy and precision than methods o f densitometry (Prior et al., 1997). 17 Others have shown reasonable agreement between these two methods at the group level, but substantial error i n individuals (Jebb, 1997). In a different study, however, densitometry was found to be more accurate and precise than D E X A in both young and elderly women (BergsmaKadijk, Baumeister, & Deurenberg, 1996). D E X A also has.the ability to measure regional body composition (Baumgartner et al., 1995). This may have an advantage in health related studies as abdominal fat appears to be a stronger risk factor for disease than total body fat. 2.8 Hologic QDR-4500W Three manufacturers o f D E X A exist (Lunar, Hologic and Norland), yet to date only a paucity o f information is available on the cross-calibration o f different manufacturers for soft tissue measurement (Jebb, 1997). Although general conclusions from the literature can be applied to most D E X A instrumentation, the exact level o f accuracy and precision for one model cannot be assumed for another. Consequently, data generated by different manufacturer's machines cannot be compared (Roubenoff et al., 1993). Moreover, discussions o f D E X A thus far have been based on pencil-beam technology and cannot be assumed for the most recent model o f D E X A , the Hologic 4500W, which uses a fan-array scanning technique. The Hologic 4500W is considered equally precise, yet more accurate than earlier Hologic pencil-beam instrumentation (1000, 1500 and 2000 series) in whole body composition analysis (Kelly, 1998a; K e l l y et a l , 1997; Visser et al., 1998). The fan-beam scanner completely and uniquely samples the subject, whereas the pencil-beam typically under samples and then relies on linear extrapolation to estimate missing data (Kelly et al., 1997). Although the fan and pencil-beam assessments are highly correlated (r =0.98) (Fuerst & Genant, 1996), fan beam 18 models compared more closely with C T scans i n the assessment o f limb fat mass (Kelly, 1998a). The precision for the fan beam i n the measure o f F M was 300 grams and 600 grams for the pencil beam. Due to superior spatial assessment, QDR-4500 has overcome some o f previous problems associated with fan-array which made this method less precise (Clasey et al., 1997). Because o f the superior sampling technology, minimal scan time, and high accuracy and precision o f Q D R - 4500, this model has been selected for two national studies supported b y the National Institute o f Health (NIH). The Health A B C Study and the N H A N E S I V (National Health and Nutrition Examination) w i l l provide large volumes o f data related to health, aging and body composition. 2.9 Limitations of DEXA D E X A , however, is not without limitations. Some suggest that its inability to detect differences i n hydration may be problematic i n the measurement o f the elderly (Roubenoff et al., 1993). Small but systematic and predictable errors i n soft tissue composition were noted with fluid balance changes i n a recent study (Pietrobelli, Wang, Formica, & Heymsfield, 1998). Similarly, another group o f researchers showed that an increase i n lean tissue mass was correlated to fluid intake (Thomsen, Jensen, & Henriksen, 1998), while others found the density of F F M to be unaffected b y declines i n total body water due to proportional losses in both water and muscle tissue seen with aging, (Deurenberg et al., 1989). Kohrt (1998) also found that fat mass measured b y D E X A appeared to be relatively unaffected by fluctuations in hydration status. Although D E X A assumes a constant value for the water content o f the F F M (73.2%), Baumgartner et al., (1995) suggested that there is no theoretical or empirical evidence that 19 suggests D E X A under or over estimates body fat i n elderly. Therefore, the effect o f hydration o n the measurement o f body composition remains unclear. A previous problem o f D E X A underestimating central regions o f body fat was not found in this study and was attributed to improvements in software and instrumentation. Beam hardening may occur in large subjects i n the trunk regions (Baumgartner et al., 1995; Gotfredsen et al., 1997) and thus may be a concern when assessing obese individuals. Further, the scanning arm, and thus the scanning area is limited i n size to approximately 190 X 60cm; again, problematic for measuring large or obese persons (Jebb & Elia, 1993). Finally, little is known about the algorithms used for analysis, which seem to be i n state o f constant review (Gotfredsen et al., 1997; Jebb & E l i a , 1993). ? Despite these possible limitations, D E X A has greater validity than U W W in the assessment o f elderly body composition. Like U W W , however, D E X A instrumentation is not highly accessible outside o f research. Practical indirect methods based on D E X A would therefore be useful. The relationship between anthropometry and D E X A has not been thoroughly explored i n the elderly and warrants further attention. 2.10 Prediction equations Several prediction equations have now been developed for specific use i n the elderly population. A summary o f the more common and more recent equations is presented in Appendix I. O f these, 8 equations were based on methods o f anthropometry and are discussed further. One o f the most widely used equations to assess body composition is that o f Durnin and . Womersley (1974)(DW); however, several have criticized its use in the elderly population. A 20 • large age-range o f subjects was used to develop the equation and o f these, only 37 females ages 50-68 years were included at the elderly end o f the spectrum. Furthermore, the S F equation was derived from reference body fat measured by densitometry. Visser and colleagues (1994) improved upon this by using more than 200 subjects with an average age o f 70 years. However, U W W and densitometry were again used to measure criterion body fat, and was therefore, still subject to problems associated with the 2 C model. Dupler (1997) considered some o f the previous limitations and used modified U W W procedures to develop new S F equations for the elderly. A g a i n , a large sample was used and the average age was 70 years. Furthermore, agerelated changes in fat patterning were considered and therefore only trunk S F sites were measured. However, this study still retains the problems with 2 C model and Siri's equation. Chapman and co-researchers (1998), predicted D E X A F F M (R = 0.96) from W T , H T 2 and the thickness o f the triceps (TRI) SF. However, the subcutaneous fat o f the T R I is only weakly correlated to F F M , and was probably not the most appropriate choice o f predictor variables (Guo et al., 1996). Furthermore, only 17 women were used to develop this equation and no cross-validation was attempted. The F M equation developed by Svendsen and colleagues (1991) included B M I , W T , H T , TRI, and the ratio o f subscapular:triceps S F ' s (SSTRI) and was based on D E X A (R =0.94). The sample size o f women was small with an « = 2 3 , and again, this 2 equation was not cross-validated. A s well, the ratio o f the number o f subjects to number of independent variables was just over 4:1, when the minimum recommended is 10:1 (Heyward & Stolarczyk, 1996b). In many o f these studies', only T R I or the sum four skinfolds ( S U M 4 S F = biceps+triceps+suprailiac+subscapular) were the only S F ' s measured, therefore it was unclear whether other S F sites might have improved the prediction equation. Waist (WC) and hip ( H C ) 21 circumferences did not significantly improve the prediction equation for Durnin and Womersley (1974), Svendsen et al. (1991) or Visser et al. (1994), but H C was included in the final equations for Dupler (1997). Waist circumference correlated strongly with both the absolute amount o f fat in the trunk measured by D E X A (r =.90 in women) and with the manually determined abdominal fat {r =.87); however, equations were not developed in this study (Baumgartner et al., 1995). O n l y two studies to date have examined more practical techniques o f body composition assessment against a 4 C model. Williams et al. (1995) found a lower S E E associated with bioelectric impedance analysis (BIA) regressed against F F M than for the sum o f 10 S F ' s and F M and therefore developed new equations F F M based on B I A only. Individual S F ' s and body circumferences were not examined in this study. A s well, only 23 women ranging from 49-80 years (m=65yrs) were measured. A similarly aged but slightly larger sample was used to validate existing equations against 4 C criterion body fat and to consider new equations for the elderly (Goran et al., 1997). H i p circumference, W T , B M I and the sum o f 9 S F ' s were highly correlated with F M , while W T , H C , and the calf skinfold (CF) were included in the final regression equation. Neither o f these 4 C equations were cross-validated for their accuracy in other samples. Because o f many changes in body composition that continue with aging, Baumgartner (1995) recommends not grouping all elderly persons together as one homogeneous group, but rather, treating each decade after 60 as a separate age cohort. Future development of prediction equations should therefore focus on narrower age ranges. A s well, prediction equations for the elderly should be based on criterion methods that involve minimal assumptions. Prediction equations based on Hologic Q D R 4 5 0 0 w i l l therefore be an improvement to existing 2C equations. 22 2.11 Development of new prediction equations The prediction equation allows the estimation o f criterion body fat from indirect measurements b y way o f regression analysis. One or several predictor (independent) variables are typically entered into the regression analysis, along with the criterion (dependent) variable. Outwardly simple, however a range o f procedures and criteria should be used to optimize the development o f new prediction equations (Guo et al., 1996; Heyward & Stolarczyk, 1996a). First, the validity o f the criterion method must be demonstrated. Second, the measurement precision o f both criterion and predictor variables should be high. Assumptions o f linearity, homogeneity and normality must be met. When a non-linear relationship between independent and dependent variables is apparent, linear transformation o f the data may be necessary. This is often the case for the relationship between S F ' s and body density, and therefore, log transformations o f the data or quadratic equations are common (Durnin & Womersley, 1974; Lohman, 1981). Strong correlations between predictor variables and the criterion measure are also requisite for the development o f a useful equation. Pearson product correlation coefficients (r) are used to describe the strength o f the statistical relationship between two variables; r >/= 0.75 indicates a good to excellent correlation (Portney & Watkins, 1993). However, often this is the only selection criterion used, and sometimes a weak scientific or biological association between the variables is overlooked. Examples o f this are when skinfold thicknesses are used to predict F F M , or B I A is used to estimate F M , and should be avoided (Guo et al., 1996). Finally, a variety o f statistical applications are necessary to determine which predictor variables should be entered into the equation, how many, in what order, and to test the stability and accuracy o f the equation (Cohen & Cohen, 1975; Guo et al., 1996). 23 When the nature o f the research is exploratory, the most common approaches are stepwise, forward, maximum R , and all possible subsets regression procedures (Brodie, 1988a; 2 Cohen & Cohen, 1975; Durnin & Womersley, 1974; Hansen et al., 1993; Teran et al., 1991; Visser et al., 1994). However, when sample sizes are small and an independent sample for external cross-validation is not available, the stepwise procedure is not recommended (Guo et al., 1996). Alternatively, Draper and Smith (1966) recommend using a combination o f both stepwise and all possible subsets procedures. The magnitude o f the multiple regression coefficient o f determination (R ) determines how much o f the prediction o f body fat can be 2 explained by the predictor variables, and the standard error o f the estimate ( S E E ) indicates how precise this prediction is. The use o f M a l l o w ' s statistic ( C ) has also been recommended when p the sample size and number o f predictor variables are small (Ott, 1984). The C statistic is the p ratio SEEp/s 2 - ( N - 2p) where SEE/? is the residual sum o f squares for a model with p parameters, and s is the residual mean square based on the regression equation with all the 2 independent variables. The lowest C value corresponds to the subset o f predictors with the p highest R and lowest S E E ; however, a C value that is close to equal the number o f regression 2 p coefficients is said to be the most stable equation when sample size is small. The equation selected should be parsimonious. Additional variables should be included i f they improve the precision o f the equation, but not too many so that multicollinearity among independent variables becomes a problem and affects the stability o f the equation (Guo et a l , 1996). To avoid this problem, the variance inflation factor (VIF) can be calculated to detect significant interrelations among the predictors. The size o f the sample required can be determined by power analysis. (Cohen & Cohen, 1975). To detect a difference in R = 0.05, with an alpha level of 0.05 and a power of 0.8, a 2 24 sample size o f n = 222 is required, whereas an n = 46 w i l l detect a difference in R = 0.15 with a 2 power o f 0.6 when three predictor variables are used. A n alternative recommendation is to ensure a m i n i m u m o f 10 to 20 subjects for each predictor variable (Heyward & Stolarczyk, 1996a). Nonetheless, a survey o f the literature demonstrates a range o f sample sizes when deriving new regression equations from as small as n = 34 to n > 200 (Chapman et al., 1998; Durnin & Womersley, 1974; Svendsen et al., 1991; Teran et a l , 1991; Visser et al., 1994). M a n y o f these studies have included men and women o f several different ages i n their sample; further inspection showed that very few investigations contained large numbers o f elderly women. Finally, cross validation on an independent sample is then recommended to test the accuracy o f the newly derived regression equation, but is often not feasible (Howell, 1997). Alternatively, when the sample sizes are large, it is acceptable to use internal cross-validation b y dividing the sample into a prediction and validation group but should not be considered an equal substitute for the more stringent external validation (Baumgartner et al., 1991; Cohen & Cohen, 1975; Teran et al., 1991). When sample sizes are small, and internal cross-validation is not appropriate, the jackknife or press technique can be employed to check robustness o f the newly derived equation (Baumgartner et al., 1991; Guo et al., 1996). U s i n g this technique, the study sample is split into 10 equal groups and regression analysis is performed 10 times with a different group eliminated each round. Residual errors are compared to the corresponding S E E of the equation to determine the validity (Guo et al., 1996). 25 2.12 Summary and study objectives The number o f elderly women in the population is growing rapidly i n North America. In order to contribute to the successful aging o f this older adult population, further research is needed to improve our understanding o f specific changes in body composition and their subsequent impact on health and functioning, as well as to learn more about factors influencing these changes. Accurate and reliable body composition assessment methods, that are also practical and easy to administer, are essential for the collection o f large volumes o f data requisite for epidemiological research. A s w e l l , private health care and fitness facilities would benefit from the availability o f simple assessment tools to evaluate body composition status and monitor the effectiveness o f exercise, diet or medical interventions. The following objectives are proposed for this research: 1) to assess the relationship between anthropometry and D E X A body fat i n women 75-80 years; 2) to test the performance o f previously published equations in these women; 3) to determine the best anthropometric predictors o f body fat i n elderly women; 4) to develop new and improved body composition prediction equations for total body fat and regional trunk fat ,~ v (i) using an appropriate selection o f predictor variables, (ii) using D E X A as the criterion method, (iii) and using appropriate regression methods; 5) to test the performance o f new prediction equations in independent samples (i) i n similarly aged women (ii) and in younger women to evaluate the impact o f age on equation development and performance. 26 3. Methods 3.1 Subjects The study sample consisted o f 40 Caucasian women and 3 Asian women between the ages o f 75-80 years. A l l participants were considered healthy and were free-living in the community. Participants were recruited through advertisements in community centres, senior centres, and local media as part o f a larger study that examined the effects o f progressive resistance exercises on muscle strength, functional ability, bone mineral density and body composition i n women 75-80 years old. More than 140 women volunteered for the study, but over half were considered ineligible because they were too young (< 75 years), too active (exercising 3 or more times per week) or required transportation assistance. Additional respondents were excluded for medical conditions outlined in the physician's clearance form (Appendix III). A final requirement for entry into the study was the participant's consent (Appendix I V ) . Ethics approval was granted by the Research Ethics Board o f the University o f British Columbia (Appendix V ) . Forty-six women participated i n the study; however, two individuals were outliers (more than 2 standard deviations from the mean) for both body fat and B M I and were eliminated from further analyses as skinfold anthropometry is considerably less reliable at extremely high body fat (Heyward & Stolarczyk, 1996b). A third participant was eliminated because her D E X A data was not available for analysis. Thus, 43 women comprised the final study sample on which the results and discussion are based. 27 3.2 Equipment and measurement procedures B o d y composition was assessed by dual energy X-ray absorptiometry ( D E X A ) and anthropometry at the baseline o f the "parent" strength training study, and by anthropometry only during the study and at the end. The purpose o f collecting body composition data iri this "parent" study was to monitor the effects o f strength training on body composition for a yearlong period. O n l y the baseline data were used for this current research. D E X A ( Q D R - 4 5 0 0 W ; V8.20a:5; Hologic Inc., Waltham, M A ) was used to measure criterion body fat. The Q D R - 4 5 0 0 W model used fan-beam technology to perform whole body scans with the subject lying supine. Subjects wore light clothing with all jewelry and metal items removed. Each scan took approximately. 5.minutes at the slow array speed. Default values for total body fat mass ( F M ) , total percent fat (%fat), regional trunk fat mass ( T F M ) and percent fat o f the trunk (%fatT) were used as criterion measures. Standard anthropometry methods were used to collect indirect measures of body fatness. Height (HT) was measured to the nearest 0.1cm using a standard stadiometer and weight ( W T ) was measured with a digital scale to the nearest 0.1kg. Waist ( W C ) and hip ( H C ) circumferences were measured to the nearest 0.1cm using a non-expandable tape measure. The site o f the W C was defined as the narrowest girth between the ribs and the iliac crest, while the H C was measured at the m a x i m u m girth around the buttocks. Harpenden calipers were used to measure the following eight skinfold (SF) sites described by Ross & Marfell-Jones (1982) and Heyward and Stolarczyk (1996b): triceps (TRI), biceps (BIC), subscapular (SS), midaxillary ( M A ) , suprailiac (SI), abdomen ( A B D ) , mid-thigh ( T H ) and medial calf (CF). Descriptions of the anatomical sites are shown below. Each SF site was marked and measured in duplicate on the right side o f the body i n rotational order, with the exception o f the abdominal SF, which was 28 measured on the left side. A third measurement was taken i f the first two differed by more than 2 m m (or 10%). The final S F measurement was the average o f the closest two S F values. Harpenden calipers were set at a constant pressure o f 9.4g/mm and calibrated regularly. 2 Skinfold Direction of fold Anatomical site TRI vertical M i d p o i n t between the acromial process and olecranon process on the posterior aspect o f the arm. BIC vertical SS diagonal Same level as marked for the triceps but o n the anterior aspect o f the arm. The inferior angle o f the scapula along the natural cleavage line. MA SI ABD TH vertical oblique vertical A l o n g the midaxillary line at the level o f the xiphoid process. Superior to the iliac crest and anterior to the midaxillary line. 2 c m lateral to the umbilicus and at the level o f the umbilicus. vertical M i d p o i n t between the inguinal crease and the patella with the knee and hip flexed at right angles and the foot supported. CF vertical A t the level o f m a x i m u m calf circumference o n the medial aspect o f the calf, again with the knee and hip at right angles. Anthropometric data were collected within one day o f the D E X A assessments. Where possible, subjects were measured at the same time o f day for the two methods. Again, the same qualified fitness appraiser conducted all anthropometric measurements to eliminate inter-rater variability. 3.3 External databases To determine whether or not existing body composition equations recommended for elderly women could accurately predict body composition i n 75-80 year old women, 8 published equations (Appendix II) were selected from the literature and tested i n this study sample. The literature was surveyed specifically for studies that derived prediction equations i n elderly women using anthropometry and S F ' s for the independent variables. Furthermore, studies were chosen for a range i n dependent variables in order to examine equations based on two (2C), three 29 (3C) and four (4C) compartment models o f body composition. Additionally, descriptive data provided in these studies were used as reference data with which to compare our current data. ' Finally, i n order to test the application o f new prediction equations for body composition, a search through Medline, Dissertation Abstracts and the Oregon Microfiche databases was conducted to find independent studies that measured similar variables to this study. More specifically, studies that measured reference body fat by D E X A , anthropometry and a minimum of 4 S F ' s i n young, middle-age and elderly women were sought out. A s a result o f this search, letters were sent to 6 external investigators requesting raw data for D E X A , anthropometry and SF's (Appendix VI). Gary Brodowicz (Brodowicz, 1999) and Richard Baumgartner (Baumgartner, 1999) shared their data sets with us. Brodowicz provided data for both elderly women and young adult women, while Baumgartner supplied data for elderly women only. A n email request was also sent to M i c h a e l Goran on Baumgartner's (1999) suggestion, but data were not available. 3.4 Data analysis SPSS (version 8.0) and B M D P software were used for the following data analyses. Before proceeding with the development o f new equations, assumptions o f the linear regression model were considered. Scatter plots and Pearson correlation analyses were used to determine the nature and strength o f the relationships between independent and dependent variables, and to evaluate the need for linear transformations. Distributions for the independent and dependent variables were observed, and skewness and kurtosis statistics were examined to determine the need for data transformations. Skewness and kurtosis values o f less than 1 were considered acceptable. The Pearson's correlation coefficient and the paired t-tests difference score for 30 repeated S F measures were used to determine the reliability o f the SF measurement. Finally, the accuracy o f D E X A i n the measurement o f total mass was examined by regressing D E X A mass against standard body weight ( W T ) . To confirm the need for new body composition prediction equations for elderly women, 8 published equations, described previously (Appendix II), were applied to the current data. Paired t-tests were used to calculate the mean differences between predicted and reference body fat for these equations, while the Pearson's correlation coefficient and the Bland-Altman (1986) comparison technique were used to assess the agreement between prediction equations and the reference method o f D E X A . The Bland-Altman technique compares the difference between predicted and reference body fat against the average value o f these two measurements. A combination o f stepwise and all possible subsets regression procedures was used to develop four new prediction equations for total fat mass (FM), total percent body fat (%Fat), trunk fat mass ( T F M ) and percent trunk fat (%TF) as recommended by Draper and Smith (1966). They suggested using stepwise procedures first to determine the number o f predictor variables included i n the "best" regression model, and then, all possible subsets procedures to select the most stable and practical equation. According to stepwise methods, the best model is determined by the subset o f predictor variables that maximizes the multiple regression coefficient (R ) and minimizes the standard error o f the estimate ( S E E ) for the prediction o f the dependent variable. However, i n this study, the adjusted R (adj. R ) was used because o f the relatively small sample 2 2 size (<100). Furthermore, predictor variables are only included i f their contribution to the regression model is significant. The all possible subsets method generates an additional equation statistic, M a l l o w ' s C ; the subset with the lowest C value is generally considered the best Overall p p model. However, when both sample size and the number o f regression coefficients are small, the 31 most stable equation has a C value approximately equal to the number o f predictor variables p (Ott, 1984). Height, W T , B M I , S F ' s ( A B D , B I C , M A , SI, SS, T R I , C F and T H ) , the sum o f B I C , T R I , SI and SS ( S U M 4 S F ) , the ratio o f SS and T R I S F ' s (SSTRI,), and trunk girths ( H C and W C ) were initially regressed against F M and %Fat. H T , W T , B M I , A B D , M A , SI, SS, S S T R I and W C were entered as predictor variables for T F M and % T F . The selection o f the final regression equations was primarily based on the adj.R , S E E , and C criteria. However, strong biological 2 p associations for the individual predictors and body fatness, and each variable's significance in previously published equations were also considered (Guo et al., 1996). N e w equations were considered useful and acceptable tools to predict total body fat in women 75-80 years i f the corresponding S E E was less than 2.5;kg for F M and less than 3.5% for %Fat (Heyward and Stolarczyk, 1996b). N o guidelines were available for the prediction o f trunk fat. Residual analyses were conducted/for the final regression equations to ensure homogeneity i n the variance o f predicted body fat for all values o f the dependent variable (Dupler, 1997). A n independent group o f women was not measured for the purpose o f external validation; therefore, the equations were validated internally. The jackknife procedure described by Guo et al. (1996) and Baumgartner et al. (1991) was used to test the internal validity o f the new equations as conventional data splitting was not recommended for sample sizes o f less than 100. The data was split into 10 almost equal groups (7 groups o f n = 4, and 3 groups o f n = 5). For each round o f the jackknife validation, one group was omitted and the regression equation was developed for the remaining nine groups. This process was repeated 10 times. The smaller the error o f the residuals (body fat predicted - body fat measured by D E X A ) for each jackknifed equation, the more stable and accurate the equation was within the sample (Guo et al, 1996). 32 A s %Fat is the body composition measure o f interest, the new equation for %Fat was applied to the independent databases o f Brodowicz (1999) and Baumgartner (1999) which included D E X A %Fat, anthropometry and S F measurements for both similarly aged women and younger women. Unfortunately, the best model for the prediction o f %Fat included the M A SF, which was not measured in either o f the other studies. Modified equations were therefore developed, using only the variables measured i n the other studies as possible predictor variables. Paired t-tests and correlations were used to determine the difference between predicted and measured %Fat. Agreement between the prediction equation and D E X A was again assessed according to Bland and Altman (1986). 3.5 Expectations 1. Existing 2 C equations selected from the literature are expected to overestimate D E X A fat i n our sample o f women ages 75-80 years; while 3 C and 4 C equations are expected to estimate D E X A fat more closely but w i l l not be reliable due to methodological limitations. 2. A s the relationship between anthropometry arid D E X A composition in elderly women is presumed more valid than that anthropometry and body density, new prediction equations based on D E X A w i l l have higher R values than those reported for 2 C equations. 2 3. Due to changes i n fat patterning and the relationship between anthropometry and total body fat with aging, new equations w i l l predict body fat more accurately (smaller difference between measured and predicted fat) and more precisely (smaller S E E , and narrower limits of agreement) i n the independent sample o f elderly women compared to the younger women. 33 4. Results 4.1 Characteristics of the study sample Results were based on data from 43 women 75-80 years old. Sample population descriptives for age, anthropometry, skinfold measures and D E X A measures are summarized i n Table 4.1.1. Table 4.1.1: Descriptive Characteristics of the Study Sample Mean s.d. Skewness Kurtosis Age H T (cm) W T (kg) 77.4 1.8 N/a N/a 158.1 6.4 0.3 -0.7 66.4 11.0 0.6 0.2 ABD Mean s.d. Skewness Kurtosis 32.1 8.6 -0.8 1.1 BIC CF MA 20.0 7.1 0.3 -0.3 26.1 8.2 0.2 -0.9 23.2 7.2 -0.8 -0.3 BMI W C (cm) H C (cm) WHR 87.4 11.6 0.2 -1.1 101.4 8.7 0.5 -0.3 0.86 0.08 N/a N/a 26.6 4.0 0.5 -0.2 SI SS 19.5 6.7 -0.1 -0.3 21.4 8.2 -0.0 -0.7 TH TRI 36.5 9.2 -0.5 -0.5 27.6 7.4 0.1 -0.4 S U M 4 S F = triceps + biceps + subscapular + suprailiac S S T R I = subscapular : triceps skinfold thickness ratio F M (kg) Mean s.d. Skewness Kurtosis 23.79 7.03 0.7 0.3 % STJM4SF SSTRI 143.7 39.6 -0.2 -0.1 0.76 0.20 -0.1 -0.4 Fat T r u n k F M (kg) % Trunk Fat FFM(kg) Total Mass(kg) 35.83 5.27 -0.0 -0.4 11.87 4.08 0.3 -0.2 34.78 6.7 -0.4 -0.5 39.78 4.5 N/a N/a 65.21 10.88 N/a N/a *n/a = not applicable The data were further analyzed to test for assumptions o f the linear regression model. Scatter plots for independent and dependent variables demonstrated the existence o f moderate to strong linear relationships between the predictor variables and dependent variables with the exception o f H T , which showed no correlation (Figure 4.1.1). Table 4.1.2 summarizes the corresponding correlation coefficients. A l l correlations were significant at p < 0.01, except for height. 34 Table 4.1.2: Correlation Between Predictor Variables and Criterion Body Fat ABD DEXA DEXA DEXA DEXA FM %FAT TRUNK FM % TRUNK FAT DEXA DEXA DEXA DEXA FM %FAT TRUNK FM % TRUNK FAT BIC CALF 0.65 0.69 0.66 0.69 0.92 0.85 0.63 0.62 N/A N/A N/A N/A SI MA 0.65 0.72 0.71 0.75 0.62. • 0.71 0.68 0.76 HT WT BMI WC HC 0.95 0.75 0.89 0.70 0.93 0.86 0.89 0.81 • 0.87 0.77 0.92 0.83 0.89 0.76 0.79 0.64 Figure 4.1.1: Fat mass vs. independent variables (a) FM vs. WT 40.00 30.00' Q • • f I • 20.00. • 10.00. I 1 50.00 60.00 0.78 0.75 0.81 0.79 0.18 -0.08 0.15 -0.08 * N / A - not applicable in w ti E SS 70.00 80.00 90.00 weight 35 TRI THIGH SUM4SF SUBTRI 0.83 0.84 0.54 0.54 N/A N/A N/A N/A 0.88 0.87 0.87 0.85 0.34 0.30 0.47 0.48 (b) FM vs. BMI 40.00. TO 3D.00-1 • • J3 o 20.00 4 10.00. 20.00 25.00 30.00 35.00 BMI (c)FM vs. HC 01 30.00' • • • I. J3 o 20.00 J • • • i 10.00 90:00 100.00 110.00 120.00 HC (cm) 36 (d) FM vs. WC 1 40.00. • • • co 1 30.00' • 1 I I J3 o *~ I 1 I 1>. B • 20.00. B • • 1 I • 1 1 • • 1 10.00. 70.00 80.00 90.00 100.00 WC (cm) (e) FM vs. A B Skinfold 10.00 20.00 30.00 SO .00 AB (mm) 37 (f) FM vs. BIC Skinfold BlC(mm) (g) FM vs. CALF Skinfold 40.00. C3 C 30.00 • ilt in ra £ J3 20.00. 3 10.00. 20.00 30.00 40.00 CALF (mm) 38 (h)FM vs. MA Skinfold 10.00 — i — 20.00 1— 30.00 MA (mm) (Q FM vs. SI Skinfold 10.00 20.00 30.00 SI (mm) 39 0) FM vs. SS Skinfold 40.00- CO C 30.00- u> E 20.00- 5 10.00 10.00 20.00 30.00 S S (mm) (QFM vs. TRI Skinfold 40.00. C 30.00' in I I £ J3 20.00. a 10.00. 10.00 20.00 30.00 T R I (mm) 40.00 (m) FM vs. SUM4SF • • 25.00 — i — 50.00 •• 75.00 • • t 100.00 125.00 SUM4SF (mm) (n) FM vs. SUBTRI 40.00 J SUBTRI 41 Figure 4.1.2: %Fat vs. Independent Variables (a)%Fatvs.WT 45.00 40.00 H 35.00 30.00 H 25.00' 50.00 1 T 60.00 70.00 1 80.00 f90.00 W e i g h t (kg) (b)%Fatvs. BMI 20.00 25.00 30.00 '35.00 BMI 42 (c)%Fatvs. HC 45.00 H 25.00 H 90.00 100.00 110.00 120.00 H C (cm) (d)%Fatvs.WC 30.00 H 70.00 80.00 90.00 100.00 W C (cm) 43 (e) %Fat vs. ABD Skinfold 45.00 • 40.00 W 35.00 H 30.00-4 25.00' ABD (mm) i r 40.00 50.00 0) %Fat vs. MA Skinfold 45.00 H 40.00' U_ 35.00' 5S 30.00' 25.00^ 10.00 1 20.00 30.00 MA (mm) 44 (g)%Fatvs. SUM4SF 45.00 A 40.00 35.00 H 30.00' 25.00H 25.00 50.00 1 75.00 r 100.00 SUM4SF (mm) r 125.00 (h)%Fatvs. SUBTRI 45.00 H 25.00 H SUBTRI 45 0)%Fatvs. SS Skinfold 45.00 40.00' rt U_ 5 35.00' S 30.00 • 25.00' 10.00 20.00 30.00 SS (mm) (i) % F a t vs. SI Skinfold 45.00' 40.00' £ 35.00-| 30.00 25.00 10.00 20.00 30.00 SI (mm) 46 (k) % F a t vs. HT 45.00 H 40.00 H 35.00. 30.00 25.00 H 150.00 160.00 HT 170.00 (cm) Figure 4.1.3: Trunk Fat Mass vs. Independent Variables (a) Trunk FM vs.WT 20.00. 15.00. in (A E JS 10.00 J c 3 5.00. 50.00 60.00 70.00 80.00 90.00 Weight (kg) 47 (b) Trunk FM vs. BMI 20.00 25.00 30.00 35.00 BMI (c) Trunk FM vs. MA Skinfold • • i 10.00 • 20.00 MA (mm) • - • • i —i— 30.00 48 Cd) Trunk FM vs.WC 20.00-1 ca C 15.00. If) in rf E 10.00-1 c 3 b 5.00-J 70.00 80.00 SO .00 100.00 W C (cm) (e) Trunk FM vs. SI Skinfold 20.00. • ca • C 15.00. tn (A ft E *J «E 10.00. c 3 5.00. 10.00 20.00 30.00 SI (mm) 49 (f) Trunk FM vs. SS Skinfold —i 10.00 1 — 20.00 30.00 SS (mm) (g) Trunk FM vs. ABD Skinfold 20.00-1 0> 15.00-1 ra E c 10.00 3 5.00 J 10.00 20.00 30.00 40.00 50.00 ABD (mm) 50 (h) Trunk FM vs. SUBTRI 20.00 J CD 15.00. • • Ul JS c 10.00 J 3 5.00-1 0.40 0.60 0.80 1.00 1.20 SUBTRI (i) Trunk FM vs. HT 20.00-1 CO C 15.00. Ul Ul ft JS c 10.00-1 3 5.00 150.00 160.00 170.00 HT (cm) 51 Figure 4.1.4: %Trunk Fat vs. Independent Variables ( a ) % F a t T r u n k vs. BMI 2D.0DH BMI ( b ) % F a t trunk v s . W C 40.00' u. S9 30.00 20.00 H . 70.00 T 80.00 1 90.00 T 100.00 W C (cm) 52 (c)%Trunk Fat vs. HT • • 40.00 H 30.00 20.00' 150.00 160.00 HT 170.00 (cm) (d)%Trunk Fatvs.WT 40.00• U- JC c 3 30.00 H 20.00 50.00 60.00 70.00 WT 80.00 90.00 (kg) 53 Second, it is important that independent variables and particularly dependent variables are normally distributed i n the sample population. Frequency distributions for the four dependent variables (Appendix VIII) and selected independent variables (Appendix I X ) showed no major departures from normality and values o f the skewness and kurtosis statistics were within the acceptable range (between +1 and - 1 ) . Therefore no data transformations were carried out. Final considerations were for the accuracy and reliability o f both the criterion methods and anthropometry methods used. Paired t-tests and correlations were used to test the reliability of the S F measurement (Table 4.1.3). The differences between repeated S F measures were all less than or equal to 0.4mm and the two measures were highly correlated (r > 0.94), thus showing similar or better values than those reported in the literature (Goran et al., 1997; Lohman etal., 1988). T a b l e 4.1.3: R e l i a b i l i t y o f S k i n f o l d M e a s u r e m e n t s Trial 1 Trial 2 Difference r ABD 31.82 31.90 -0.09 0.95 BIC 20.07 19.87 0.20 0.94 CF 26.20 25.94 0.25 0.94 MA 23.28 22.88 0.40 0.97 SS 21.47 21.31 0.16 0.99 SI 19.47 19.44 0.04 0.96 TRI 27.84 27.53 0.32 0.94 TH 36.76 .36.37 0.38 0.98 A l l significant at p < 0.05 Although testing the accuracy and reliability o f D E X A were not specific objectives o f this study (these have been documented previously in the literature review), it was o f interest to see how closely D E X A total mass ( T M ) compared with body weight ( W T ) measured by traditional weigh scales. A near perfect correlation was demonstrated between the two measurement methods (Figure 4.1.5); however, paired t-test results indicated that D E X A underestimated total body mass by 1.2kg, on average (Table 4.1.4). --, 54 Figure 4.1.5: D E X A Total Body Mass Regressed Against Standard Body Weight — , 50.00 , , , 60.00 70.00 80.00 , — 90.00 D E X A Mass (kg) Table 4.1.4: Prediction of Total Body Mass from D E X A Comparison Standard body mass - D E X A body mass r .999 Mean Diff. 1.2kg s.d.(mean) 0.49 P(mean) <0.001 4.2 Comparisons with existing databases Before continuing with the planned analyses, current data were compared with published body composition data for elderly women to examine similarities and differences between data sets and to identify any extreme outliers or unusual characteristics (Table 4.2.1). The body composition literature was surveyed specifically for studies that measured body fat in elderly women using both D E X A and anthropometry. A s well, studies that provided body composition information on women over the age o f 75 years were considered suitable. Data shared with us 55 by Brodowicz (1999) and Baumgartner (1999) were also included. N o remarkable differences were observed; however, there were some inconsistencies. Table 4.2.1: Summary of Current and Previously Published Population Descriptives U.B.C. BAUM(1999) BATJM(1995) BROD(1999) VISSER(1994) SVEND(1991) n 43 101 82 31 128 23 Age 77.4(1.8) 74.5 (5.6) 71-80 71.1 (4.6) 70.2 (5.3) 75(0) HT(cm) 158.1 (6.4) 155.9(6.8) 158.3(6.2) 161.3 (6.2) 161.6(6.1) 158.9 (6.9) WT(kg) 66.4(11.0) 64.8 (12.6) 63.1 (10.9) 65.1 (10.1) 68.1 (9.5) 65.5(11.6) BMI 26.6 (4.0) 26.7 (5.0) 25.1 (3.6) 25.0(3.5) 26.1 (3.6) 25.9(4.3) WC(cm) 87.4(11.6) 91.9(11.7) 87.8 (9.8) N/A N/A N/A U.B.C. BAUM(1999) BAUM(1995) BROD(1999) VISSER(1994) SVEND(1991) n 43 101 82 31 128 23 SS(mm) 21.4 (8.2) 20.7 (9.6) 21.9(9.9) 19.5 (7.0) 19.8(7.5) N/A SI(mm) BlC(mm) TRI(mm) FM(kg) 19.5 (6.7) 20.0 (7.1) 27.6 (7.4) 23.8 (7.0) N/A . N / A 22.6 (8.3) 26.4 (9.3) N/A N/A N / A 24.5 (8.2) 19.8(7.3) 10.7 (3.9) 20.8 (5.3) 25.8 (7.0) 19.8(8.0) 11.8(4.5) 19.8(5.1) N/A N / A 21.7(8.8) N/A N/A HC(cm) 101.4(8.7) 104.1 (11.4) 101.5(8.6) N/A N/A N/A %FAT 35.8(5.3) 39.6(7.5) 38.0 (6.8) 39.1 (5.6) 43.3 (6.1) 33.7 (9.9) WHR 0.86 (.08) 0.88 (.07) 0.87 (.06) N/A N/A 0.84 (.08) Trunk FM(kg) 11.9(4.8) N/A 11.8(4.2) N/A N/A N/A * N / A - n o t applicable A s the regression equation is strongly influenced by the relationship between the independent and dependent variables, it was important to compare the current findings for the correlation between anthropometry and criterion body fat with those described in the literature. Correlation coefficients were examined across several study populations and are presented in Table 4.2.2. N o t all authors performed the same analyses, and thus, data sets for Table 4.2.1 and Table 4.2.2 are somewhat different. Data for elderly women were not provided by Dupler (1997) or Chapman e t a l . (1998). Table 4.2.2: Summary of Current and Previously Published Correlations for Anthropometry and Criterion Body Fat U.B.C. BAUM(1999) BROD(1999) GORAN(1997) BAUM(1995) VISSER(1994) Dependent Variable D E X A F M (Hologic) D E X A F M (Lunar) D E X A F M (Lunar) F M (4C model) D E X A F M (Lunar) B o d y Density SS 0.78 0.77 0.65 0.61 N/A -0.39 TRI 0.83 0.75 0.60 0.68 0.68 -0.28 56 BIC 0.92 N/A 0.61 N/A N/A -0.27 ABD 0.65 N/A N/A 0.67 N/A N/A MA 0.62 N/A N/A 0.72 N/A N/A SUM4SF 0.88 N/A N/A N/A N/A -0.4 Table 4.2.2 (cont'd) U.B.C. BAUM(1999) BROD(1999) GORAN(1997) BAUM(1995) VISSER(1994) Dependent Variable WT 0.95 0.96 0.90 0.88 N/A N/A D E X A F M (Hologic) D E X A F M (Lunar) D E X A F M (Lunar) F M (4C model) D E X A F M (Lunar) Body Density BMI 0.93 0.91 0.86 0.85 0.93 -0.61 WC 0.87 0.85 N/A 0.72 N/A N/A HC 0.89 0.93 N/A 0.83 0.93 N/A 4.3 Performance of previously published equations Eight anthropometry equations from the literature have been selected to test their ability to predict D E X A body fat i n our sample o f elderly women. These equations have been referred to previously (Appendix II) and are summarized here i n Table 4.3.1. Table 4.3.1: Previously Published Equations Selected for Analyses Author Chapman et al. (1998) Dupler(1997) Dupler(1997) Durnin & Womersley (1974) Goran etal. (1997) Svendsen et al. (1991) Visser etal. (1994) Visser et al. (1994) Equation FFM(kg) = 0.582(WT) - 0.397(TRI) + 0.392(HT) - 48.956 (a)%Fat = 0.1688(BMI) + 0.542(HC) - 0.1639(WT) - 7.9498 (b)FM = 0.2449(WT) + 0.5218(HC) - 0.076(TC) - 37.8619 D = 1.1339 - 0.0645 [log (BIC + TRI + SI + SS)] *for elderly women b F M = 0.31(HC) + 0.22(CALF) + 0.31(WT)-31.33 F M = 0 .63(TRI)+4.47(BMI)+9.32(SUBTRI)+1.35(WT)+1.04(HT) -192.48 (a) D =-0.0356riog(BIC +TRI + SI+ SS)1 +1.0688 (b) D =-0.0022(BMI)+ 1.0605 b b Paired t-test comparisons were conducted to determine the difference between predicted and measured F M and %Fat from these equations and are shown in Tables 4.3.2 and 4.3.3, respectively. A l l previously published equations significantly overestimated F M and %Fat when applied to our data (p<0.001), with the exception o f the Svendsen equation, which significantly underestimated body fat. 57 Table 4.3.2: Prediction of F M from Published Equations Comparison C H A P M A N E Q N- D E X A F M DUPLER EQNa - D E X A F M GORAN EQN - DEXA F M SVENDSEN EQN - DEXA F M r Mean Diff. 0.92 1.92 0.92 4.05 0.94 2.63 0.97 -3.30 S.D. 2.72 2.53 2.48 3.51 t 4.64 10.27 6.96 -6.17 P <0.001 O.001 <0.001 <0.001 Table 4.3.3: Prediction of % F a t from Published Equations Comparison DUPLER EQNb - D E X A % F A T D&W EQN - DEXA %FAT VISSER EQNa - D E X A %FAT VISSER EQNb - D E X A % F A T r Mean Diff. 0.76 4.77 0.84 4.38 0.84 9.02 0.86 8.20 S.D. 3.47 2.87 3.35 2.68 t 9.03 10.03 17.64 20.07 p O.001 <0.001 O.001 O.001 The correlation coefficients for predicted and measured body fat were all >0.75, despite the significant differences between these measures. Moreover, correlations were higher for the prediction o f F M (.92-.97) than for %Fat (.76-.86). However, further analysis o f four o f the better performing equations showed poor agreement between predicted and measured body fat i n all cases (Figure 4.3.1). Both the Dupler equation (Fig.4.3.1c) and the Durnin.& Womersely equation (Fig.4.3.1d) appeared to overestimate %Fat at low levels o f body fat but were reasonable accurate at high body fat levels. The corresponding limits o f agreement between predicted and measured body fat are summarized in Table 4.3.4. Together, these results demonstrate the inability o f existing equations to accurately estimate body composition i n the current sample o f women 75-80 years o f age. 58 Figure 4.3.1: Agreement Between Predicted and Measured Fat from Published Equations (a) Chapman Equation 10.00 < Mean 7.60' 5.00 4 «5 2.50 U- — o £ Mean = 1.927* * c 0.00 H 0> -2.50 • Q -5.00' -10.00' 10.00 1 20.00 — I — 30.00 40.00 Average FM (kg) (b) Goran Equation Mean 20.00 Average FM (kg) 59 (c) Dupler Equation (ii) Mean 35.00 Average % F a t (d) Durnin & Womersely Equation Mean U_ 5.00. — 2.50. Mean = 4 * 3 8 . • at o c <u S • • • " m D.DOJ -2-50. •7.50 J •10.00. 1— 1— 25.00 30.00 35.00 40.00 .45.00" Average % F a t 60 Table 4.3.4: Limits of Agreement for Previously Published Equations and D E X A Comparison C H A P M A N E Q N vs. D E X A F M G O R A N E Q N vs. D E X A F M D U P L E R E Q N b vs. D E X A % F A T D & W E Q N vs. D E X A % F A T Difference 1.92kg 2.63kg 4.77% 4.38% s.d. (diff) 2.72kg 2.48kg 3.47% 2.87% d +/- 2 X SD -3.52 to 7.36 -2.33 to 7.59 -2.17 to 11.71 -1.38 to 10.12 4.4 Development of new prediction equations Four new prediction equations to estimate fat mass (FM), percent fat (%Fat), trunk fat mass ( T F M ) , and percent trunk fat (%TF) in women aged 75-80 years were derived using a combination o f all possible subsets and stepwise regression procedures. Prior to equation development, a preliminary stepwise regression was performed for F M and all predictor variables to examine the overall data (Appendix X ) . A s expected, S F sites o f the limbs (BIC, TRI, C F and T H ) did not significantly contribute to the explanation o f body fatness i n elderly women and were not entered i n subsequent regression analyses. Stepwise regression analyses for each o f the dependent variables were performed first to determine the number and selection of significant predictors according to maximum adj./? and minimum S E E criteria (Appendix 2 XI). F o l l o w i n g this, all possible subsets regression analyses were used to evaluate other possible prediction models that might be more stable (appropriate C ), practical and biologically P meaningful (Appendix XII). Equations for F M and %Fat using only S F measurements as predictor variables were similarly developed (Table 4.4.3). Regression outputs were included i n Appendices X I and XII. The group o f predictor variables entered into the equation development for F M and %Fat were H T , W T , B M I , A B D , M A , SI, S S , S U M 4 S F , SSTRI,. H C and W C ; while H T , W T , B M I , A B D , M A , SI, S S , S S T R I and W C were entered'into the.TFM and % T F regression analyses. A set o f possible regression models were selected using the above criteria and are presented in 61 Table 4.4.1. A single equation was then proposed for each o f the dependent variables: F M ( E Q N 1 ) , %Fat ( E Q N 2 ) , T F M ( E Q N 3 ) and % T F (EQN4) (Table 4.4.2). Table 4.4.1: New Regression Models for the Prediction of Body Fat DEXA Predictor Variables FM WT, HT, M A WT, HT, M A , SSTRI WT, HT, M A , H C WT, HT, M A , W C BMI, M A HT, WT, M A BMI, M A , SSTRI BMI, MA, W C WT, HT, M A , W C WT, BMI, M A , W C HT, M A , W C HT, M A , WC, A B D %FAT TFM % TF Adj. R 2 0.95 0.96 0.96 0.95 0.84 0.84 0.85 0.84 0.90 0.90 0.83 0.84 Cp SEE CV 4.46 1.77 3.78 4.20 4.25 4.61 1.63 3.74 3.77 4.54 3.9 3.99 1.53kg 1.46kg 1.50kg 1.51kg 2.14% 2.12% 2.04% 2.10% 1.27kg 1.28kg 2.76% 2.72% 6.4% 6.1% 6.3% 6.3% 6.0% 5.9% 5.7% 5.9% 10.7% 10.8% 7.9% 7.8% Table 4.4.2: Best New Prediction Equations for Body Fat 1 2 3 4 Adj. New Prediction Equations Eqn FM %Fat TFM %TF = = = = R 2 0.95 0.84 0.90 0.83 0.611(WT) - .231(HT) + . 1 4 3 ( M A ) + 16.462 0.341 ( W T ) -- .339(HT) + . 2 8 5 ( M A ) + 60.122 0 . 1 8 5 ( W T ) - .008(HT) + . 1 1 2 ( M A ) + . 1 3 6 ( W C ) - 2.072 0 . 3 8 7 ( M A ) •- .227(HT) + .356(WC) + 30.659 Cp SEE CV 4.46 4.61 3.77 3.9 1.53kg 2.12% 1.27kg 2.76% 6.4% 5.9% 10.7% 7.9% Table 4.4.3: New Skinfold Equations for Total Body Fat DEXA Predictor Variables FM FM %FAT %FAT TRI, B I C , C A L F , A B D BIC, C A L F MA, CALF, SUM4SF SUM4SF, C A L F Regression method A l l poss. subsets Stepwise A l l poss. subsets Stepwise Adj. R 2 0.87 0.86 0.77 0.77 Cp SEE 5.04 2.56kg 2.66kg 2.52% 2.51% 2.93 CV 10.8% 11.2% 7.0% 7.0% A l l regression models included the M A skinfold and some combination o f H T , W T or B M I , which together, explained 70% or more o f the variation in body fat. Additionally, measures o f central fat ( H C , W C and SSTRI) were important in the prediction o f F M ; however, 62 H C and W C were not statistically significant. The model which included H T , W T , M A and S S T R I involved the measurement o f essentially 5 variables which exceeded the recommended ratio o f 10-20 subjects for every predictor variable (Heyward & Stolarczyk, 1996b), and was somewhat less stable than the others ( C =1.77). Thus, the model with H T , W T and M A was p chosen for F M . Similarly, for %Fat, the contribution from S S T R I was significant but not for W C . The equation with B M I , M A and S S T R I , again, involved the measurement o f 5 predictor variables and was ruled out. The combination o f H T , W T and M A was marginally better (smaller S E E ) than that o f B M I and M A , and was therefore chosen for the best %Fat model. For T F M , the model which included H T , W T , M A and W C was superior to the 3-variables equations and all predictors were significant. Once again, the model with W T , B M I , M A and W C involved essentially 5 variables. Finally, the best equation to predict % T F included H T , M A and W C . Although the addition o f the A B D S F improved the equation, it was not significant. Residual analyses were conducted for the four new equations (Figures 4.4.1- 4.4.4). The agreements between predicted and measured fat for the new F M and %Fat equations were stronger than that for previously published equations (Figure 4.3.1) indicated b y a tighter clustering o f residual data (Svendsen et al., 1991). N o excessive trends in the residuals were apparent (ie.homogeneity o f variance was not violated). However, the magnetude o f residual variability was much larger for the trunk fat equations, which reflected the higher errors associated T F M and % T F . . 63 Figure 4.4.1: Residual Analyses for the New F M Equation (a) H i s t o g r a m o f R e s i d u a l s Dependent Variable: FM ; 161 14' i 1 1 12 10 -2.50 -1.50 -2.00 -1.00 -.50 .50 0.00 1.50 1.00 2.50 2.00 Regression Standardized Residual 64 (c) Scatter plot of residuals vs. predicted F M Dependent Variable: F M •g <u CC In (/> <u a> (D Q TJ <U N ° • "E <D "D a • • rf 3a • • 55 2? - 2 a? OJ a? -3- 3 - 2 - 1 0 1 2 Regression Standardized Predicted Value (d) Partial regression plot for F M and Height Dependent Variable: FM • D B • • a D • • • oa -6 20 -10 HEIGHT 65 (e) Partial regression plots for F M and Weight Dependent Variable: FM 20 l -20 • ° ° • ° -10 WEIGHT (f) Partial regression plots for F M and the M A skinfold Dependent Variable: FM • • • • c • • • MA 66 Figure 4.4.2: Residual Analyses for the New %Fat Equation (a) Histogram of residuals Dependent Variable: % F A T & C 0) 4 Std. Dev'= .96 2 Mean = 0.00 N = 43.00 -2.50 -2.00 -1.50 -.50 -1.00 0.00 .50 1.00 1.50 2.50 2.00 3.00 Regression Standardized Residual (b) Normal P-P plot of regression standardized residual Dependent Variable: % F A T 1.00 / / JD Q Au .50 QL B O •o D • 25 a • u u U / / D / <D 13 <1> Q. UJ o.oo 0.00 .25 .50 Observed Cum Prob 67 V (c) Scatter plot of residuals vs. predicted % F a t Dependent Variable: % F A T Regression Standardized Predicted Value (d) Partial regression plot for % F a t and Height Dependent Variable: % F A T • • a a B 2 d? • • • • a ° D 0 • O o a • o J a -2 • D o • • -10 o 0 • • % • 10 20 HEIGHT 68 (e) Partial regression plot for % F a t and Weight Dependent Variable: % F A T a a Bo • -20 ° • 30 -10 WEIGHT (f) Partial regression plot for % F a t and M A Skinfold Dependent Variable: % F A T i< 69 Figure 4.4.3: Residual Analyses for the New T F M Equation (a) Histogram of residuals Dependent Variable: T F M : 8 , 6 -2.00 -1.50 -1.00 -1.75 -1.25 -.50 -.75 0.00 -.25 .50 .25 1.00 .75 1.50 1.25 2.00 1.75 2.25 Regression Standardized Residual (b) Normal P-P plot of regression standardized residual Dependent Variable: T F M 0.00 .25 .50 .75 1.00 Observed C u m P r o b 70 (c) Scatter plot of residuals vs. predicted T F M Dependent Variable: T F M 0) CC S JD d) Q - 3 - 2 - 1 0 1 2 Regression Standardized Predicted Value (d) Partial regression plot for T F M and W T , if'-, ri Dependent Variable: T F M g o °S • • • 9 2 LL 10 20 WT 71 (e) Partial regression plot for, T F M and H T Dependent Variable: TFM • ff ° a • tfP -10 10 HT (f) Partial regression plot for T F M and M A Dependent Variable: TFM • • B • •tan -10 MA 72 (g) Partial regression plot for T F M and W C Dependent Variable: T F M Figure 4.4.4: Residual Analyses for the New % T F Equation (a) Histogram of residuals Dependent Variable: % T F 10 1 1 -1.25 -.75 -.25 .25 .75' 1.25 1.75 2.25 -1.00 -.50 0.00 . .50 1.00 1.50 2.00 2.50 Regression Standardized Residual 73 (b) Normal P-P plot of regression standardized residual Dependent Variable: % T F CD UJ 0.00 0.00 .25 .50 Observed Cum Prob (c) Scatter plot of residuals vs. predicted % T F Dependent Variable: % T F ay <u Q o in cu - 2 - 1 0 1 2 Regression Standardized Predicted Value 74 (d) Partial regression plot for % T F and M A Dependent Variable: % T F 3 ° ° LL I-6 -10 MA (e) Partial regression plot for % T F and W C Dependent Variable: % T F . 20 10 • % TF • g a a a ° cn "a • •10 -20 -10 10 20 30 WC 75 (g) P a r t i a l regression p l o t for % T F a n d H T Dependent Variable: % T F • a • ° " ° -20 10 HT Overall, the total body fat equations ( F M and %Fat) were superior to the regional trunk fat equations ( T F M and % T F ) , for both the adj.i? value and the coefficient o f variance (C.V.), 2 and met the guidelines for acceptable prediction equations ( S E E < 2.5kg and < 3.5%, respectively) according to Heyward and Stolarczyk (1996a). Moreover, equations using only skinfolds as predictor variables proved inferior (smaller adj.i? and larger S E E ) to those that 2 included a combination o f skinfolds and anthropometry. Equations for F M and T F M explained more o f the variance i n body fat (adj./? = .95 and .90, respectively) than the corresponding %Fat 2 and % T F equations (adj.i? = .84, .83). However, the precision o f the percent fat equations 2 ( C . V . % F a t = 5.9%, C . V . % T F = 7.9%) was greater than the fat mass equations ( C . V . F M = 6.4%, C . V . T F M = 10.7%). Lohman (1981) suggested that the values o f S E E and C . V . were more important i n the selection and comparison of prediction equations than that o f maximum or adj J? . In light o f this, the %Fat equation would be recommended over the F M equation. Moreover, %Fat is the measure o f interest associated with important health and functional 76 implications, not total fat. Thus, the new %Fat equation was subsequently validated and tested for its performance in independent samples. 4.5 Validation of new prediction equations The study sample was not considered large enough for internal cross-validation using the conventional data-splitting method, and an independent sample for external validation was not available. Instead, the jackknife procedure was used to test the stability and accuracy o f the new %Fat equation within the sample. Summaries o f the residuals for each round o f the jackknife procedure for both equations are shown in table 4.5.1. Except for round 6, each jackknifed equation significantly predicted body fat in the corresponding omitted group o f subjects. Averages for the 10 rounds o f regression analysis are summarized i n Table 4.5.2. The smaller and closer the error o f the residuals is to the S E E o f the jackknifed equation, the more accurate the equation. L o w average jackknife statistics (s.d. =1.54kg; s.d. =1.95%) are considered favourable (Heyward & Stolarczyk, 1996). These results therefore indicated that the %Fat equation was valid within the sample. Table 4.5.1: Summary of Residuals for Jackknife Validation % F a t Equation Round 1 2 3 4 5 6 7 8 9 10 Mean Diff. b/w Jackknifed Estimate of % F a t and" D E X A % F a t • i ' .' - ' ;• 0.096 1.326 0.320 . -1.211 -0.146 1.531 -0.888 -1.698 -0.173 0.659 77 s.d. (diff) n t P 2.406 3.395 0.641 2.675 1.993 0.848 2.149 2.767 0.312 2.352 4 4 4 4 4 5 4 5 5 4 0.080 0.781 0.999 -0.905 -0.146 4.038 -0.826 -1.372 -1.106 0.627 0.941 0.492 0.392 0.432 0.893 0.016 0.469 0.242 0.349 0.565 T a b l e 4.5.2: J a c k k n i f e d E s t i m a t e s (average o f 10 p r e d i c t i o n equations a n d r e s i d u a l analyses) Prediction E q n . %Fat Adi. R 0.835 2 SEE 2.14 Residual Analysis %Fat Diff. 0.184% s.d. 1.95% 4.6 Performance of new prediction equations External databases for both similarly aged women and younger women were obtained to test the performance of the new equations and to examine the impact of age. Descriptive summaries of the independent databases shared by Gary Brodowicz (Department of Public Education, Portland State University) and Richard Baumgartner (Clinical Nutrition Laboratories, School of Medicine, University of New Mexico) are listed in Appendix XIII. Unfortunately, the predictor variables included in the new equations were not all measured in these independent samples and thus did not allow for their direct application. Additionally, a Lunar manufactured D E X A instrument was used by both Baumgartner and Brodowicz to assess criterion body fat, and at present, no conversion equations between manufacturers are available. In order to test the performance of an equation derived from this study sample in the independent samples of women, 2 modified equations for %Fat were developed using only the variables measured in the Brodowicz (EQN5) and Baumgartner (EQN6) databases. Table 4.6.1 lists the new equations derived using the maximum adj.i? , minimum SEE and appropriate C 2 criteria. Regression outcomes are appended (Appendix XIY). T a b l e 4.6.1: M o d i f i e d P r e d i c t i o n E q u a t i o n s Eqn# 5 6 Prediction Equation %Fat= %Fat= Adj.R 0.82 0.80 2 9.819 + . 1 6 2 ( S U M 4 S F ) + . 6 5 2 ( B M I ) - .261(SS) 9.198 + . 6 9 6 ( B M I ) + . 2 9 5 ( T R I ) 78 Cp n/a n/a SEE 2.21 2.37 CV 6.2% 6.6% p Paired t-test comparisons were conducted to determine the difference between measured and predicted body fat in similarly aged women (Table 4.6.2) and in younger women (Table 4.6.3). The modified equations significantly underestimated %Fat i n both groups o f elderly women, yet accurately predicted %Fat i n the younger women. Residual graphs (Figure 4.6.1) indicated that the error in the prediction o f %Fat increased with body fat in the elderly women. Graphs for the younger women showed that the new equation underestimated %Fat at low body fat levels and overestimated %Fat at high body fat. Therefore, despite its accuracy, the equation was not reliable for this population. Fufhermore, the limits o f agreement for predicted and measured fat were wider for the younger population than for the older population (Table 4.6.4). Thus, the equations performed with less variability in the elderly women. Table 4.6.2: Paired t-Test Comparisons for Elderly Women Comparison %Fat(BROD[) - E Q N 5 %Fat(BAUM) - EQN6 n 31 100 r Mean Diff. .727 6.63 .805 5.12 S.D. 3.91 4.45 CV 9.99 11.25 t 9.44 11.52 P <0.001 <0.001 Table 4.6.3: Paired T-Test Comparisons for Younger Women Comparison % F a t ( B R O D ) - EC/N5 2 n 33 r Mean Diff. .887 -0.717 S.D. 5.43 CV 18.37 t -0.76 p 0.454 Table 4.6.4: Limits of Agreement for Modified Equations and D E X A Comparison % F a t ( B R O D , ) - %Fat(Eqn5) % F a t ( B A U M ) - %Fat(Eqn6) % F a t ( B R O D ) - %Fat(Eqn5) 2 Difference 6.63 5.12 3.91 4.45 SD -0.717 5.43 79 d +/- 2 X SD -1.19 to 14.45 -4.20 to 14.02 -11.58 to 10.14 Figure 4.6.1: Agreement Between Predicted and Measured % F a t (a) Brodowicz elderly women data -f • — /• Mean = 6 . 6 3 -10.00 J 20.00 1 1 25.00 30.00 1 35.00 1 — 40.00 Average %Fat 80 (b) Baumgartner data 15.00. Mean 10.00 1 • 1 » % « . • >. • . • . 5.00 H » 4V • •t c w. •» • •. 5 . 1 2~7 Mean = «• • 0.00' -5.00. -10.00. 20.00 30.00 40.00 — i — 50.00 Average %Fat (c) Brodowicz younger women data Mean 10.00. 5.00. 0> 0.00. c I -5.00. -10.00. 20.00 25.00 30.00 35.00 40.00 Average %Fat 81 5. Discussion A review o f the literature indicated that existing anthropometry prediction equations may not be valid for estimating body composition i n women 75 years and older. The intent o f this research, therefore, was to further explore and confirm the need for improved prediction equations for this elderly population and to derive new equations based on D E X A criterion fat i n a sample o f healthy women 75-80 years o f age. 5.1 New prediction equations for women 75-80 years A l l but one o f the previously published body composition prediction equations significantly overestimated body fatness in our sample and showed poor agreement with current D E X A measured fat. Further analysis o f our data, however, revealed strong correlations between anthropometry and D E X A fat and thus supported the development o f new equations for this population. Four new prediction equations were developed for F M , %Fat, T F and % T F in women 75-80 years bid (Table 4.4.2). A common group o f anthropometric variables surfaced as the best predictors o f body fat: H T , W T , B M I , M A , S S B T R I , W C , and H C (Table 4.4.1). O f these, the M A S F was common to all. A n important finding o f this research was that there was no single "best" equation; rather, several alternatives were acceptable. Due to the strong inter-correlations among anthropometric predictor variables, small differences in SF values that are not biologically significant can alter the regression equation. This perhaps explains why so many different equations are presented i n the literature, even when methodologies in the equation development are the same. 82 In terms o f equation diagnostics, adj.2? and S E E values for the new equations were 2 comparable to and i n some cases better than those for reported for published equations. Within the current sample o f edlerly women, the goodness o f fit was better for F M (adj./? = 0.95) than 2 for %Fat (adj./? = 0.84) due to slightly lower correlations for anthropometry and %Fat than for 2 anthropometry and F M . However, the %Fat equation ( C V = 5.9%) was more precise than the equation for F M ( C V = 6.4%). In each case, total body fat equations were more precise than regional body fat equations ( C V = 7.8%, 10.7%). Residual analyses revealed no excessive trends for the F M and %Fat equations, but indicated a greater error in the prediction o f trunk fat with increasing trunk fat (Figures 4.4.1-4.4.4). It is likely that D E X A is not sensitive enough in the measurement o f trunk fat and this has been raised before (Baumgartner et al., 1995). A s the %Fat equation demonstrated a smaller error, and as %Fat is ultimately the measure o f interest, only the %Fat equation was further analyzed. A n independent sample was not measured for external validation o f the new equation, therefore, only the internal validity was tested. Due to the small sample size, the jackknife technique was used over the conventional data splitting method. The low residual error for each round o f the jackknife procedure compared to the S E E o f the corresponding jackknifed equation indicated good internal validity for the %Fat equation (Table 4.5.2). Several factors affect the development and performance o f a regression equation including the nature o f the sample from which the equations were derived, choice o f anthropometric predictors and criterion body fat, and the regression procedures used. Each o f these is discussed further to help explain differences between our new equations and published equations, and w h y one equation may be better or more appropriate than another. 83 5.2 Nature of the sample population The study participants were primarily Caucasian, middle class women between the ages o f 75 and 80 years. A l l subjects were considered healthy and were living independently in the community. Although the demographics o f this sample may not be representative o f all women 75-80 years, they are consistent with those described in the literature. Conclusions based on results from this study may hot be widely generalized to all elderly women as it is well known that individuals who volunteer for studies tend to be more active and healthy than those less inclined. Furthermore, our results may not apply to women o f different ethnic and cultural background. The average age o f our participants exceeded most other studies in which equations were derived b y approximately 7 years (Table 4.2.1). This was an important distinction as one o f the objectives o f this research was to determine whether or not the relationship between anthropometry and body fatness continues to change with advancing age. I f significant changes in body composition and fat distribution are apparent with each decade beyond 60 years, as suggested b y Baumgartner (1995), then it would be reasonable to expect that equations carefully derived i n 60 year old women would not perform as well when applied to women i n the their 70's and 80's. This could explain why the Goran equation (4C), derived in women o f average age 68, did not predict body fat adequately i n our sample. Similarly, women in the Visser (70yrs), Dupler (70yrs) and Durnin & Womersley (50-68 yrs) studies were all younger. However, these studies all used U W W , and thus, the independent effects o f age on equation performance are confounded by the problems associated with U W W . Although Chapman et al. (Chapman et al., 1998) developed equations in women with mean age o f 75 using D E X A as the reference method, their equation was unable to significantly 84 predict body fat i n our sample. This study had a relatively small n o f 17, thus limiting the precision and accuracy o f the prediction equation. A l l four equations showed a similar lack o f agreement with D E X A body fat measurements (Figure 4.3.1). Therefore, it was difficult to isolate and comment on the effects o f age. T o our knowledge, the only other database involving a large group o f women over the age of 75 where D E X A (or 4 C model) was used to measure body composition is that o f Baumgartner et al. (Baumgartner et al., 1995); however, no equations were derived for this group. 5.3 Predictor variables Predictor variables measured i n this study exhibited strong statistical and biological associations with criterion body fat. This is an important factor in linear regression analyses to ensure the development o f robust prediction equations. A range o f S F ' s were measured, along with circumferences, height and weight to evaluate the overall relationships between anthropometry and criterion body fat. This was a key distinction o f our study as often only one SF is measured and very seldom are circumferences considered. A survey o f existing equations indicated that H T , W T , B M I , S U M 4 S F , T R I , C A L F , S S T R I and H C are the most common predictors o f body fat i n elderly women. The best individual predictors of.body fat i n our study participants were W T , B M I , B I C , S U M 4 S F , and H C ; however, the best regression models all included the M A skinfold. This skinfold site does not appear i n any other equation perhaps because it is not often measured in body composition studies. The M A S F was not as strongly correlated to body fat as some o f the other skinfolds, yet significantly contributed to the explanation i n body fat after W T or B M I was entered. A s body fat is expected to accumulate more centrally with age, there is strong biological support for 85 the inclusion o f M A . Moreover, the M A SF may be related to the internalization o f body fat which was not explained b y B I C or T R I . Clearly, the M A skinfold should be considered a useful predictor o f body fat i n elderly women in the future. Other studies have shown that S F ' s alone did not predict body fat as well as when they were in combination with H T , W T or B M I . This too was the case with our data. Although the use o f B M I in younger populations has been criticized, it is reasonable to conclude that for a given height, over-weightness is more likely due to excess fat than to extreme musculature or high bone mineral density among the elderly population. In fact, B M I explains 73% and 86% o f the variance i n %Fat and F M , respectively in this study sample. However W T and H T together seemed to explain the variation i n body fat more so than B M I . Perhaps the ratio o f weight to height-squared is not appropriate in elderly women. Finally, some concern has been raised over the use o f the SF i n the elderly because o f changes i n compressibility and elasticity o f the S F , reduced muscle tone, and the internalization o f body fat (Baumgartner et al., 1995). Repeated measures tests for the various S F ' s (Table 4.1.4), and scatter plots with body fat indicated that S F ' s are reliable and useful measures for body composition prediction i n elderly women. Moreover, there is no evidence that this relationship diminishes with age i n our sample. Perhaps the problems associated with U W W have contributed to earlier observations o f poor agreement between anthropometry and body fat in the elderly. 5.4 Criterion body fat The measurement o f body composition in the elderly has been a topic o f great debate in the literature. Clearly, 3C and 4 C methods that involve minimal assumptions about the physical 86 and chemical properties o f the major body components should be used in the aging population (Baumgartner et al., 1995; Going et al., 1995; Kohrt, 1998; Williams et al., 1995). Reference body fat was measured by D E X A ( Q D R - 4 5 0 0 W ; Hologic, Inc.) in this study and, therefore, not subject to the measurement errors associated with U W W and the 2 C model. The fan-beam technology o f the QDR-4500 is considered more accurate than pencilbeam scanners i n the assessment o f body composition due to superior sampling techniques, and has demonstrated high accuracy when compared to 4 C measures o f F M and F F M i n elderly persons ( K e l l y et al., 1997; Visser et al., 1998). Additionally, the Q D R - 4 5 0 0 has demonstrated low measurement error (300g) for F M (Kelly, 1998a). Existing equations standardized to D E X A used earlier models o f D E X A as w e l l as different manufacturers (Chapman et al., 1998; Svendsen et al., 1991), and therefore it is likely that the new equations are an improvement over these. Equations based on 4 C criterion body composition are considered to be the most valid i n the aging population as they require the fewest assumptions (Goran et al., 1997; Heymsfield et al., 1989; W i l l i a m s et al., 1995). However, where accuracy is gained in the 4 C model, precision may be lost due to an accumulation o f error associated with the use o f multiple assessment techniques (Guo et al., 1996). A final advantage i n using the QDR-4500 instrumentation in our study is the connection to epidemiological research. The National Institute o f Health has selected the QDR-4500 model to obtain body composition data in the next national health and nutrition survey ( N H A N E S IV) and i n their study on health, aging and body composition (Health A B C ) (Kelly, 1999). B o d y composition predicted b y our new equations can be directly compared to the mounting collection of normative data on health and body composition in the elderly. 87 Based on this information, body fat measured i n our study was presumed more accurate and precise than much o f the existing data for the elderly. Average F M and % F A T values were lower than those reported in the literature (Table 4.2.1) which would explain the over-prediction o f body fat when published equations were applied to our data. Published F M values obtained from 3 C and 4 C models compared more closely to current D E X A F M than did published 2 C %Fat values to D E X A %Fat. In studies where U W W was used as the criterion method, reported mean % F A T values were more than 7% higher than current D E X A %Fat. This is consistent with assumptions i n the literature that U W W , together with Siri's formula, erroneously overestimates fatness i n the elderly. Two studies seemed to be outside the range o f average body fat values. Mean body fat from the Svendsen (1991) study was lower than in this study and all others reported, which may reflect ethnic differences among Northern European populations and those typical of North America. Earlier versions o f D E X A , like that used by Svendsen, have been shown to underestimate total body fat due to difficulties i n measuring trunk fat (Kohrt, 1998; Snead et al., 1993). This could also explain the poor performance o f the Svendsen equation in our sample despite other similarities i n the methodology o f these two studies. Williams and colleagues (1995) used 4 C methods to measure body composition in older adults (49-80 yrs) and reported average fat values o f 40%. They found that equations based on anthropometry were unsatisfactory; however, at high body fat levels anthropometry methods are known to be less reliable. Moreover, both studies had small n's o f 17 and 23 women, respectively. D E X A , however, is not without limitations. D E X A does account for the hydration status of the body, which may change with aging (Roubenoff et al., 1993). However, this has been somewhat debated in the literature. The possibility that D E X A may systematically 88 underestimate total F M (Table 4.1.4) would introduce further error when predicted F M is divided by standard body weight to calculate %Fat. However, D E X A ' s underestimation o f total body mass may be related to an error in the measurement o f the F F M component and may not affect the measure o f F M . D E X A ' s accuracy in the measurement o f body components still warrants further research. 5.5 Regression procedures A final factor affecting the development and performance o f new regression equations is the regression procedure. A combination o f stepwise and all possible subsets regression procedures was used to develop new regression models in this investigation. Most studies simply use stepwise regression and select the final equation based on statistics alone. A l l possible subsets allows one to examine all possible combinations to determine i f one equation may have more practical value or be more biologically meaningful. Moreover, one can better understand the true nature o f the relationship between anthropometry and body fat when several models are considered. Furthermore, due to the multi-collinearity present among anthropometry predictor variables, all possible subsets regression was recommended over the more commonly used methods o f stepwise regression (Dupler, 1997; Guo et al., 1996). Alternatively, Draper and Smith (1966) suggested using stepwise methods first, followed by all possible subsets procedures in order to make the most informed decisions with respect to max. adj./? , min. S E E and 2 appropriate C criteria when selecting the final equations. To m y knowledge, the only other p studies that used all possible subsets regression procedures were those o f Dupler (1997) and Durnin and Womersley (1974). 89 Based on these statistical criteria, there were little differences between the best subsets described i n Table 4.4.1. The recommended number o f prediction variables for a sample o f 40 was 2-4 (Heyward & Stolarczyk, 1996a). It was useful to look for patterns that emerged in all possible subsets. H T , . W T , B M I and M A explained most o f the variance i n body fatness. The addition o f the central fat measure did not markedly improve the precision or predictability o f the F M or %Fat equations. However, H C was important i n the prediction o f body fat i n both the Goran and Dupler equations. A s expected, central fat measurements contributed significantly to the prediction and precision o f the trunk fat equations. 5.6 Performance of the modified equations Neither o f the modified F M and %Fat equations was able to accurately predict D E X A fat in the independent databases o f elderly women shared by Brodowicz (1999) and Baumgartner (1999). However, i n the younger .sample, %Fat was significantly predicted but not F M . This was unexpected. Further analysis showed that the limits o f agreement for predicted and measured fat were much wider in the younger sample than for the samples o f elderly women. These results emphasize the importance o f examining the agreement between two methods recommended b y B l a n d and Altman (1986) and o f not relying solely on the correlation between two methods or the average measurement difference. There are several explanations for why these modified equations may have performed poorly i n external samples. One, the best predictors o f body fat in elderly women were not measured i n these independent samples and therefore a lesser equation was tested. Two, M A and H C may become increasingly important i n the prediction o f body fat i n elderly women. Three, inter-rater differences i n the measurement o f anthropometry may have affected the 90 relationship between some of the predictor variables and criterion fat. Finally, different manufacturers of D E X A machines have not been cross-calibrated (Shepherd, 1999), and therefore, inter-method differences may contribute to the poor agreement between our equations and Lunar versions of D E X A . 5.7 Summary and recommendations A n important finding of this study was that neither existing equations nor the newly derived equations were able to accurately and reliably predict body fat in independent samples of elderly women. Some of the prediction error can be attributed to inter-method differences and differences in D E X A manufacturer, but the lack of agreement between methods also emphasizes the problem of sample specificity with regression equations. Equations will always perform better in the sample from which they were derived and must be interpreted with caution when applied externally. A second major finding of this research was that a single "best" equation did not exist for these data, but rather, several alternative models provided similar equation statistics and regression coefficients. However, total body fat equations were more precise than regional trunk fat equations, and percent fat equations were more precise than fat mass equations. Furthermore, the combination of WT, HT (or BMI) and SF's was better than SF's alone. Nonetheless, this study demonstrated that a strong relationship between anthropometry and D E X A exists among elderly women and that internally valid equations for %Fat can be proposed for this population. The equation involves simple and practical measurements and would be useful tools in epidemiological research and health screening practice. Moreover, it is reasonable to conclude that prediction equations based on D E X A have greater face validity in 91 elderly women than those based on densitometry, as the D E X A model is associated with fewer assumptions.. Furthermore, this is the only study to use all possible subsets regression and a 3 C model for criterion fat in elderly women and the first study to use the QDR-4500 version o f D E X A . The use o f Q D R - 4 5 0 0 in two future national surveys conducted by the N I H w i l l enable the comparison o f body fat predicted by the new equation to a large normative database related to health, body composition and aging. 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(1995). Practical techniques for assessing body composition in middle-aged and older adults. Medicine and Science in Sports and Exercise, 27(5), 776-783. 100 7. Appendices 101 > u O N lif 2 « 3 vn vo s S b b CN cu 6J5 C co o oo O N I l< O S vo cu , Ml \< a ct s H fe S 3 SI CQ CQ CO oo oo V O V O fe fe" ffl oo £ \ ~> v vo 3 OO 0 £ u CQ U s §H Q. >- Q > s .2 "O U £ E fe fe u U fe fe 2 vo •* O N O N 2 Q O N »—' ca ca (U U t-l u <D O N O N O N O N o ca Vis leg m O N O N 1—1 Vis s O N •* icB 102 t-i \S ca -»-» FFM(kg) = 0.582(WT) - 0.397(TRI) + 0.392(HT) - 48.956 Chapman, 1998 (b)FM = 0.2449(WT) + 0.5218(HC) - 0.076(TC) - 37.8619 D = 1.1339 - 0.0645 [log (BIC + TRI + SI + SS)] %Fat = 495/Db - 450 Dupler, 1997 Durnin & Womersley, 1974 Visser et al., 1994 68.2 0.8% 0.0082 0.0113 0.58 0.67 oo oo (N fN CN 0.0100 2.43 N/A 4.0% 1.09 N/A 2.5% 0.928 cv N/A i 1.95 kg SEE ro Q (m=70.2) 60-87 (m=70.2) 60-87 I/O %Fat = 495/Db - 450 -192.48 m Visser etal., 1994 (a) D = - 0.0356[log(BIC + TRI + SI + SS)] +1.0688' Svendsen et al., 1991 N/A 0.841 oo ©' b FM = 0.31(HC) + 0.22(CALF) + 0.31(WT) - 31.33 FM = 0 .63(TRI)+4.47(BMI)+9.32(SUBTRI)+1.35(WT)+1.04(HT) Goran, 1997 50-68 0.626 0.96 >/-> r-- (m=70) 65-81 (m=70) 65-81 (m=82) 76-95 Age range r- b (a)%Fat = 0.1688(BMI) + 0.542(HC) - 0.1639(WT) - 7.9498 . t-» Dupler, 1997 FM = WT - FFM Equation Author Z, 1.0% 1.1%' os .—H o SO © ST © + (N j= o <n 9 $ II II N= £ 103 A p p e n d i x III: M e d i c a l Clearance UBC Department of Family Practice and the Seniors interAction Society M a r c h 25th, 1998 Dear Doctor: Y o u r patient has expressed interest in entering a study o f exercise effectiveness on measures o f bone density, muscular strength, body composition, functional mobility and psychosocial well-being in healthy women aged 75-80 years. The study population w i l l be assigned to either an exercise or control group. Y o u r patient would like to participate in the exercise group which w i l l require her attendance three times per week for the next full year. The first twelve weeks o f the exercise program w i l l be supervised by specialized trainers and be held at Executive Fitness facility at U B C . A t the end o f the twelve weeks, participants w i l l continue their exercises independently either at U B C or a fitness centre o f their choice and w i l l be monitored monthly. Exercise sessions w i l l run for approximately one hour, and w i l l include a light warm-up on cardio-equipment, strength training with free-weights and resistance equipment, and a stretch/cool-down component. Participants w i l l receive free memberships for the U B C ' s Executive Fitness facility for the duration o f the study. Subjects w i l l be excluded from this study with: 1. restricted limb or trunk movement 2. medical contraindications to maximum muscle strength testing 3. uncontrolled hypertension or diabetes 4. symptomatic cardiorespiratory disease 5. severe renal or hepatic disease 6. uncontrolled epilepsy 7. progressive neurological disease 8. dementia 9. marked anemia (with a hemoglobin less than 100G/L) 10. marked obesity with inability to exercise 11. medication with betablockers, Warfarin, C N S stimulants, hormone replacement therapy, or bone enhancing drugs 12. subjects w i l l also be excluded i f they are already performing intense cardiovascular/strength enhancing exercise for more than 30 minutes, three times per week We would be grateful i f you decide your patient is suitable. 104 Appendix IV: Informed Consent Strength Training Study in Older Adult Women, Ages 75-83 years J.E. Taunton, M.D., E.C. Rhodes, PhD., M.Donnelly, M.D., A.D.Martin, PhD., J.Elliott, P.T. The purpose o f this investigation is to examine the effects o f a progressive strength training program on measures o f bone density, muscle strength, balance, functional ability and psychosocial well-being among older adult women, aged 75-83 years. Adherence to exercise programs w i l l also be analyzed. Specific research objectives are as follows: 1. To determine the effect o f a short (12 week) and long term (1 year) progressive resistance exercise program on muscular strength and endurance o f the large muscles o f the body; 2. T o assess the effect o f a one-year resistance exercise program on the maintenance o f bone mineral density; 3. T o determine changes i n body composition (body fatness) following a short and long term resistance exercise program; 4. T o assess the impact o f short (12 week) and long term resistance training on balance and functional abilities; 5. T o evaluate the relationship between strength gains and improvements in functional status 6. T o explore the influence o f a regular exercise program on the quality o f life and psychological health in older adult women; 7. To assess exercise compliance i n this population. 105 Y o u w i l l perform tests o f strength, balance and functional ability, and complete questionnaires on psychological health, personal demographics and exercise compliance. Body composition and bone mineral density w i l l be assessed by Dual-energy X-ray Absorptiometry ( D E X A ) . Additional anthropometric measures (height, weight and selected girths) w i l l also be taken. Y o u may experience some muscle soreness and fatigue. The exercise program w i l l be performed three times per week for one full year. The initial 12 weeks o f exercise w i l l be supervised by a specialized trainer. Exercisers w i l l continue the program for an additional 9 months on their own and w i l l keep track o f their workouts using a training log. In signing this consent form you state that you have read and understand the description of the tests, the exercise intervention and their complications. Y o u enter the battery o f tests and experiment w i l l i n g l y and may withdraw at any time. Additionally, your identity and test results w i l l be kept i n confidence andSwill become the property o f the above investigators. For safety, exercise trainers w i l l have acqess to your personal and medical information. C O N S E N T I have read the above comments and understand the explanation, and I wish to proceed with the tests and experiment. In agreeing to such an examination, I waive any legal recourse against members o f the staff of: The John M . Buchanan Fitness & Research Centre, the U . B . C . Aquatic Centre, and the Lonsdale location of North Shore Recreation Centres. Date: Witness: Subject: (print) (print) (signature) (signature) 106 A p p e n d i x VI: L i s t o f Contact A u t h o r s Authors Wattanapenpaiboon N . , Lukito W . , Strauss B . J . , Hsu-Hage B . H . , Wahlqvist M . L . and Stroud D.B. Institution Monash University Department o f Medicine, Monash medical Centre, Melbourne, Australia Title Agreement o f skinfold measurement and bioelectrical impedance analysis (BIA) methods with dual energy X - r a y absorptiometry ( D E X A ) i n estimating total body fat in Anglo-Celtic Australians Source International Journal o f Obesity & Related Metabolic Disorders. 22(9): 854-60, 1998 Sept. Subjects 130 females ages 26-86 years Related methods Percent body fat was estimated by the four skinfold thickness measurement and D E X A . Authors Brodowicz G . R . , Mansfield R . A . , M c C l u n g M . R . and Althoff S.A. Institution Dep. Public Health Education, Portland State University, Portland, Oregon Title Measurement o f body composition i n the elderly: Dual energy X-ray absorptiometry, underwater weighing, bioelectircal impedance analysis and anthropometry. Source Gerontology 40(6). 1994. 332-339. Subjects 48 men and women (ages 26-40 years) 44 older men and women (ages 65-85 years) Related methods Percent body fat was estimated using skinfold measurements and D E X A Authors Nelson M . E . , Fiatarone M . A . , Layne J.E., Trice I., Economos C D . , Fielding R . A . , ma R., Pierson R . N . and Evans W . J . Institution Human Physiology Lab, J M - U S D A - H N R C , Boston, M A Title Analysis o f body-composition techniques and models for detecting change i n soft tissue with strength training. Source American Journal o f Clinical Nutrition 63(5). 1996. 678-686. Subjects 39 women ages 50-70 years. 108 Related Methods B o d y composition was assessed using anthropometry and D E X A Authors Pritchard J.E., Nowson C . A . , Strauss B . J . , Carlson J.S., Kaymakci B . and Wark J.D. Institution Department o f Medicine, University o f Melbourne, The Royal Melbourne Hospital, Melbourne, Australia Source European Journal o f Clinical Nutrition. 1993. 47, 216-228. Title Evaluation o f dual energy X-ray absorptiometry as a method o f measurement o f body fat. Subjects 8 adult women ages 19-58 years Related methods Measurement o f body fat from D E X A and skinfold anthropometry (4-sites) Authors Baumgartner R . N . , Stauber P . M . , M c H u g h D . , Koehler K . M . and Garry P.J. Institution Clinical Nutrition Laboratories, School o f Medicine, University o f New M e x i c o . Source Journal o f Gerontology: Medical Sciences. 1995. 50A(6), M 3 0 7 - M 3 1 6 . Title Cross-sectional age differences i n body composition i n persons 60+ years o f age. Subjects 181 women ages 60-95 years Related methods B o d y composition was quantified using D E X A and anthropometry (4 skinfold sites) Authors Hansen N . J . , Lohman T . G . , Going S.B., H a l l M . C . , Pamenter R . W . , Bare L . A . , Boyden T.W. and Houtkooper L . B . Institution Departments o f Exercise and Sport Sciences and of Nutrition and Food Science, University o f Arizona and Department o f Veterans Affairs Medical Center, Tucson, Arizona Source Journal o f A p p l i e d Physiology. 1993. 75(4), 1637-41. Subjects 100 women ages 28-39 years Related methods B o d y composition was assessed using D E X A and anthropometry (9 skinfold sites) 109 Appendix VII: Letter of Request for Data To W h o m It M a y Concern: I am a graduate student i n the School o f Human Kinetics at the University o f British Columbia and currently working on m y thesis for a Masters o f Science degree under the supervision o f Dr. A l a n D . Martin. The primary objective o f my research is to examine the relationship between anthropometry and body composition measured by dual-energy x-ray absorptiometry i n elderly women ages 75 to 80 years, and to determine whether or not new skinfold equations are needed to more accurately predict body fat in this population. To date, we have conducted body composition assessments on forty-six elderly women. Anthropometric measurements included eight skinfold thicknesses, four body girths, height, and weight. Estimates for whole body fat, bone mineral content, and non-fat-non-bone lean body tissue were obtained using QDR-4500 Hologic instrumentation. Although not a substitute for true cross-validation, testing our equation in similar data bases o f elderly women w i l l help us to evaluate its stability and accuracy. Additionally, applying our equation to data bases o f younger women (peri- and early post-menopausal) w i l l enable us to demonstrate the need for new body composition prediction equations specific to women over the age o f 75 years. In order to pursue the secondary purpose o f my research, requests for additional data bases are necessary. Recent work conducted by you and your colleagues (reference) is o f interest to me and I would greatly appreciate your permission to access this data for secondary analysis. The intended use o f your data is for my thesis publication for which you w i l l receive acknowledgment. If journal publication opportunities arise, we can further discuss your contribution and co-authorship possibilities. W e are open to your suggestions i f there are any other terms you would like to include. Sincerely, Andrea Dalton 110 Appendix VIII: Distribution of Dependent Variables Figure 1: D E X A Fat Mass Figure 2: D E X A % Body Fat Appendix IX: Distributions of Independent Predictor Variables Figure 1: A b d o m i n a l S F Thickness 5.0 15.0 10.0 25.0 20.0 35.0 30.0 Figure 2: Biceps S F Thickness 45.0 40.0 5.0 50.0 Figure 3: C a l f S F Thickness 10.0 15.0 20.0 25.0 30.0 35.0 7.5 12.5 17.5 22.5 27.5 32.5 Figure 4: Midaxilary S F Thickness J7 Nl Ml N N 5.0 12.5 17.5 22.5 27.5 32.5 37.5 15.0 20.0 25.0 30.0 35.0 40.0 112 10.0 15.0 20.0 25.0 30.0 35.0 7.5 12.5 17.5 22.5 27.5 32.5 37.5 Figure 5: Suprailiac SF Thickness 2.5 7.5 5.0 12.5 10.0 17.5 15.0 22.5 20.0 27.5 25.0 Figure 6: Subscapular SF Thickness 5.0 32.5 30.0 Figure 7: Thigh SF Thickness 40.0 60.0 50.0 70.0 20.0 17.5 25.0 22.5 30.0 35.0 27.5 32.5 37.5 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 12:5 17.5 22.5 27.5 - 32.5 37.5 42.5 Figure 9: S U M 4 S F 30.0 15.0 12.5 Figure 8: Triceps SF Thickness 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 20.0 10.0 7.5 35.0 Figure 10: S S T R I Ratio 80.0 100.0 120.0 140.0 90.0 110.0 130.0 .38 .50 .44 113 .63 .56 .75 .69 .81 .88 1.00 1.13 1.25 ' .94 1.06 1.19 Figure 11: Height Figure 12: Weight Figure 15: Waist Circumference 65.0 70.0 75.0 80.0 85.0 90.0 95.0 100.0 105.0 67.5 .72.5 77.5 82.5 87.5 92.5 97.5 102.5 107.5 114 Appendix X : Preliminary Stepwise Multiple Regression for F M Variables Entered/Removed 3 Model 1 Variables Entered Variables Removed Method WEIGHT Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). HEIGHT Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). MIDAX1 Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). subscap/tric eps sf ratio Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). 2 3 4 a. Dependent Variable: total fat mass in kg 115 Model Summary Model 1 2 3 4 R .948 .970 .978° .980 a b d R Square .898 .941 .956 .961 Std. Error of the Estimate 2.2763 1.7558 1.5326 1.4565 Adjusted R Square .895 .938 .953 .957 a. Predictors: (Constant), WEIGHT b. Predictors: (Constant), WEIGHT, HEIGHT c. Predictors: (Constant), WEIGHT, HEIGHT, MIDAX1 d. Predictors: (Constant), WEIGHT, HEIGHT, MIDAX1, subscap/triceps sf ratio ANOVA e Model 1 2 3 4 Regression Residual Total Regression Residual Total Regression Residual Total Regression Residual Total Sum of Squares 1865.484 212.450 2077.934 1954.617 123.317 2077.934 1986.324 91.610 2077.934 1997.325 80.609 2077.934 df 1 41 42 2 40 42 3 39 42 4 38 42 Mean Square 1865.484 5.182 F 360.013 a 317.008 .000 662.108 2.349 281.870 .000° 499.331 2.121 235.389 .000 b. Predictors: (Constant), WEIGHT, HEIGHT c. Predictors: (Constant), WEIGHT, HEIGHT, MIDAX1 d. Predictors: (Constant), WEIGHT, HEIGHT, MIDAX1, subscap/triceps sf ratio 116 .000 977.309 3.083 a. Predictors: (Constant), WEIGHT e. Dependent Variable: total fat mass in kg Sig. b d Coefficients Model 1 2 3 (Constant) WEIGHT (Constant) WEIGHT HEIGHT (Constant) WEIGHT HEIGHT MIDAX1 (Constant) 4 WEIGHT HEIGHT MIDAX1 subscap/triceps sf ratio 3 Unstandardized Coefficients Std. Error B 2.152 -16.509 .032 ^607 6.761 .027 .046 5.934 18.731 .664 -.247 16.462 .028 .040 .611 -.231 .143 .039 5.696 .027 .038 .038 1.253 18.295 .624 -.238 .166 -2.854 Standardiz ed Coefficient s Beta t -7.672 Sig. .000 .948 18.974 2.771 .000 .008 1.037 -.225 24.721 -5.377 2.774 .000 .000 .008 .953 -.211 22.156 -5.735 .000 .000 .146 3.674 3.212 .001 .003 .974 -.217 .170 -.082 23.247 -6.193 4.328 -2.277 .000 .000 .000 .028 a. Dependent Variable: total fat mass in kg Excluded Variables Model 1 HEIGHT BMI TRISF1 SUBSCAP1 MIDAX1 BICEP1 ILIAC1 ABD1 THIGHSF1 CALFSF1 SUM4SF WAISTG1 HIPG1 WHR subscap/triceps sf ratio Beta In -.225 .423 .293 .185 .171 t -5.377 a 5.320 a 4.949 2.736 a a 3.213 a .373 ,131 4.396 2.925 a .163 a a .1>30 . .Q99 a a .321 a .180 a .215 a .029 a -.018 a 6 2.218 2.461 Sig. .000 .000 .000 .009 Partial Correlation -.648 .644 .616 .397 .720 .006 .032 .420 .676 .571 .239 .331 .651 .018 .363 .000 .601 .249 1.791 .081 .272 .528 .600 .083 -.324 117 .472 .453 .000 .112 1.951 .844 .237 .451 .003 1.623 " 4.751 Collinearity Statistics Tolerance .058 .748 .790 .642 .357 .234 .295 .193 -.051 .858 .827 Excluded Variables Model 2 BMI TRISF1 SUBSCAP1 MIDAX1 BICEP1 I LI A C 1 ABD1 THIGHSF1 CALFSF1 SUM4SF WAISTG1 HIPG1 WHR subscap/triceps sf ratio 3 BMI TRISF1 SUBSCAP1 BICEP1 ILIAC1 ABD1 THIGHSF1 CALFSF1 SUM4SF WAISTG1 HIPG1 WHR subscap/triceps sf ratio 4 BMI TRISF1 SUBSCAP1 BICEP1 ILIAC1 ABD1 THIGHSF1 CALFSF1 SUM4SF WAISTG1 HIPG1 WHR Beta In .084 6 Sig. .883 Partial Correlation .024 .781 3.674 .001 .507 2.285 1.807 .963 .028 .078 .341 1.369 2.951 -.185 .005 .854 t b .187 b .050 .146 b b .257 .105 '.085 .045 .066 b b b b b .200 -.017 b b .149 -.037 -.041 b -.232 b b c .113° -.059° .158° .013° .012° .039 .025° c .073 -.123° .127 c c -.071° -.082° .074 .070 .118 .152 .018 .149 3.141 3.444 .1 -722 -.844 -.982 -.467 1.795 -.935 1.885 .243 .246 .939 .568 .838 -1.519 d d d .003 .440 .449 .124 .342 .001 .483 .344 .278 .152 .210 .266 -.134 -.155 -.076 .189 .762 .849 .179 .093 .404 .332 .643 .081 .356 .067 .809 .807 .354 .573 .407 1.665 .137 .104 .149 .361 .712 .631 .628 .667 .630 .272 .186 .214 .427 -.030 .280 -.150 4.661E-03 -.268 .281 .151 .384 .478 .666 .583 .149 .292 .039 .040 .151 .092 .135 -.239 .261 .166 .187 .726 .791 4.291 E-03 -1.862 -2.277 .070 .028 -.289 -.347 .882 .025 1.048 .301 .220 .065 .734 .170 .201 .298 .229 .112 .151 .056 .638 .078 .473 d d Collinearity Statistics Tolerance 4.806E-03 1.249 1.902 .342 .384 .022 d .474 .014 d .328 .745 .054 .608 d .190 .851 .182 .031 .218 .564 .143 d -.436 .666 -.071 .120 d 1.219 .008 .114 d -.041 .092 -.040 d 1.359 -.955 .231 .346 .196 -.155 a. Predictors in the Model: (Constant), WEIGHT b. Predictors in the Model: (Constant), WEIGHT, HEIGHT c. Predictors in the Model: (Constant), WEIGHT, HEIGHT, MIDAX1 d. Predictors in the Model: (Constant), WEIGHT, HEIGHT, MIDAX1, subscap/triceps sf ratio e. Dependent Variable: total fat mass in kg 118 .177 .571 Appendix XI: Stepwise Multiple Regression Analyses (a) Equation development for F M Variables Entered/Removed 3 Model 1 Variables Entered Variables Removed Method WT Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). HT Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). MA Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). subscap/tric eps sf ratio Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). 2 3 4 a. Dependent Variable: total fat mass in kg 119 Model Summary Model 1 2 R .948 .970 3 4 a R Square .898 b .978 .941 c .956 .980 d Std. Error of the Estimate Adjusted R Square .895 2.2763 .938 1.7558 .953 .961 1.5326 .957 1.4565 a. Predictors: (Constant), WT b. Predictors: (Constant), WT, HT c. Predictors: (Constant), WT, HT, MA d. Predictors: (Constant), WT, HT, MA, subscap/triceps sf ratio ANOVA e Model 1 2 3 4 Regression Residual Total Regression Residual Total Regression Residual Total Regression Residual Total Sum of Squares 1865.484 212.450 2077.934 df 1954.617 123.317 2077.934 1986.324 91.610 2077.934 1997.325 80.609 2077.934 Mean Square 1865.484 1 41 42 2 F 360.013 Sig. .000 977.309 3.083 317.008 .000 b 662.108 2.349 281.870 .000 c 499.331 2.121 235.389 .000 d 5.182 40 42 3 39 42 4 38 42 a. Predictors: (Constant), W T b. Predictors: (Constant), WT, HT c. Predictors: (Constant), WT, HT, MA d. Predictors: (Constant), WT, HT, MA, subscap/triceps sf ratio e. Dependent Variable: total fat mass in kg 120 a Coefficients Model 1 2 3 4 (Constant) WT (Constant) WT HT (Constant) WT HT MA (Constant) WT HT MA subscap/triceps sf ratio 3 Unstandardized Coefficients B Std. Error 2.152 -16.509 .607 18.731 .664 -.247 16.462 .032 6.761 .027 .046 5.934 .028 .611 -.231 .143 18.295 5.696 -2.854 .038 .038 1.253 .624 -.238 .166 .040 .039 .027 a. Dependent Variable: total fat mass in kg 121 Standardiz ed Coefficient s Beta t -7.672 .948 18.974 1.037 -.225 24.721 -5.377 2.774 .953 -.211 .146 .974 -.217 .170 -.082 2.771 22.156 -5.735 3.674 3.212 23.247 -6.193 4.328 -2.277 Sig. .000 .000 .008 .000 .000 .008 .000 .000 .001 .003 .000 .000 .000 .028 Excluded Variables' Model 1 HT BMI Beta In -.225 .423 ABD MA SI SS SUM4SF subscap/triceps sf ratio WC 2 3 4 t -5.377 a 5.320 a .131 2.218 a . .171 :163 3.213 a 2.925 2.736 4.751 -.324 a .185 .321 a a '- 018 HC BMI ABD MA SI SS SUM4SF subscap/triceps sf ratio WC HC BMI ABD SI SS SUM4SF subscap/triceps sf ratio WC HC BMI ABD SI SS SUM4SF WC HC a ; .180 .215 .084 1.791 a 1.951 .149 1.807 3.674 2.285 a b .085 .146 .105 .050 b b b .781 2.951 -.982 b .200 -.041 -.017 b b -.185 1.722 -.467 b .149 -.232° .012 b .246 .243 -.935 c .013 -.059° .073 -.082° C .838 -2.277 -1.519 c .078 .001 .028 .440 .005 .332 .854 .093 .643 .807 .809 .356 .407 .028 .453 .420 .397 .601 -.051 .720 .676 .472 .357 .858 .295 .024 .193 4.806E-03 .272 .651 .234 .278 .507 .344 .628 -.030 .266 -.076 .186 .189 4.661 E-03 .124 .427 -.155 .040 .039 -.150 .135 -.347 .712 .631 .361 .272 .849 .478 .384 .281 .149 .791 .025 4.291 E-03 .078 d .342 .638 .473 .384 d 1.249 .220 .201 .022 .092 .081 .058 .883 .237 .331 .474 d d -.041 .009 .000 .748 .644 -.239 .074 .114 .003 .006 Tolerance .844 .137 .104 c .118 .032 Collinearity Statistics 1.665 -.123° .127 .018 Sig. .000 .000 Partial Correlation -.648 .149 d d .734 . 1.359 .182 .666 1.219 .231 -.436 d .882 a. Predictors in the Model: (Constant), W T b. Predictors in the Model: (Constant), WT, HT c. Predictors in the Model: (Constant), WT, HT, MA d. Predictors in the Model: (Constant), WT, HT, MA, subscap/triceps sf ratio e. Dependent Variable: total fat mass in kg (b) Equation development for %Fat 122 .261 .056 .166 .187 .112 .218 .143 .120 .196 .177 -.071 Variables Entered/Removed Model 1 Variables Entered Variables Removed 3 Method SUM4SF Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). BMI Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). MA Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). 2 3 • 4 SUM4SF 5 subscap/tric eps sf ratio Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). a. Dependent Variable: P C F A T 123 Model Summary Model 1 R 2 3 .867 .901 .920 4 .918 5 .928 a b R Square .751 .811 c .847 d .843 e Std. Error of the Estimate 2.6606 2.3474 Adjusted R Square .745 .802 2.1396 .835 .835 .861 2.1385 2.0382 .851 a. Predictors: (Constant), SUM4SF b. Predictors: (Constant), SUM4SF, BMI c. Predictors: (Constant), SUM4SF, BMI, MA d. Predictors: (Constant), BMI, MA e. Predictors: (Constant), BMI, MA, subscap/triceps sf ratio ANOVA Model 1 2 3 4 Regression Residual Total Regression Residual Total Regression Residual Total Regression Residual 5 Total Regression Residual Total Sum of Squares 876.879 290.232 1167.111 df 946.696 220.415 1167.111 988.565 178.546 1167.111 984.181 182.929 1167.111 1005.099 162.011 1167.111 f Mean Square 876.879 1 41 42 2 F 123.873 Sig. .000 473.348 5.510 85.901 .000 b 329.522 4.578 71.978 .000 c 492.091 107.602 .000 d 335.033 80.650 .000 e 7.079 40 42 3 39 42 2 40 4.573 42 3 39 4.154 42 a. Predictors: (Constant), SUM4SF b. Predictors: (Constant), SUM4SF, BMI c. Predictors: (Constant), SUM4SF, BMI, MA d. Predictors: (Constant), BMI, MA e. Predictors: (Constant), BMI, MA, subscap/triceps sf ratio f. Dependent Variable: P C F A T 124 a Coefficients Model 1 2 3 Unstandardized Coefficients B 20.711 .171 (Constant) SUM4SF (Constant) SUM4SF BMI (Constant) SUM4SF BMI 5 Std. Error 1.418 .015 2.862 11.548 9.503E-02 .598 7.950 3.070E-02 .025 .168 2.867 .031 .162 .755 MA (Constant) 4 3 .073 .220 6.157 BMI MA (Constant) 2.204 .882 .268 7.139 BMI MA subscap/triceps sf ratio .096 .053 2.146 .094 .053 1.760 .932 .300 -3.949 Standardiz ed Coefficient s Beta t 14.608 Sig. .000 4.035 .000 .867 11.130 .481 .456 3.755 3.560 2.773 .979 .156 .576 .301 .674 .367 .711 .410 -.151 4.670 3.024 2.794 9.220 5.019 3.327 9.931 5.672 -2.244 .000 .001 .001 .008 .334 .000 .004 .008 .000 .000 .002 .000 .000 .031 a. Dependent Variable: P C F A T Excluded Variables' Model 1 HT WT BM| ABD MA SI SS subscap/triceps sf ratio WC HC 2 HT WT ABD MA SI SS subscap/triceps sf ratio WC HC Beta In .> ,-.125 .166 a a . .456 a ... .015 .151 a -.122 a -.314 a -.153 a .157 a a t -1.637 1.286 Sig. .109 .206 .199 Collinearity Statistics Tolerance .998 .357 .018 .202 .376 .442 Partial Correlation -.251 .490 .287 .440 -.122 .249 .085 -.269 .159 .769 .225 .366 .222 3.560 .001 .113 1.304 .911 .200 -.780 -1.641 -1.764 .109 -.251 1.125 .267 .175 .309 -.929 .359 -.147 .931 1.459 .152 b -.934 .356 -.148 .101 b .880 .384 .301 b 3.024 .004 .133 b .851 .400 .185 a -.066 -.136 -.405 b b .140 .360 .436 .397 .135 .196 -2.473 .018 -.368 .156 .302 -.147 b -1.937 -.160 b -1.045 .013 b .105 125 .060 .917 -.296 .769 -.165 .201 .017 .298 Excluded Variables' Model 3 HT WT ABD SI SS subscap/triceps sf ratio WC ' . HC 4 5 .191 .068 .471 c -.368 -167 -.246° c c .041 -.123 .098 d d d d .156 -2.456 -2.484 -1.774 .352 c .104 -.128 -.151 -.219 .071 SI SS WC HC SUM4SF .076 .504 SI SS subscap/triceps sf ratio WC WT ABD .640 .019 .018 .084 .727 -1.120 .675 -.067 HT -.179 -.148° HT WT ABD HC SUM4SF .270 Sig. .237 • .071° d d d d d -.059 -.117 .116 .110 .155 e e e e e -.100 .033 .218 e e e -1.042 -.939 1.085 1.030 -1.080 -2.244 -1.590 .642 .979 .304 .354 .285 .309 .287 .031 .120 .525 .334 -.963 -.935 1.355 .342 .356 .183 -.651 .306 1.442 .519 .761 1.146 .884 .259 .382 .158 a. Predictors in the Model: (Constant), SUM4SF b. Predictors in the Model: (Constant), SUM4SF, BMI c. Predictors in the Model: (Constant), SUM4SF, BMI, MA d. Predictors in the Model: (Constant), BMI, MA e. Predictors in the Model: (Constant), BMI, MA, subscap/triceps sf ratio f. Dependent Variable: P C F A T (c) E q u a t i o n development for T F M 126 Collinearity Statistics Tolerance .928 .222 t -1.202 Beta In : ... -.078° Partial Correlation -.191 .109 .357 -.370 -.374 .155 -.277 .057 -.165 -.149 .171 .163 -.170 -.338 -.247 .102 .155 -.154 -.150 .215 .183 .142 -.105 .050 .228 .763 .194 .296 .948 .228 .480 .383 .277 .785 .198 .329 .155 .945 .228 .476 .383 .117 .154 .320 .151 Variables Entered/Removed 3 Model 1 Variables Entered Variables Removed Method WC Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). WT Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). SI Stepwise (Criteria: Probabilityof-F-to-ent er<= .050, Probabilityof-F-to-rem ove >= .100). 2 3 a. Dependent Variable: trunk fat mass in kg Model Summary Model 1 2 3 R .922 .937 .951 a b c R Square .850 .879 .904 Adjusted R Square .846 .873 .896 Std. Error of the Estimate 1.6034 1.4581 1.3163 a. Predictors: (Constant), W C b. Predictors: (Constant), WC, WT c. Predictors: (Constant), WC, WT, SI 127 ANOVA Model 1 2 Regression Residual Total Regression Residual 3 Total Regression Residual Total Sum of Squares 595.217 d df 105.408 Mean Square 595.217 1 41 700.624 2.571 42 615.581 2 85.044 307.790 40 700.624 633.054 67.571 700.624 F 231.519 Sig. .000 144.768 .000 121.794 .000° 3 39 42 211.018 1.733 a. Predictors: (Constant), W C b. Predictors: (Constant), WC, WT c. Predictors: (Constant), W C , WT, SI d. Dependent Variable: trunk fat mass in kg Model 1 2 (Constant) WC (Constant) 3 WC WT (Constant) WC WT SI Unstandardized Coefficients B Std. Error -16.594 1.886 .326 -15.772 .217 1.736 .040 .178 1.633 .038 .124 .038 .039 .131 -14.317 .124 b 2.126 42 Coefficients a 3 Standardiz ed Coefficient s Beta .021 .922 .042 .613 .353 a. Dependent Variable: trunk fat mass in kg 128 t -8.797 15.216 -9.086 5.383 Sig. .000 .000 .000 .000 .004 .504 3.095 -8.769 4.648 .000 .000 .333 .203 3.230 3.176 .003 .003 Excluded Variables' Model 1 HT WT Beta In .016 BMI ABD MA 2 SI SS subscap/triceps sf ratio HT BMI ABD MA SI SS 3 subscap/triceps sf ratio HT BMI ABD MA SS subscap/triceps sf ratio t a .353 .329 .142 .192 2.800 a 1.899 a 2.721 3.038 1.092 a a a -.117 .210 .115 .190 .203 .139 .258 3.095 a .215 .123 -.094 1 -1.283 -1.795 a b 1.660 b 1.660 3.030 b b 3.176 1.367 b b -.031 -.093 .159° -.041° -.427 -1.547 1.357 b c -.469 1.508 .114° .004° -.040° .040 -.625 a. Predictors in the Model: (Constant), W C b. Predictors in the Model: (Constant), W C , W T c. Predictors in the Model: (Constant), W C , WT; SI' d. Dependent Variable: trunk fat mass in kg (d) Equation development for % T F 129 Sig. .798 .004 .008 .065 .010 .004 .281 .207 .080 .105 .105 .004 .003 .179 .672 .130 .183 .641 .140 .968 .536 Partial Correlation .041 Collinearity Statistics Tolerance .979 .405 .228 .440 .288 .234 .620 .395 .433 .170 -.199 .638 .610 .287 .669 .453 .214 .181 .609 .638 .608 .286 -.276 .257 .257 .437 -.068 -.243 .215 -.076 .238 .007 -.101 .672 .600 .659 .177 .330 .421 .225 .599 Variables Entered/Removed Variables Entered Model 1 3 Variables Removed Method WC Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). MA Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). HT Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). 2 3 I I | a. Dependent Variable: PCTRUNK Model Summary Model 1 2 3 R .832 .892 .918° a b R Square .693 .796 .843 Adjusted R Square .686 .786 .831 Std. Error of the Estimate 3.7574 3.0987 2.7574 a. Predictors: (Constant), WC b. Predictors: (Constant), WC, MA c. Predictors: (Constant), WC, MA, HT 130 ANOVA d Model 1 2 3 Regression Residual Total Regression Residual Total Regression Residual Total Sum of Squares 1306.671 df 578.834 Mean Square 1306.671 1 41 1885.505 F 92.554 Sig. .000 750.711 78.182 .000 b 529.659 7.603 69.662 .000 c 14.118 42 1501.422 2 384.083 40 42 1885.505 1588.977 296.528 1885.505 9.602 3 39 42 a. Predictors: (Constant), W C b. Predictors: (Constant), W C , MA c. Predictors: (Constant), W C , MA, HT d. Dependent Variable: P C T R U N K Coefficients Model 1 2 (Constant) WC (Constant) - 3 WC MA (Constant) WC MA HT Unstandardized Coefficients B Std. Error -7.388 4.421 .482 .050 -3.812 .342 .374 30.659 .356 .387 -.227 3 Standardiz ed Coefficient s Beta 3.731 .052 .083 10.687 .046 .074 .067 a. Dependent Variable: P C T R U N K 131 .832 t -1.671 9.621 .591 .402 -1.022 6.611 4.504 Sig. .102 .000 .313 .000 .614 2.869 7.697 .000 .007 .000 .416 -.218 5.222 -3.393 .000 .002 a Excluded Variables' Model 1 HT WT Beta In -.202 -.112 .328 BMI ABD ,288 MA 2 .402 .384 .314 .004 SI SS subscap/triceps sf ratio HT WT ABD 3 a a a .131 .219 .125 -.036 WT BMI ABD SI SS subscap/triceps sf ratio -.619 1.862 .539 .070 -.097 .282 4.504 .000 .000 .051 .973 .002 .580 .542 .303 .005 .034 a -3.393 -.784 b b 2.490 1.303 2.020 .882 b b SI SS subscap/triceps sf ratio Sig. .019 4.078 2.012 a b b -.409 1.237 1.165 b .195 .175 .125° .177 -.005 c c 1.400 1.807 -.035 -.570 c c -.045° a. Predictors in the Model: (Constant), W C b. Predictors in the Model: (Constant), W C , MA c. Predictors in the Model: (Constant), W C , MA, HT d. Dependent Variable: PCTRUNK ^ Partial Correlation -.360 t -2.440 2.837 a a -.218 -.116 .350 BMI a 1 > (e) Equation development for F M using SF's only 132 .007 .438 .017 .200 .050 .383 .685 .224 .251 .170 .079 .973 .572 Collinearity Statistics Tolerance .979 .234 .228 .409 .620 -.477 -.125 .669 .977 .234 .638 .610 .287 .370 .204 .228 .495 -.065 .197 .186 .221 .160 .177 .308 .140 .281 -.006 -.092 .403 .254 .662 .495 .396 .231 .662 Variables Entered/Removed Variables Entered Model 1 Variables Removed 3 Method BICEP1 Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). CALFSF1 Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). 2 a. Dependent Variable: total fat mass in kg Model Summary Model 1 ' J I R .916 a Std. Error of 1 the Estimate j 2.8602 Adjusted R R Square ,• Square .839 .835 .864 .857 2.6572 I I2 1 .930 a. Predictors: (Constant), BICEP1 b b. Predictors: (Constant), BICEP1, CALFSF1 ANOVA Model 1 2 Regression Residual Total Regression Residual Total Sum of Squares 1742.512 df c 1 Mean Square 1742.512 335.422 41 1795.508 2 897.754 40 7.061 2077.934 282.426 2077.934 F 212.995 Sig. .000 127.149 .000 8.181 42 42 a. Predictors: (Constant), BICEP1 b. Predictors: (Constant), BICEP1, CALFSF1 c. Dependent Variable: total fat mass in kg 133 a b Coefficients' Model 1 2 (Constant) BICEP1 (Constant) BICEP1 CALFSF1 Unstandardized Coefficients B Std. Error 5.578 1.322 3.379 1.467 .912 Standardiz ed Coefficient s Beta .063 .810 .163 .069 .060 Model 1 2 ABD MA SI SS TRISF1 CALFSF1 THIGHSF1 SUM4SF ABD MA SI SS TRISF1 THIGHSF1 SUM4SF Beta In .007 -.001 -.003 .119 .221 .190 .056 .204 t a a a a a a a a -.068 -.053 -.035 .111 b b b .083 -.013 -.039 1.138 1.141 b 1.779 .155 b -.028 b .000 .027 .813 .190 11.712 2.740 Sig. .934 .990 .969 .262 .055 .009 .457 .211 .751 1.270 -.784 -.644 -.411 b 2.304 14.594 .000 .009 0 1.980 2.740 .188 Sig. .000 .916 a. Dependent Variable: total fat mass in kg Excluded Variables t 4.221 .438 .523 .684 .261 .083 -.357 .723 1.026 .311 a. Predictors in the Model: (Constant), BICEP1 b. Predictors in the Model: (Constant), BICEP1, CALFSF1 c. Dependent Variable: total fat mass in kg (f) Equation development for %Fat using SF's only 134 Partial Correlation .013 -.002 -.006 .177 .299 .397 .118 .197 -.125 -.103 -.066 .180 .274 -.057 .162 Collinearity Statistics Tolerance .510 .534 .494 .359 .294 .706 .705 .151 .462 .507 .485 .359 .290 .583 .149 Variables Entered/Removed Model 1 Variables Entered Variables Removed 3 Method SUM4SF Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). CALFSF1 Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). 2 a. Dependent Variable: P C F A T Model Summary Model 1 2 R .867 .885 a b R Square .751 .783 Std. Error of the Estimate 2.6606 2.5189 Adjusted R Square .745 .772 a. Predictors: (Constant), SUM4SF b. Predictors: (Constant), SUM4SF, CALFSF1 ANOVA Model 1 2 Regression Residual Total Regression Residual Total Sum of Squares 876.879 290.232 1167.111 913.324 253.786 1167.111 df c Mean Square 1 41 123.873 456.662 71.976 7.079 42 2 40 42 6.345 a. Predictors: (Constant), SUM4SF , b. Predictors: (Constant), SUM4SF, CALFSF1 c. Dependent Variable: P C F A T 135 F 876.879 Sig. .000 a .000 b *> Coefficients Model 1 2 1 Unstandardized Coefficients B Std. Error 20.711 1.418 (Constant) SUM4SF .171 (Constant) Beta .015 19.172 SUM4SF CALFSF1 Standardiz ed Coefficient s .867 1.488 .149 .135 .017 .056 .753 .210 t 14.608 11.130 12.885 8.599 2.397 Sig. .000 .000 .000 .000 .021 a. Dependent Variable: PC FAT Excluded Variables Model 1 2 Beta In .015 .151 -.122 -.314 ABD MA SI SS TRISF1 BICEP1 CALFSF1 a .250 .336 .210 THIGHSF1 ABD THIGHSF1 a a a a a .058 -.06'7 .105 -.120 -.259 .234 a b MA SI SS TRISF1 BICEP1 t a b b b b ; .280 -.035 b b .113 1.304 -.780 -1.641 1.194 0 Sig. .911 .200 .440 .109 .240 .093 .021 1.718 2.397 .604 .550 .599 .358 .424 -.530 .930 -.809 -1.402 ' '1.182 1.4.81 -.352 .169 .245 ' .147 .727 a. Predictors in the Model: (Constant), SUM4SF b. Predictors in the Model: (Constant), SUM4SF, CALFSF1 c. Dependent Variable: P C F A T 136 Partial Correlation .018 .202 -.122 -.251 .185 .262 .354 .095 -.085 .147 -.128 -.219 .186 .231 -.056 Collinearity Statistics Tolerance .376 .442 .249 .159 .137 .151 .708 .671 .350 .427 .249 .156 .137 .148 .561 Appendix XII: AH Possible Subsets Regression Analyses (a) Equation development for F M BMDP9R - ALL POSSIBLE SUBSETS REGRESSION /INPUT T I T L E IS 'REGRESSION FOR BODY COMPOSITION". F I L E = ' A:\BDYCMP2.DAT' . VARIABLES = 3 1 . CASES=44. FORMATS'31F8.2' . /VARIABLE NAMES ARE GROUP, AGE, HEIGHT, WEIGHT, BMI, TRISF, SUBSCPSF, MIDAXSF, BICEPSF, ILIACSF, ABDSF, THIGHSF, CALFSF, SUMSFU, SUMSFL, SUBTRI, SUM4SF, LOGSUM4, WAISTG, HIPG, WHR, THIGHG, TRUNKFAT, PCTRUNK, STFAT, TOTFAT, STLEAN, TOTLEAN, STPCFAT, TOTPCFAT, TOTWT. USE= TOTFAT, WAISTG, HIPG, SUBTRI, HEIGHT, WEIGHT, BMI, SUM4SF, MIDAXSF, SUBSCPSF, ILIACSF, ABDSF. /REGRESS DEPENDENT= TOTFAT. INDEPENDENT = WAISTG, HIPG, SUBTRI, HEIGHT, WEIGHT, BMI, SUM4SF, MIDAXSF, SUBSCPSF, ILIACSF, ABDSF. /END. , DATA AFTER TRANSFORMATIONS CASE 19 NO. WAISTG 1 2 3 4 5 6 7 CASE NO. 20 HIPG 16 SUBTRI 3 HEIGHT 7 .10 SUBSCPSF ILIACSF 11 ABDSF 26 TOTFAT 81 50 99 19 00 14 88 00 101 28 20 19 98 00 107 24 90 17 107 50 108 32 20 26 86 70 101 19 10 23 102 20 114 36 30 27 86 50 96 17 00 19 19 20 HIPG WAISTG 0 83 34 40 1 25 27 60 0 69 39 80 0 93 41 00 0 78 40 00 0 97 45 50 0 69 28 00 16 SUBTRI 166 60 64 50 23 18461 00 165 70 66 20 24 22630 00 164 00 28 75 40 31082 10 154 70 78 40 32 32286 80 163 90 24 66 60 22763 00 158 10 78 50 31 28038 20 156 80 60 20 24 19610 10 3 4 5 HEIGHT WEIGHT BMI 11 ABDSF 26 TOTFAT 00 20 40 70 80 60 20 80 00 10 00 90 50 60 7 10 SUBSCPSF ILIACSF 8 9 10 72 11 87 19 103 32 50 30 40 70 50 20 95 17 105 26 119 27 50 90 00 00 00 50 0 26 0 37 0 36 58 162 40 60 17296 30 98 174 10 90 22712 90 71 161 90 80 39753 60 4 WEIGHT 17 SUM4SF BMI MIDAXSF 24 72 00 17 20 11 94. 20 28 00 03 111. 00 31 20 76 121. 00 26 50 79 89. 60 20 70 41 131. 00 28 10 49 77. 30 25 00 17 SUM4SF 8 MIDAXSF 61 20 23 20 64 05 13 40 70 30 23 19 83 40 29 70 91 40 34 87 139 50 35 40 44 NUMBER OF CASES READ. 137 CASES WITH DATA MISSING OR BEYOND LIMITS REMAINING NUMBER OF CASES 1 43 SUMMARY STATISTICS FOR EACH VARIABLE VARIABLE 19 20 16 3 4 5 17 8 7 10 11 26 WAISTG HIPG SUBTRI HEIGHT WEIGHT BMI STJM4SF MIDAXSF SUBSCPSF ILIACSF ABDSF TOTFAT STANDARD DEVIATION MEAN 87 101 0 158 66 26 88 23 21 19 32 23785 42558 38605 76442 05814 40581 57000 37791 20000 38023 45349 10233 85813 11 .56382 8 .66178 0 .20099 . 6 .42240 10 .98312 ' 4 .02438 26 70828 7 20305 8 19030 6 69173 8 54925 7033 81977 COEFFICIENT OF VARIATION SMALLEST VALUE 0 .132270 0 .085434 0 262931 0 040633 0 165394 0 151463 0 302205 0 310476 0 383078 0 343986 0 266313 0 295714 " LARGEST VALUE 66 .20000 87 90000 0 39000 147 50000 47 00000 18 83000 23 50000 6 10000 4 60000 3 50000 5 40000 11076 50000 108 .00000 123 .70000 1 25000 174 10001 96 00000 35 77000 139 50000 38 60000 36 30000 35 30000 48 60000 42201 50000 CORRELATIONS WAISTG 19 WAISTG HIPG SUBTRI HEIGHT WEIGHT BMI SUM4SF MIDAXSF SUBSCPSF ILIACSF ABDSF TOTFAT 19 20 16 3 4 5 17 8 7 10 11 26 1 0 0 0 0 0 0 0 0 0 0 0 000 720 576 145 875 879 831 601 845 624 616 871 MIDAXSF 8 MIDAXSF SUBSCPSF ILIACSF ABDSF TOTFAT 8 7 10 11 26 1 0 0 0 0 FIRST DIGITS OF 19 20 4 26 5 17 7 10 11 8 16 3 WAISTG HIPG WEIGHT TOTFAT BMI SUM4SF SUBSCPSF ILIACSF ABDSF MIDAXSF SUBTRI HEIGHT 000 653 739 653 624 HIPG 20 SUBTRI 16 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 000 265 296 899 812 796 511 663 630 641 893 000 060 378 397 481 411 740 375 392 344 HEIGHT 3 1 0 -0 0 0 -0 0 0 0 000 395 097 049 126 019 031 093 184 SUBSCPSF ILIACSF 7 10 ABDSF 11 1 0 0 0 1 000 0 645 000 718 685 776 1 000 0 802 0 650 WEIGHT 4 1 0 0 0 0 0 0 0 000 874 802 529 727 569 590 948 1 0 0 0 0 0 0 BMI 5 SUM4SF 17 000 844 516 803 608 599 928 1 0 0 0 0 0 TOTFAT CORRELATIONS 7* 88* 889* 8889* 87888* 867789* 6656687* 66565768* 655657676* 5233347334* 1231 1 * SUBSETS WITH 138 1 VARIABLES 000 747 917 867 790 875 R-SQUARED ADJUSTED R-SQUARED 0.897759 0.895265 52.51 0.860936 0.857544 85 .47 BMI 0.796944 0.791991 142.74 HIPG 0.764781 0.759044 171.53 SUM4SF 0.759458 0.753591 176.30 WAISTG 0.601565 0.591847 317.62 SUBSCPSF 0.422324 0.408234 478.05 ILIACSF 0.415886 0.401639 483.81 ABDSF 0.389721 0.374836 507.23 MIDAXSF 0.118139 0.096630 750.30 SUBTRI CP WEIGHT SUBSETS WITH R-SQUARED ADJUSTED R-SQUARED 0.940654 0.937687 16.12 HEIGHT 0.940080 0.937084 16.63 WEIGHT BMI 0.936936 0.933783 19.45 HEIGHT BMI 0.934637 0.931368 21.50 WEIGHT SUM4SF 0.918738 0.914675 35.73 WEIGHT MIDAXSF 0.917868 0.913762 36.51 0.915778 0.911567 38.38 WEIGHT ILIACSF 0.913875 0.909568 40.09 WEIGHT SUBSCPSF 0.908957 0.904405 44.49 WEIGHT ABDSF 0.906644 0.901976 46.56 HIPG WEIGHT 2 VARIABLES CP HIPG WEIGHT BMI SUBSETS WITH R-SQUARED ADJUSTED R-SQUARED 0.955913 0.952522 4.46 HEIGHT WEIGHT MIDAXSF 0.954274 0.950757 5.93 WEIGHT BMI MIDAXSF 0.951488 0.947757 8.42 HEIGHT WEIGHT SUM4SF 0.950879 0.947100 8.97 WEIGHT BMI SUM4SF 0.950258 0.946431 9.52 HEIGHT BMI MIDAXSF 0.948117 0.944126 11.44 HEIGHT BMI SUM4SF 0.947659 0.943633 11.85 HEIGHT WEIGHT ILIACSF 0.946559 0.942448 12.83 WEIGHT BMI*' ILIACSF CP 139 3 VARIABLES 0.945239 0.941027 14.01 HEIGHT WEIGHT ABDSF 0.944845 0.940603 14.37 HIPG HEIGHT WEIGHT SUBSETS WITH 4 VARIABLES R-SQUARED ADJUSTED R-SQUARED CP 0.961151 0.957061 1.77 VARIABLE 16 SUBTRI 3 HEIGHT 4 WEIGHT 8 MIDAXSF INTERCEPT COEFFICIENT -2849.16 -238.172 624.126 165.516 18323.2 T-STATISTIC -2.26 -6.19 23 .22 4.32 0.960639 0.956495 2.23 VARIABLE 16 SUBTRI 4 WEIGHT 5 BMI 8 MIDAXSF INTERCEPT COEFFICIENT -3153.26 342.465 717.670 162.583 -19385.8 T-STATISTIC -2.48 7.94 6.11 4.21 0.958910 0.954585 3.78 HIPG 0.958435 0.954060 0.958098 HEIGHT WEIGHT MIDAXSF 4.20 WAISTG HEIGHT WEIGHT MIDAXSF 0.953687 4.50 HEIGHT BMI MIDAXSF 0.957782 0.953338 4.79 HIPG WEIGHT BMI MIDAXSF 0.957309 0.952815 5.21 SUBTRI WEIGHT BMI SUM4SF 0.957262 0.952763 5.25 WAISTG WEIGHT BMI MIDAXSF 0.957025 0.952502 5.46 HEIGHT WEIGHT SUM4SF SUBSCPSF 0.957007 0.952482 5.4 8 WEIGHT BMI SUM4SF SUBSCPSF SUBTRI SUBSETS WITH 5 VARIABLES R-SQUARED ADJUSTED R-SQUARED CP 0.962983 0.957980 2.13 VARIABLE 16 SUBTRI 3 HEIGHT 4 WEIGHT 17 SUM4SF 8 MIDAXSF INTERCEPT COEFFICIENT -3174.70 -204.646 575.594 29.7873 122.154 14869.3 T-STATISTIC -2.50 -4.51 12.89 1.35 2.46 0.962850 0.957830 2.25 VARIABLE 16 SUBTRI 4 WEIGHT 5 BMI 17 SUM4SF 8 MIDAXSF INTERCEPT COEFFICIENT -3463.42 332.015 610.808 32.3078 115.914 -17388.1 -STATISTIC -2.73 7.71 4.48 1.48 2.35 0.962669 0.957624 2 .41 VARIABLE 16 SUBTRI 3 HEIGHT 4 WEIGHT 8 MIDAXSF 7 SUBSCPSF INTERCEPT COEFFICIENT -4730.78 -200.727 582.406 142.450 99.8403 15014.0 T-STATISTIC -2.39 -4.10 13 .47 3.35 1.23 140 0.962666 0.957621 2.42 HIPG SUBTRI HEIGHT WEIGHT MIDAXSF 0.962623 0.957572 2.45 SUBTRI WEIGHT BMI MIDAXSF SUBSCPSF 0.962364 0.957278 2.69 HIPG SUBTRI WEIGHT BMI MIDAXSF 0.961424 0.956211 3.53 HEIGHT WEIGHT SUM4SF MIDAXSF SUBSCPSF 0.961394 0.956177 3.55 SUBTRI HEIGHT WEIGHT MIDAXSF ABDSF 0.961356 0.956134 3.59 WAISTG SUBTRI HEIGHT WEIGHT MIDAXSF 0.961271 0.956037 3.66 SUBTRI HEIGHT WEIGHT MIDAXSF ILIACSF STATISTICS FOR 1 BEST' SUBSET MALLOWS' CP 1.77 SQUARED MULTIPLE CORRELATION 0.96115 MULTIPLE CORRELATION 0.98038 ADJUSTED SQUARED MULT. CORR. 0.95706 RESIDUAL MEAN SQUARE 2124377.831358 STANDARD ERROR OF EST. 1457.524556 F-STATISTIC 235.03 NUMERATOR DEGREES OF FREEDOM 4 DENOMINATOR DEGREES OF FREEDOM 38 SIGNIFICANCE (TAIL PROB.) 0.0000 *** N O T E VARIABLE NO. NAME 16 3 4 8 INTERCEPT SUBTRI HEIGHT WEIGHT MIDAXSF *** THE ABOVE F-STATISTIC AND ASSOCIATED SIGNIFICANCE TEND TO BE LIBERAL WHENEVER A SUBSET OF VARIABLES IS SELECTED BY THE CP OR ADJUSTED R-SQUARED CRITERIA. REGRESSION COEFFICIENT STANDARD ERROR STAND. COEF. TSTAT. 2TAIL SIG. 18323.2 -2849.16 -238.172 624.126 165.516 5702.46 1258.76 38.4637 26.8804 38.3240 2.605 -0.081 -0.217 0.975 0.169 3.21 -2.26 -6.19 23.22 4.32 0.003 0.029 0.000 0.000 0.000 CONTRITOLBUTION ERANCE TO R-SQ 0.790229 0.828870 0.580311 0.663755 0.00524 0.03920 0.55116 0.01907 (b) Equation development for %Fat BMDP9R - ALL POSSIBLE SUBSETS REGRESSION /INPUT T I T L E IS 'REGRESSION FOR BODY COMPOSITION' . FILE='A:\BDYCMP2.DAT'. VARIABLES = 3 1 . CASES = 44. FORMAT= '31F8.2'. /VARIABLE NAMES ARE SUBJECT, AGE, HEIGHT, WEIGHT, BMI, TRISF, SUBSCPSF, MIDAXSF, BICEPSF, ILIACSF, ABDSF, THIGHSF, CALFSF, SUMSFU, SUMSFL, SUBTRI, SUM4SF, LOGSUM4, WAISTG, HIPG, WHR, THIGHG, TRUNKFAT, PCTRUNK, STFAT, TOTFAT, STLEAN, TOTLEAN, STPCFAT, TOTPCFAT, TOTWT. USE= TOTPCFAT, HEIGHT, WEIGHT, BMI, ILIACSF, 141 ABDSF, MIDAXSF, SUBSCPSF, WAISTG, HIPG, SUBTRI, SUM4SF. /REGRESS DEPENDENTS TOTPCFAT. INDEPENDENT = HEIGHT, WEIGHT, BMI, ILIACSF, ABDSF, SUBSCPSF, WAISTG, HIPG, SUBTRI, SUM4SF. MIDAXSF, /END. NUMBER OF CASES READ CASES WITH DATA MISSING OR BEYOND LIMITS . REMAINING NUMBER OF CASES . . . . . . . 44 1 43 SUMMARY STATISTICS FOR EACH VARIABLE VARIABLE STANDARD DEVIATION MEAN 30 TOTPCFAT 35.83023 COEFFICIENT OF VARIATION 5.27147 SMALLEST VALUE 0.147123 LARGEST VALUE 24.50000 46.70000 CORRELATIONS HEIGHT 3 TOTPCFAT 30 -0.083 WAISTG 19 TOTPCFAT 30 0.769 WEIGHT 4 BMI 5 0.754 HIPG 0.863 SUBTRI 16 20 0.758 0.301 ILIACSF 10 ABDSF 11 0.721 SUM4SF 17 0.690 ADJUSTED R-SQUARED 0.751324 0.745259 26.38 SUM4SF 0.744395 0.738161 28.20 BMI 0.591202 0.581232 68.47 WAISTG 0.574301 0.563918 72.92 HIPG 0.569190 0.558682 74.26 WEIGHT 0.555044 0.544191 77.98 SUBSCPSF 0.519526 0.507807 87.32 ILIACSF 0.510147 0.498199 89.78 MIDAXSF 0.476218 0.463443 98.70 ABDSF 0.090573 0.068392 200.09 SUBTRI 0.714 TOTPCFAT 30 0.867 1.000 SUBSETS WITH R-SQUARED MIDAXSF 8 CP 142 1 VARIABLES SUBSCPSF 7 0.745 SUBSETS WITH R-SQUARED ADJUSTED R-SQUARED 0.843104 0.835259 4.25 BMI 0.811053 0.801606 12.67 BMI SUM4SF 0.805450 0.795723 14.15 BMI ILIACSF 0.791234 0.780796 17.88 BMI ABDSF 0.768728 0.757165 23.80 SUBTRI SUM4SF 0.767009 0.755359 24.25 SUBSCPSF SUM4SF 0.766944 0.755291 24.27 HEIGHT SUM4SF 0.763897 0.752092 25.07 HIPG SUM4SF 0.761465 0.749538 25.71 MIDAXSF SUM4SF 0.761204 0.749265 25.78 WEIGHT SUM4SF 2 VARIABLES CP MIDAXSF SUBSETS WITH R-SQUARED ADJUSTED R-SQUARED CP 0.860686 0.849969 1.63 VARIABLE 5 BMI 8 MIDAXSF 16 SUBTRI INTERCEPT 0.852639 0.841304 3.74 BMI 0.849348 0.837759 0.847717 3 VARIABLES COEFFICIENT 0.931890 0.299125 -3.92679 7.13194 MIDAXSF WAISTG 4.61 HEIGHT WEIGHT MIDAXSF 0.836002 5.04 ABDSF MIDAXSF 0.847646 0.835926 5.05 BMI MIDAXSF SUBSCPSF 0.847360 0.835618 5.13 HEIGHT BMI MIDAXSF 0.847280 0.835533 5.15 BMI ILIACSF MIDAXSF 0.846887 0.835109 5.25 BMI MIDAXSF SUM4SF 0.846557 0.834753 5.34 WEIGHT BMI MIDAXSF 0.844753 0.832811 5.81 BMI MIDAXSF HIPG BMI SUBSETS WITH R-SQUARED ADJUSTED R-SQUARED CP 0.867866 0.853957 1.'74 0.867853 0.853943 1.74 VARIABLE 5 BMI '-• '8 MIDAXSF 7 SUBSCPSF 17 SUM4SF ' INTERCEPT VARIABLE T-STATISTIC 9.91 5.65 -2.22 4 VARIABLES COEFFICIENT 0.793308 0.205923 -0.236875 0.0953064 6.61611 -STATISTIC 5.18 2.99 -2.46 2.41 COEFFICIENT T-STATISTIC 143 5 8 16 17 0.867183 0.853202 1.92 0.865320 0.851143 0.864025 BMI MIDAXSF SUBTRI SUM4SF INTERCEPT BMI 0.758689 0.234806 -4.34828 0.0430038 9.74766 4.98 3 .41 -2.46 1.44 ABDSF MIDAXSF SUBTRI 2.41 BMI ILIACSF MIDAXSF SUBTRI 0.849712 2.75 HEIGHT BMI MIDAXSF SUBTRI 0.863819 0.849484 2.80 WEIGHT BMI MIDAXSF SUBTRI 0.863306 0.848917 2.94 BMI MIDAXSF SUBSCPSF SUBTRI 0.862904 0.848472 3.04 HEIGHT WEIGHT MIDAXSF SUBTRI 0.862277 0.847780 3.21 BMI MIDAXSF WAISTG SUBTRI 0.861045 0.846418 3.53 MIDAXSF HIPG SUBTRI BMI (c) E q u a t i o n development for T F M BMDP9R - ALL POSSIBLE SUBSETS REGRESSION /INPUT T I T L E IS 'REGRESSION FOR BODY FILE='A:\BDYCMP2.DAT'. VARIABLES = 3 1 . CASES=44. FORMAT='3.1F8.2' . COMPOSITION'. /VARIABLE NAMES ARE GROUP, AGE, HEIGHT, WEIGHT, BMI, TRISF, SUBSCPSF, MIDAXSF, BICEPSF, ILIACSF, ABDSF, THIGHSF, CALFSF, SUMSFU, SUMSFL, SUBTRI, SUM4SF, LOGSUM4, WAISTG, HIPG WHR, THIGHG, TRUNKFAT, PCTRUNK, STFAT, TOTFAT, STLEAN, TOTLEAN, STPCFAT, TOTPCFAT, TOTWT. USE= TRUNKFAT, BMI, SUBTRI, WAISTG. /REGRESS MIDAXSF, DEPENDENT= TRUNKFAT. INDEPENDENT = MIDAXSF, SUBTRI, WAISTG. SUBSCPSF, ABDSF, ILIACSF, HEIGHT, WEIGHT, SUBSCPSF, ABDSF, ILIACSF, HEIGHT, WEIGHT, BMI, /END. NUMBER OF CASES READ CASES WITH DATA MISSING OR BEYOND LIMITS . . REMAINING NUMBER OF CASES 44 1 43 SUMMARY STATISTICS FOR EACH VARIABLE VARIABLE 23 TRUNKFAT MEAN 11866.58840 STANDARD DEVIATION 4084.30318 COEFFICIENT OF VARIATION 0.344185 144 SMALLEST VALUE 4009.00000 LARGEST VALUE 22012.0000 CORRELATIONS MIDAXSF 8 TRUNKFAT 23 0.677 SUBTRI 16 TRUNKFAT R-SQUARED 23 0.468 SUBSCPSF 7 0.814 WAISTG 19 0.922 ABDSF 11 0.656 ILIACSF 10 0.707 HEIGHT 3 WEIGHT 4 0.150 0.889 TRUNKFAT 23 1.000 SUBSETS WITH 1 VARIABLES SUBSETS WITH 2 VARIABLES ADJUSTED R-SQUARED 0.849552 0.845882. 0.790695 0.785590 49.19 0.782746 0.777447 52.54 BMI 0.662285 0.654048 103.29 SUBSCPSF 0.499487 0.487279 171.88 ILIACSF 0.458117 0.444901 189.31 MIDAXSF 0.430259 0.416363 201.05 ABDSF 0.219307 0.200266 289.93 SUBTRI 0.022363 -0.001482 372.91 HEIGHT .24.39 WAISTG WEIGHT R-SQUARED ADJUSTED R-SQUARED 0.878617 0.872548 14 .14 WEIGHT 0.877753 0.871641 14.51 0.874179 0.867888 16 .01 BMI 0.873047 0.866699 16.49 MIDAXSF WAISTG 0.861994 0.855094 21.15 ABDSF WAISTG 0.855503 0.848279 23 .88 SUBTRI 0.853911 0.846606 24.55 SUBSCPSF WAISTG 0.850315 0.842831 26.07 SUBSCPSF WEIGHT 0.850134 0.842641 26.14 ILIACSF WEIGHT 0.849813 0.842304 26.28 MIDAXSF WEIGHT CP ILIACSF WAISTG WAISTG WAISTG WAISTG SUBSETS WITH 145 3 VARIABLES BMI 5 0.885 R-SQUARED ADJUSTED R-SQUARED 0.903556 0.896138 5.63 ILIACSF WEIGHT WAISTG 0.901751 0.894194 6.40,,MIDAXSF WEIGHT WAISTG 0.899309 0.891563 ' 7.42 MIDAXSF BMI WAISTG 0.895142 0.887076 9.18 ILIACSF BMI WAISTG 0.887882 0.879258 12 .24 HEIGHT "WEIGHT WAISTG 0.887876 0.879251 12 .24 MIDAXSF HEIGHT WEIGHT 0.886631 0.877910 12.77 ABDSF WEIGHT WAISTG 0.886609 0.877887 12.78 WEIGHT BMI WAISTG 0.886593 0.877870 12.78 MIDAXSF WEIGHT BMI 0.884749 0.875883 13.56 BMI WAISTG CP HEIGHT SUBSETS WITH 4 VARIABLES R-SQUARED ADJUSTED R-SQUARED CP 0.912721 0.903534 3.77 VARIABLE 8 MIDAXSF 3 HEIGHT 4 WEIGHT 19 WAISTG INTERCEPT COEFFICIENT 112.034 -81.4047 184.823 136.490 -2071.93 T-STATISTIC 3 .29 -2.19 4.15 3 .29 0.910894 0.901515 4.54 VARIABLE 8 MIDAXSF 4 WEIGHT 5 BMI 19 WAISTG INTERCEPT COEFFICIENT 110.701 92.8691 228.082 137.129 -14917.5 T-STATISTIC 3.22 2.22 1.97 3 .22 0.909271 0.899721 5.23 ILIACSF HEIGHT WEIGHT WAISTG 0.909000 0.899421 5.34 MIDAXSF ILIACSF WEIGHT WAISTG 0.908682 0.899070 5.47 MIDAXSF HEIGHT BMI WAISTG 0.908009 0.898325 5.76 ILIACSF WEIGHT BMI WAISTG 0.905787 0.895869 6.70 ILIACSF HEIGHT BMI WAISTG 0.904524 0.894474 7.23 ILIACSF WEIGHT SUBTRI WAISTG 0.904112 0.894019 7.40 ABDSF ILIACSF WEIGHT WAISTG 0.903561 0.893409 7.63 SUBSCPSF ILIACSF WEIGHT WAISTG STATISTICS FOR 'BEST' SUBSET MALLOWS' CP SQUARED MULTIPLE CORRELATION MULTIPLE CORRELATION ADJUSTED SQUARED MULT. CORR. 3.77 0.91272 0.9553 6 0.903 53 146 RESIDUAL MEAN SQUARE 1609196.603463 STANDARD ERROR OF EST. 1268.541132 F-STATISTIC 99.35 NUMERATOR DEGREES OF FREEDOM 4 DENOMINATOR DEGREES OF FREEDOM 38 SIGNIFICANCE (TAIL PROB.) 0.0000 VARIABLE NO. NAME 8 3 4 19 REGRESSION COEFFICIENT STANDARD ERROR -2071.93 112.034 -81.4047 184.823 136.490 6001.15 34.0674 37.2480 44.5079 41.4993 INTERCEPT MIDAXSF HEIGHT WEIGHT WAISTG STAND. COEF. -0 0 -0 0 0 507 198 128 497 386 TSTAT. 2 TAIL SIG. -0 3 -2 4 3 0.732 0.002 0.035 0.000 0.002 35 29 19 15 29 CONTRITOL- BUTION ERANCE TO R-SQ 0.636279 0.669514 0.160337 0.166370 0.02484 0.01097 0.03961 0.02485 (d) Equation development for % T F BMDP9R - ALL POSSIBLE SUBSETS REGRESSION /INPUT T I T L E IS REGRESSION FOR BODY COMPOSITION'. FILE='A:\BDYCMP2.DAT'. VARIABLES = 31. CASES = 4 4 . FORMAT= '31F8.2*. 1 /VARIABLE NAMES ARE SUBJECT, AGE, HEIGHT, WEIGHT, BMI, TRISF, SUBSCPSF, MIDAXSF, BICEPSF, ILIACSF, ABDSF, THIGHSF, CALFSF, SUMSFU, SUMSFL, SUBTRI, SUM4SF, LOGSUM4, WAISTG, HIPG, WHR, THIGHG, TRUNKFAT, PCTRUNK, STFAT, TOTFAT, STLEAN, TOTLEAN, STPCFAT, TOTPCFAT, TOTWT. USE= PCTRUNK, HEIGHT, WEIGHT, BMI, ILIACSF, ABDSF, MIDAXSF, SUBSCPSF, WAISTG. /REGRESS DEPENDENT = PCTRUNK. INDEPENDENT = HEIGHT, WEIGHT, BMI, ILIACSF, ABDSF, MIDAXSF, SUBSCPSF, WAISTG. METHOD=RSQ. NUMBER=1. MAXVAR=4. /END. NUMBER OF CASES READ CASES WITH DATA MISSING OR BEYOND LIMITS . . REMAINING NUMBER OF CASES '. 44 1 43 SUMMARY STATISTICS FOR EACH VARIABLE STANDARD COEFFICIENT 147 SMALLEST LARGEST VARIABLE MEAN 24 PCTRUNK DEVIATION 34.78140 OF VARIATION 6.70022 VALUE 0.192638 VALUE 18.80000 45.70000 CORRELATIONS HEIGHT WEIGHT 3 PCTRUNK 24 -0.076 WAISTG 19 PCTRUNK 24 0.832 BMI 4 0.703 5 ILIACSF 10 0.806 ABDSF MIDAXSF 8 11 0.754 0.692 SUBSCPSF 7 0.757 0.793 PCTRUNK 24 1.000 SUBSETS WITH R-SQUARED ADJUSTED R-SQUARED 0.693008 0.685521 36.93 -.VARIABLE:' ,19 WAISTG INTERCEPT 0.649656 0.641111 47.66 BMI '. 0.628911 0.619860 '52.79 SUBSCPSF 0.573753 0.563356 66.43 MIDAXSF 0.569096 0.558586 67.58 ILIACSF 0.493573 0.481221 86.26 WEIGHT 0.478375 0.465653 90.02 ABDSF 0.005829 -0.018419 1 VARIABLES CP. • „>••., ' v^- ••>. COEFFICIENT 0.482344 -7.38783 T-STATISTIC 9.62 206.90 HEIGHT SUBSETS WITH R-SQUARED ADJUSTED R-SQUARED CP 0.808713 0.799148 10.31 0.796297 0.786112 13.39 MIDAXSF WAISTG 0.783175 0.772334 16.63 ILIACSF WAISTG 0.760479 0.748503 22.24 BMI ILIACSF 0.744417 0.731638 26.22 ABDSF WAISTG 0.732768 0.719407 29.10 HEIGHT WAISTG 0.729205 0.715665 29.98 MIDAXSF SUBSCPSF 0.721231 0.707293 31.95 SUBSCPSF WAISTG VARIABLE 5 BMI 8 MIDAXSF INTERCEPT 2 VARIABLES COEFFICIENT 0.942066 0.433055 -0.296173 148 T-STATISTIC 7.01 5.77 0.717691 0.703576 32.83 BMI ABDSF 0.717429 0.703300 32.89 BMI WAISTG SUBSETS WITH 3 VARIABLES R-SQUARED ADJUSTED R-SQUARED CP 0.842733 0.830635 .90 0.824160 0.810634 8 .49 BMI MIDAXSF WAISTG 0.820099 0.806261'^ . • '9' :50 BMI ILIACSF MIDAXSF 0.815597 0.801412'., MIDAXSF WAISTG 0.815497 0.801304 .... 10 .64 HEIGHT BMI MIDAXSF 0.815144 0.800924 10 .72 HEIGHT WEIGHT MIDAXSF 0.815080 0.800855 10 .74 WEIGHT • BMI MIDAXSF 0.814341 0.800060 10 92 HEIGHT ILIACSF WAISTG 0.813634 0.799298 11 10 BMI ABDSF MIDAXSF 0.813038 0.798657 11 24 BMI MIDAXSF SUBSCPSF VARIABLE 3 HEIGHT 8 MIDAXSF 19 WAISTG INTERCEPT 10 .61 ILIACSF COEFFICIENT -0.227498 0.386580 0.355864 30.6591 SUBSETS WITH T-STATISTIC -3.39 5.22 7.70 4 VARIABLES R-SQUARED ADJUSTED R-SQUARED CP 0.855181 0.839937 2.82 0.850447 0.834704 3.99 HEIGHT ABDSF MIDAXSF WAISTG 0.848821 0.832908 4.3 9 HEIGHT WEIGHT MIDAXSF WAISTG 0.848122 0.832135 4.57 HEIGHT BMI MIDAXSF WAISTG 0.846067 0.829864 5.07 WEIGHT BMI MIDAXSF WAISTG STATISTICS FOR VARIABLE 3 HEIGHT 10 ILIACSF 8 MIDAXSF 19 WAISTG INTERCEPT COEFFICIENT -0.211881 0.177608 0.291657 0.325986 29.5499 'BEST' SUBSET MALLOWS' CP 2.82 SQUARED MULTIPLE CORRELATION 0.85518 MULTIPLE CORRELATION 0.92476 ADJUSTED SQUARED MULT. CORR. 0.83994 RESIDUAL MEAN SQUARE 7.185717 STANDARD ERROR OF EST. 2.680619 F-STATISTIC 56.10 NUMERATOR DEGREES OF FREEDOM 4 DENOMINATOR DEGREES OF FREEDOM 38 SIGNIFICANCE (TAIL PROB.) 0.0000 149 T-STATISTIC -3.22 1.81 3.27 6.81 VARIABLE NO. NAME 3 10 8 19 INTERCEPT HEIGHT ILIACSF MIDAXSF WAISTG REGRESSION COEFFICIENT STANDARD -ERROR 29.5499 ; -0.211881 0.177608 0.291657 0.325986 10.4076 . 0" 0657440 0 0982729 0. 0890948 o".0478898 STAND. COEF. TSTAT. 2 TAIL SIG. 4 -0 0 0 0 2 -3 1 3 6 0 0 0 0 0 410 203 177 314 563 84 22 81 27 81 007 003 079 002 000 CONTRITOLBUTION ERANCE TO R-SQ 0 0 0 0 959651 395619 0.01245 415416 0.04084 557870 0.17659 (e) Equation development for F M using S F ' s only BMDP9R - ALL POSSIBLE SUBSETS REGRESSION /INPUT T I T L E IS 'REGRESSION FOR BODY COMPOSITION'. FILE='A:\BDYCMP2.DAT'. VARIABLES = 31. CASES=44. FORMAT='31F8.2'. /VARIABLE NAMES ARE GROUP, AGE, HEIGHT, WEIGHT, BMI, TRISF, SUBSCPSF, MIDAXSF, BICEPSF, ILIACSF, ABDSF, THIGHSF, CALFSF, SUMSFU, SUMSFL, SUBTRI, SUM4SF, LOGSUM4, WAISTG, HIPG, WHR, THIGHG, TRUNKFAT, PCTRUNK, STFAT, TOTFAT, STLEAN, TOTLEAN, STPCFAT, TOTPCFAT, TOTWT. USE= TOTFAT, MIDAXSF, SUBSCPSF, ILIACSF, ABDSF, SUM4SF, TRISF, BICEPSF, THIGHSF, CALFSF. /REGRESS DEPENDENT= TOTFAT. INDEPENDENT = MIDAXSF, SUBSCPSF, ILIACSF, ABDSF, BICEPSF, THIGHSF, CALFSF. /END. NUMBER OF CASES READ CASES WITH DATA MISSING OR BEYOND LIMITS . . REMAINING NUMBER OF CASES SUM4SF, TRISF, 44 1 43 SUMMARY STATISTICS FOR EACH VARIABLE VARIABLE 8 7 10 11 17 6 9 12 13 26 MIDAXSF SUBSCPSF ILIACSF ABDSF SUM4SF TRISF BICEPSF THIGHSF CALFSF TOTFAT STANDARD DEVIATION MEAN 23 21 19 32 88 27 19 36 26 23785 20000 38023 45349 10233 37791 58605 95814 52791 05000 85813 7 8 6 8 26 7 7 9 8 7033 20305 19030 69173 54925 70828 41837 06035 16677 19786 81977 COEFFICIENT OF VARIATION 0 0 0 0 0 0 0 0 0 0 310476 383078 343986 266313 302205 268917 353758 250953 314697 295714 150 SMALLEST VALUE 6 4 3 5 23 11 4 14 11 11076 10000 60000 50000 40000 50000 00000 40000 80000 30000 50000 LARGEST VALUE 38 36 35 48 139 45 34 53 41 42201 60000 30000 30000 60000 50000 20000 60000 00000 20000 50000 CORRELATIONS MIDAXSF 8 MIDAXSF SUBSCPSF ILIACSF ABDSF SUM4SF TRISF BICEPSF THIGHSF CALFSF TOTFAT 8 7 10 11 17 6 9 12 13 26 1 0 0 0 0 0 0 0 0 0 000 653 739 653 747 652 682 305 509 624 THIGHSF 12 THIGHSF CALFSF TOTFAT *** ERROR 12 13 26 1.000 0.588 0.537 SUBSCPSF ILIACSF 7 10 1 0 0 0 0 0 0 0 0 000 718 685 917 788 800 460 450 776 CALFSF 13 1.000 0.631 1 0 0 0 0 0 0 0 000 802 867 748 712 451 466 650 ABDSF 1 0 0 0 0 0 0 11 SUM4SF 17 000 790 698 700 448 564 645 1 0 0 0 0 0 TRISF 000 929 921 574 540 875 1 0 0 0 0 6 BICEPSF 9 000 840 635 512 834 1 0 0 0 000 543 542 916 TOTFAT 26 1.000 *** COVARIANCE MATRIX OF INDEPENDENT VARIABLES IS SINGULAR. COMPUTATIONS CANNOT PROCEED BECAUSE THE FOLLOWING VARIABLES ARE (UP TO TOLERANCE) LINEAR COMBINATIONS OF THE OTHER VARIABLES. THESE, OR OTHER VARIABLES, NEED TO BE ELIMINATED BEFORE RERUNNING THIS PROGRAM UNLESS YOU SPECIFY METHOD=NONE IN THE REGRESSION PARAGRAPH. VARIABLE NO. NAME 10 ILIACSF BMDP9R - ALL POSSIBLE SUBSETS REGRESSION /INPUT T I T L E IS 'REGRESSION FOR BODY COMPOSITION'. FILE='A:\BDYCMP2.DAT'. VARIABLES = 31. CASES = 44 . FORMAT='31F8.2' . /VARIABLE NAMES ARE GROUP, AGE, HEIGHT, WEIGHT, BMI, TRISF, SUBSCPSF, MIDAXSF, BICEPSF, ILIACSF, ABDSF, THIGHSF, CALFSF, SUMSFU, SUMSFL, SUBTRI, SUM4SF, LOGSUM4, WAISTG, HIPG, WHR, THIGHG, TRUNKFAT, PCTRUNK, STFAT, TOTFAT, STLEAN, TOTLEAN, STPCFAT, TOTPCFAT, TOTWT. USE= TOTFAT, MIDAXSF., SUBSCPSF, ABDSF, SUM4SF, TRISF, BICEPSF, THIGHSF, CALFSF. /REGRESS DEPENDENT= TOTFAT. INDEPENDENT = MIDAXSF, SUBSCPSF, ABDSF, SUM4SF, TRISF, BICEPSF, THIGHSF, CALFSF. /END. NUMBER OF CASES READ 44 151 CASES WITH DATA MISSING OR BEYOND LIMITS . . REMAINING NUMBER OF CASES . . . . . . . . 1 43 SUMMARY STATISTICS FOR EACH VARIABLE VARIABLE 8 7 11 17 6 9 12 13 26 STANDARD DEVIATION MEAN MIDAXSF SUBSCPSF ABDSF. SUM4SF TRISF BICEPSF THIGHSF CALFSF TOTFAT 23 21 32 88 27 19 36 26 23785 20000 38023 10233 37791 58605 95814 52791 05000 85813 7 8 8 26 7 7 9 8 7033 COEFFICIENT OF VARIATION SMALLEST VALUE 0 0 0 0 0 0 0 0 0 6 4 5 23 11 4 14 11 11076 20305 19030 54925 70828 41837 06035 16677 19786 81977 310476 383078 266313 302205 268917 353758 250953 314697 295714 LARGEST VALUE 10000 60000 40000 50000 00000 40000 80000 30000 50000 38 36 48 139 45 34 53 41 42201 60000 30000 60000 50000 20000 60000 00000 20000 50000 CORRELATIONS MIDAXSF 8 MIDAXSF SUBSCPSF ABDSF SUM4SF TRISF BICEPSF THIGHSF CALFSF TOTFAT 8 7 11 17 6 9 12 13 26 1 0 0 0 0 0 0 0 0 000 . 653 653 747 652 682 305 509 624 CALFSF 13 CALFSF TOTFAT 13 26 SUBSCPSF A B D S F S U M 4 S F 7 11' 17 1.000 0.631 1 1 0 0 0 0 0 0 0 000 685 917 788 ' 800 460 450 776 1 0 0 0 0 0 0 000 790 698 700 448 564 645 1 0 0 0 0 0 TRISF BICEPSF 9 6 000 929 921 574 540 875 1 0 0 0 0 000'" 840 635 512 834 1 0 0 0 THIGHSF 12 000 543 542 916 TOTFAT 26 1.000 R-SQUARED ADJUSTED R-SQUARED 0.838579 0.834642 12.11 BICEPSF 0.764781 0.759044 35.48 SUM4SF 0.696306 0.688899 57.16 TRISF 0.601565 0.591847 87.16 SUBSCPSF 0.415886 0.401639 145.95 ABDSF 0.397992 0.383309 151.62 CALFSF 0.389721 0.374836 154.23 MIDAXSF 0.288299 0.270940 186.35 THIGHSF SUBSETS WITH 1 VARIABLES SUBSETS WITH 2 VARIABLES CP 152 1 000 0 588 0 537 R-SQUARED ADJUSTED R-SQUARED 0.864083 0.857287 6.04 BICEPSF CALFSF 0.852984 0.845633 9.55 TRISF BICEPSF 0.844835 0.837077 12.13 0.843644 0.835826 12.51 SUBSCPSF BICEPSF 0.840826 0.832868 13.40 BICEPSF THIGHSF 0.838607 0.830538 14.10 ABDSF BICEPSF 0.838580 0.830509 14.11 MIDAXSF BICEPSF 0.800234 0.790246 " 26.25 SUM4SF CALFSF 0.770366 0.758884 35.71 ABDSF SUM4SF 0.769173 0.757632 36.09 SUBSCPSF SUM4SF CP SUM4SF BICEPSF SUBSETS WITH R-SQUARED ADJUSTED R-SQUARED CP 0.874285 0.864615 4.81 0.868471 0.858354 6.65 SUBSCPSF BICEPSF CALFSF 0.867657 0.857477 6.90 SUM4SF BICEPSF CALFSF 0.866193 0.855900 7.37 ABDSF BICEPSF CALFSF 0.865513 0.855167 7.58 MIDAXSF BICEPSF CALFSF 0.864527 0.854106 7.90 BICEPSF THIGHSF CALFSF 0.853908 0.842670 11.26 0.853881 0.842641 11.27 ABDSF TRISF BICEPSF 0.853608 0.842347 11.35 MIDAXSF TRISF BICEPSF 0.853165 0.841870 11.49 SUM4SF TRISF BICEPSF VARIABLE 6 TRISF 9 BICEPSF 13 CALFSF INTERCEPT 3 VARIABLES COEFFICIENT 177.953 660.606 150.217 1779.24 SUBSCPSF TRISF T-STATISTIC 1.78 6.15 2.57 BICEPSF SUBSETS WITH 4 VARIABLES R-SQUARED ADJUSTED R-SQUARED CP 0.879872 0.867226 5.04 VARIABLE 11 ABDSF 6 TRISF 9 BICEPSF 13 CALFSF INTERCEPT COEFFICIENT -93.7022 213.383 694.333 173.133 2539.80 T-STATISTIC -1.33 2.08 6.35 2 .87 0.878405 0.865605 5.50 VARIABLE 6 TRISF 9 BICEPSF 12 THIGHSF 13 CALFSF COEFFICIENT 224.316 650.480 -69.7242 179.341 T-STATISTIC 2.08 6.06 -1.13 2.82 153 INTERCEPT 2490.55 0.877466 0.864567 5.80 MIDAXSF TRISF BICEPSF CALFSF 0.875600 0.862505 6.39 ABDSF SUM4SF BICEPSF CALFSF 0.875340 0.862218 6.47 SUBSCPSF TRISF BICEPSF CALFSF 0.874709 0.861520 6.67 SUM4SF BICEPSF CALFSF 0.873179 0.859830 7.16 SUBSCPSF ABDSF BICEPSF CALFSF 0.872203 0.858751 7.46 MIDAXSF SUM4SF BICEPSF CALFSF 0.871551 0.858030 7.67 MIDAXSF SUBSCPSF BICEPSF CALFSF 0.869039 0.855254 8.47 SUBSCPSF BICEPSF TRISF THIGHSF SUBSETS WITH CALFSF 5 VARIABLES R-SQUARED ADJUSTED R-SQUARED CP 0.885418 0.869934 5.28 VARIABLE 11 ABDSF 6 TRISF 9 BICEPSF 12 THIGHSF 13 CALFSF INTERCEPT COEFFICIENT -105.875 272.235 686.867 -81.5849 210.189 3470.91 T-STATISTIC -1.50 2.46 6.34 -1.34 3.19 0.885025 0.869488 5.40 VARIABLE 8 MIDAXSF 6 TRISF 9 BICEPSF 12 THIGHSF 13 CALFSF INTERCEPT COEFFICIENT -119.684 271.249 693.861 -99.7542 210.579 3389.92 T-STATISTIC -1.46 45 31 -1.56 3.18 STATISTICS FOR 1 BEST 1 SUBSET MALLOWS' CP 4.81 SQUARED MULTIPLE CORRELATION 0.87429 MULTIPLE CORRELATION 0.93503 ADJUSTED SQUARED MULT. CORR. 0.86461 RESIDUAL MEAN SQUARE 6698123.276117 STANDARD ERROR OF EST. 2588.073275 F-STATISTIC 90.41 NUMERATOR DEGREES OF FREEDOM 3 DENOMINATOR DEGREES OF FREEDOM 39 SIGNIFICANCE (TAIL PROB.) 0.0000 VARIABLE NO. NAME INTERCEPT 6 TRISF 9 BICEPSF 13 CALFSF REGRESSION COEFFICIENT STANDARD ERROR 1779.24 177.953 660.606 150.217 1688.23 100.027 107.447 58.4348 STAND. COEF. 0 0 0 0 TSTAT. 253 188 663 175 154 1 1 6 2 05 78 15 57 2TAIL SIG. 0 0 0 0 CONTRITOLBUTION ERANCE TO R-SQ 298 083 0 289635 0 000 0 277114 0 014 0 694960 0 Appendix XIII: Regression Outputs for Final Prediction Equations (a) E Q N 1 - F M Variables Entered/Removed b Model 1 Variables Entered Variables Removed MA, HT, W T Method Enter a a. All requested variables entered. b. Dependent Variable: total fat mass in kg Model Summary Model 1 R .978 a R Square .956 Std. Error of I the Estimate Adjusted R Square .953 1.5326 I a. Predictors: (Constant), MA, HT, W T ANOVA b Model 1 Regression Residual Total Sum of Squares 1986.324 df 91.610 2077.934 3 39 42 Mean Square 662.108 2.349 F 281.870 Sig. .000 a. Predictors: (Constant), MA, HT, WT b. Dependent Variable: total fat mass in kg j Coefficients 3 . Uristandardized Coefficients Model 1 (Constant) HT WT MA •B . 16.462 Std. Error 5.934 Standardiz ed Coefficient s Beta t 2.774 Sig. .008 .000 -.231 .040 -.211 -5.735 .611 .028 .953 22.156 .143 .039 .146 a. Dependent Variable: total fat mass in kg (b) EQN2-%Fat 155 3.674 .000 .001 a Variables Entered/Removed 13 Model 1 Variables Removed Variables Entered MA, HT, W T Method Enter 3 a. All requested variables entered. b. Dependent Variable: P C F A T Model Summary R Model 1 .922 a R Square .849 Std. Error of the Estimate 2.1233 Adjusted R Square .838 a. Predictors: (Constant), MA, HT, WT ANOVA b Model 1 Regression Residual Total Sum of Squares 991.283 175.827 1167.111 df 3 Mean Square 330.428 F 73.292 Sig. .000 4.508 39 42 a. Predictors: (Constant), MA, HT, WT b. Dependent Variable: P C F A T Coefficients 3 Model 1 (Constant) HT WT MA Unstandardized Coefficients Std. Error B 60.122 8.220 .341 .038 .054 -.339 .285 .056 Standardiz ed Coefficient s Beta -.413 .711 .390 a. Dependent Variable: P C F A T (c) E Q N 3 - T F M 156 t 7.314 -6.070 8.942 5.294 Sig. .000 .000 .000 .000 a Variables Entered/Removed Model Variables Entered WC, HT MA. WT Variables Removed Method Enter a 1 13 a. All requested variables entered. b. Dependent Variable: trunk fat mass in kg Model Summary Std. Error of the Estimate 1.2685 Adjusted R Model R R Square Square 1 .955 .913 .904 a. Predictors: (Constant), WC, HT, MA, WT a ANOVA Model 1 Regression Residual Total Sum of Squares 639.475 61.149 700.624 df b 4 38 42 Mean Square 159.869 1.609 F 99.347 Sig. .000 a. Predictors: (Constant), WC, HT, MA, WT b. Dependent Variable: trunk fat mass in kg Coefficients Model 1 (Constant) HT WT MA WC Unstandardized Coefficients B Std. Error -2.072 6.001 -8.140E-02 .037 .185 .045 .034 .112 .136 .041 3 Standardiz ed Coefficient s Beta -.128 .497 .198 .386 a. Dependent Variable: trunk fat mass in kg (d) EQN4-%TF 157 t -.345 -2.185 4.153 3.289 3.289 Sig. .732 .035 .000 .002 .002 a Variables Entered/Removed , 13 Model 1 Variables Entered Variables Removed WC, HT, M A Method Enter a a. All requested variables entered. b. Dependent Variable: PCTRUNK Model Summary Model 1 R .918 a R Square .843 Adjusted R Square .831 . Std. Error of the Estimate 2.7574 a. Predictors: (Constant), WC, HT, MA ANOVA Model 1 Regression Residual Total Sum of Squares 1588.977 296.528 1885.505 df b 3 39 42 Mean Square 529.659 7.603 F 69.662 Sig. .000 a. Predictors: (Constant), WC, HT, MA b. Dependent Variable: P C T R U N K Coefficients' Model 1 (Constant) HT MA WC Unstandardized Coefficients Std. Error B 30.659 10.687 -.227 .067 .387 .074 .046 .356 Standardiz ed Coefficient s Beta -.218 .416 .614 a. Dependent Variable: P C T R U N K 158 t 2.869 -3.393 5.222 7.697 Sig. .007 .002 .000 .000 a Appendix XIV: Descriptive Summaries for Independent Databases Baumgartner Data for Elderly Women (n=100) ( B A U M ) Mean SD AGE WT HT BMI TRI 74.47 5.59 64.84 12.63 155.92 6.81 26.66 5.03 22.62 8.35 SS WAIST 20.68 9.60 91.87 11.66 HIP THIGH TOTFAT(g) %FAT 104.05 11.41 47.83 5.61 Brodowicz Data for Elderly W o m e n (n=31) ( B R O D i ) Mean SD AGE HT WT TRI BIC SI 71.13 1.61 65.08 20.76 10.73 19.82 19.50 39.13 25813.87 4.62 0.06 10.13 5.25 3.89 7.29 7.00 5.64 7005.63 SS %FAt TOTFAT(g) Brodowicz Data for Younger Women (n=33) (BROD2) Mean SD Age HT 33.39 4.72 1.66 0.07 TRI BIC SI SS %Fat TOTFAT(g) 63.48 19.61 9.35; .8.84 7.80 15.73 15.18 29.56 19276.67 4.83 7.80 8.65 8.95 8145.80 WT 159 26429.19 9294.52 39.57 7.47 Appendix X V : Stepwise Multiple Regression for Modified %Fat Eqn (a) using variables from Brodowicz study Variables Entered/Removed 3 Model 1 Variables Entered Variables Removed Method SUM4SF Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). BMI Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). SS Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). 2 3 a. Dependent Variable: PCFAT Model Summary Model 1 2 3 R .867 .901 .915° a b R Square .751 .811 .837 Adjusted R Square .745 .802 .824 Std. Error of the Estimate 2.6606 2.3474 2.2103 a. Predictors: (Constant), SUM4SF b. Predictors: (Constant), SUM4SF, BMI c. Predictors: (Constant), SUM4SF, BMI, SS 160 ANOVA d Model 1 2 3 Regression Residual Total Regression Residual Total Regression Residual Total Sum of Squares 876.879 290.232 1167.111 946.696 " ^220.415 .1167.111 976.575 .190.535 1167.111 Mean Square 876.879 7.079 , df 1 41 42 2 40 42 3 39 42 F 123.873 Sig. .000 473.348 5.510 85.901 .000 325.525 4.886 66.631 .000° a. Predictors: (Constant), SUM4SF b. Predictors: (Constant), SUM4SF, BMI c. Predictors: (Constant), SUM4SF, BMI, S S d. Dependent Variable: P C F A T Coefficients Model 1 2 3 (Constant) SUM4SF (Constant) SUM4SF BMI (Constant) SUM4SF BMI SS Unstandardized Coefficients B Std. Error 20.711 1.418 .171 .015 11.548 2.862 9.503E-02 .025 .598 .168 9.819 2.784 .162 .036 .652 .160 -.261 .105 3 Standardiz ed Coefficient s Beta .867 .481 .456 .818 .497 -.405 a. Dependent Variable: PCFAT 161 t 14.608 11.130 4.035 3.755 3.560 3.527 4.496 4.082 -2.473 Sig. .000 .000 .000 .001 .001 .001 .000 .000 .018 a b Excluded Variables' 1 Model 1 2 3 HT WT BMI TRI SS BIC SI subscap/triceps sf ratio HT WT TRI SS BIC SI subscap/triceps sf ratio HT WT TRI BIC SI subscap/triceps sf ratio Beta In -.125 .166 .456 .250 -.314 .336 -.122 -.153 -.066 -.136 .204 -.405 .145 ,133 -.147 -.089 -.193° .013° -.013 .000° .046° a a a a a a a a b b b b b b b c C t -1.637 1.286 3.560 1.194 -1.641 1.718 -.780 -1.764 -.929 -.934 1.101 -2.473 .767 .851 -1.937 -1.336 -1.410 .067 -.065 -.002 .309 a. Predictors in the Model: (Constant), SUM4SF b. Predictors in the Model: (Constant), SUM4SF, BMI c. Predictors in the Model: (Constant), SUM4SF, BMI, S S d. Dependent Variable: PCFAT (b) using variables from Baumgartner study 162 Sig. .109 .206 .001 .240 .109 .093 .440 .085 .359 .356 .278 .018 .447 .400 .060 .189 .167 .947 .948 .999 .759 Partial Correlation -.251 .199 .490 .185 -.251 .262 -.122 -.269 -.147 -.148 .174 -.368 .122 .135 -.296 -.212 -.223 .011 -.011 .000 .050 Collinearity Statistics Tolerance .998 .357 .287 .137 .159 .151 .249 .769 .931 .222 .136 .156 .135 .196 .769 .915 .217 .109 .117 .169 .191 Variables Entered/Removed Model 1 Variables Removed Variables Entered 3 Method BMI Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). TRI Stepwise (Criteria: Probabilityof-F-to-ent er <= .050, Probabilityof-F-to-rem ove >= .100). 2 a. Dependent Variable: P C F A T Model Summary Model 1 2 R .863 .898 a b R Square .745 .807 Std. Error of the Estimate 2.6965 2.3722 Adjusted R Square .738 .797 a. Predictors: (Constant), BMI b. Predictors: (Constant),'-BMI, TRI ANOVA Model 1 Regression Residual Total 2 Regression Residual Total Sum of Squares 868.996 df c 1 Mean Square 868.996 F 119.514 Sig. .000 83.696 .000 298.115 41 7.271 942.009 2 471.005 40 5.628 1167.111 225.102 1167.111 42 42 a. Predictors: (Constant), BMI b. Predictors: (Constant), BMI, TRI c. Dependent Variable: P C F A T 163 a b Coefficients Model 1 2 (Constant) BMI (Constant) BMI TRI 3 Standardiz ed Coefficient s Unstandardized Coefficients B Std. Error 5.800 1.130 2.778 .103 .696 .295 2.619 .151 .082 9.198 a. Dependent Variable: P C F A T ' ' '• Beta .863 t 2.088 10.932 .531 .415 4.608 3.602 2 HT WT TRI SS subscap/triceps sf ratio WC HC HT WT SS subscap/triceps sf ratio WC HC .001 .000 .001 - : Excluded Variables Model 1 3.511 Sig. .043 .000 Beta, In .001 .003 .415 .146 -.050 .048 t a a a a a a .168 -.027 -.075 -.031 .007 a b b b .016 .017 3.602 1.105 -.579 .286 1.249 -.386 -.518 -.241 .085 .150 .341 b .022 .043 0 b b a. Predictors in the Model: (Constant), BMI b. Predictors in the Model: (Constant), BMI, TRI c. Dependent Variable: P C F A T 164 .219 -.091 .045 .194 Collinearity Statistics Tolerance .991 .237 .363 .355 .844 .228 .341 .881 .735 -.039 .014 .024 .055 .228 .310 Sig. .987 .986 .001 .276 .566 .777 .701 .608 .811 .933 Partial Correlation .003 .003 .495 .172 -.062 -.083 .978 .232 .295 .807
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The relationship between anthropometry and body composition assessed by dual-energy x-ray absorptiometry… Hill, Andrea Dalton 2000
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Title | The relationship between anthropometry and body composition assessed by dual-energy x-ray absorptiometry in women 75-80 years old : are new skinfold equations needed? |
Creator |
Hill, Andrea Dalton |
Date Issued | 2000 |
Description | A link between age-related changes in body composition (BC) and the increased prevalence of disease and disability in old age has been well established (Chumlea & Baumgartner, 1989; Going et al., 1995; Shephard, 1997). Consequently, B C assessment is becoming increasingly important in the evaluation o f the health and functional status of the older adult. Individuals 75 years and older comprise one of the fastest growing segments of the population in North America (Canada, 1999; Donatelle & Davis, 1994), yet current B C measurement techniques may not be accurate or reliable in this older age group. The intent of this research was to develop new body fat prediction equations in elderly women based on anthropometry and the criterion method of dual energy X-ray absorptiometry (DEXA), which is considered to be more valid than conventional densitometry among the aging population (Baumgartner et al., 1995; Kohrt, 1998; Visser et al., 1998). Anthropometry, skinfold (SF) anthropometry, and DEXA (Hologic QDR-4500W) body fat data were initially collected in a sample of 43 women 75-80 years old (m = 77.4yrs) as part of a larger study investigating the effects of strength training on strength, function, bone mineral density (BMD), and BC. Eight BC prediction equations for the elderly were selected from the literature and applied to these data. The correlation, between prediction equations and DEXA ranged from 0.76-0.97. However, paired t-tests difference scores (δ) showed that all but one o f the equations overestimated DEXA body fat i n these older aged women (δ ranged from -3.3kg to 4.0kg and 4.4% to 9.0%; p<0.001 in all cases). New equations were derived for FM , %Fat, trunk fat mass (TFM) and percent trunk fat (%TF) using a coffiblnation of stepwise and all possible subsets regression procedures, as both total and regional' percent fat are important health indicators (Going et al., 1995). The following were entered as predictor variables: weight (WT), height (HT), BMI, hip circumference (HC), waist circumference (WC), SF's o f the subscapular (SS), suprailiac (SI), abdominal (ABD), and midaxillary (MA) sites, the SS to triceps skinfold ratio (SSTRI), and the sum o f triceps, biceps, SI and SS (SUM4SF); except H C and SUM4SF were not included in the trunk fat regressions. Ultimately, the measure of interest in body composition assessment is the value %Fat and thus supports using the %Fat equation over that for F M . Moreover, %Fat equation was associated with less error ( C.V.[sub Fat] = 5.9%; C.V.[sub FM] = 6.4%). The %TF equation, however, was less precise than the equation for total %Fat and therefore was not considered further in this research. Subsequent analysis showed the %Fat equation to be internally valid using the jackknife method for data splitting. Finally, %fat equations developed in this study sample were tested in two independent samples of elderly women (71.1yrs and 74.5 yrs) and one sample of younger women (33.4 yrs) shared by Baumgartner (1999) and Brodowicz (1999). Both independent studies used DEXA instruments manufactured by Lunar. New equations were derived for this application using only the variables measured in these independent studies as the predictor variables. The modified prediction equations were reasonably correlated (r = .73, .81) with %Fat from DEXA (Lunar) in the elderly women, yet paired t-tests results showed that the new equations significantly underestimated %fat by 6.6% ± 3.9 (p< 0.001)(BROD), and 5.1% ± 4.5 (p< 0.001)(BAUM). An unexpected finding was the accurate prediction of %Fat in the younger women (δ = -0.7% ± 5.4; p = 0.45). The correlation between predicted and measured %Fat was also stronger (r = .89). However, the two methods were not interchangeable as a trend in the residuals indicated that %Fat was underpredicted at low body fat and overpredicted at high body fat in the younger women. A major finding of this study was that neither existing equations nor the newly derived equations were able to accurately and reliably predict body fat in independent samples of elderly women. Some of the prediction error can be attributed to inter-method differences and differences in DEXA manufacturer, but this lack of agreement also emphasizes the problem of sample specificity with regression equations. Equations will always perform better in the sample from which they were derived and must be interpreted with caution when applied externally. A second major finding of this research was that a single "best" equation did not exist for these data, but rather, several alternative models provided similar equation statistics and regression coefficients. However, the combination of WT, HT (or BMI) and SF's was better than SF's alone. Nonetheless, this study demonstrated that a strong relationship between anthropometry and DEXA exists among elderly women and that internally valid equations can be proposed for this population. Moreover, it is reasonable to conclude that prediction equations based on DEXA have greater face validity in elderly women than those based on densitometry, as the DEXA model is associated with fewer assumptions. Due to.the relatively small sample size, the new %Fat equation cannot be recommended at this time. However, this study shows promise for future use of DEXA and anthropometry in elderly women. |
Extent | 5978835 bytes |
Genre |
Thesis/Dissertation |
Type |
Text |
File Format | application/pdf |
Language | eng |
Date Available | 2009-07-10 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0077361 |
URI | http://hdl.handle.net/2429/10644 |
Degree |
Master of Science - MSc |
Program |
Human Kinetics |
Affiliation |
Education, Faculty of Kinesiology, School of |
Degree Grantor | University of British Columbia |
Graduation Date | 2000-11 |
Campus |
UBCV |
Scholarly Level | Graduate |
Aggregated Source Repository | DSpace |
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