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The relationship between anthropometry and body composition assessed by dual-energy x-ray absorptiometry.. 2000

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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? by Andrea Dalton H i l l B.Sc. , The University of 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 S C I E N C E 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 B R I T I S H C O L U M B I A August 2000 © Andrea Christine Dalton H i l l , 2000 In p resent ing this thesis in partial fu l f i lment of the requ i rements fo r an advanced deg ree at the Univers i ty of British C o l u m b i a , I agree that the Library shall make it f reely available fo r re ference and study. I further agree that pe rm i s s i on for extens ive c o p y i n g o f this thesis fo r scholar ly p u r p o s e s may be granted by the head of my depa r tmen t or by his o r her representat ives. It is u n d e r s t o o d that c o p y i n g or pub l i ca t i on of this thesis for f inancial gain shall no t be a l l owed w i t hou t my wr i t ten pe rm i s s i on . Depa r tmen t of £ C { \ O O L - of- -rAvMAM KtlOGTlCS The Univers i ty of Brit ish C o l u m b i a V a n c o u v e r , C a n a d a Date Ati^USr 23 s DE-6 (2/88) Abstract A link between age-related changes in body composition (BC) and the increased prevalence o f disease and disability in old age has been wel l established (Chumlea & Baumgartner, 1989; Going et al., 1995; Shephard, 1997). Consequently, B C assessment is becoming increasingly important in the evaluation of the health and functional status of the older adult. Individuals 75 years and older comprise one o f 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 o f 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 ( 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 QDR-4500W) body fat data were initially collected in a sample o f 43 women 75-80 years old (m = 77.4yrs) as part o f a larger study investigating the effects of 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 .3kg to 4.0kg and 4.4% to 9.0%; p<0.001 in all cases). New equations were derived for F M , %Fat, trunk fat mass ( T F M ) 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), B M I , hip circumference (HC), waist circumference (WC) , SF ' s of 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 (SUM4SF) ; except H C and S U M 4 S F were not included in the trunk fat regressions. New Equations Adj. R 2 Cp SEE FM = 0.611(WT) - .231(HT) + .143(MA) + 16.462 0.95 4.46 1.53kg %Fat = 0.341 (WT) - .339(HT) + .285(MA) + 60.122 0.84 4.61 2.12% TFM = 0.185(WT) - .008(HT) + .112(MA) + .136(WC)-2.072 0.90 3.77 1.27kg %FT = 0.387(MA) - .227(HT) + .356(WC) + 30.659 • 0.83 3.9 2.76% 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 . o / o F a t = 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 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 D E X A instruments manufactured by Lunar. New equations were ii derived for this application using only the variables measured in these independent studies as the predictor variables. Modified Equations Adj. R 2 SEE BROD %Fat = 9.819 + .162(SUM4SF) + .652(BMI) - .261(SS) 0.82 2.21 BAUM %Fat = 9.198 + .696(BMI) + .295(TRI) 0.80 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 .001) (BAUM). A n unexpected finding was the accurate prediction o f %Fat in 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 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 o f the prediction error can be attributed to inter-method differences and differences in D E X A manufacturer, but this lack of agreement also emphasizes the problem of sample specificity with regression equations. Equations w i l l 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 W T , H T (or B M I ) 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 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 in elderly women. t in Table of Contents : Abstract - i i List of Tables v i List of Figures v i i Acknowledgements v i i i Dedication ix 1. Introduction 1 1.1 Rationale 1 1.2 Purpose 4 2. Review of the Literature 5 2.1 Health care implications of an aging society 5 2.2 Study of human body composition 6 2.3 Age-related changes in body composition 7 2.4 Conventional methods of body composition assessment 9 2.5 Limitations of conventional methods 12 2.6 Advances in body composition technology 14 2.7 Support for D E X A as the criterion method for body composition 16 2.8 Hologic QDR-4500 18 2.9 Limitations o f D E X A 19 2.10 Prediction equations 20 2.11 Development of 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 4 iv 4.1 Characteristics of study sample 34 4.2 Comparisons with existing databases 55 4.3 Performance of previously published equations 57 4.4 Development of new prediction equations 61 4.5 Validation of new prediction equations 77 4.6 Performance o f modified prediction equations 78 5. Discussion 82 5.1 New 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 / , 93 7. Appendices l i 101 Appendix I: Previously Published Body Composition Prediction Equations 102 Appendix II: Select Published Prediction Equations 103 Appendix III: Medical Clearance 104 Appendix I V : Informed Consent 105 Appendix V : Ethics Approval 107 Appendix V I : List o f Contact Authors 108 Appendix VI I : Letter o f Request for Data 110 Appendix XIII : Distribution of Dependent Variables I l l Appendix DC: Distribution of Independent Variables 112 Appendix X : Preliminary Stepwise Multiple Regression Analysis 115 Appendix X I : Stepwise Multiple Regression Analyses 119 Appendix XI 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 Lis t of Tables Number and Ti t le 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 56 Coefficients Table 4.3.1: Previously Published Equations Selected for Analyses 57 Table 4.3.2: Prediction of FMfrom Published Equations 58 Table 4.3.3: Prediction of%Fat from Published Equations .'. 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 79 Table 4.6.3: Paired t-Test Comparisons for Younger Women 79 Table 4.6.4: Limits of Agreement for Modified Equations and DEXA 79 vi L i s t of Figures Number and Ti t le 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 4 7 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 59 Equations 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 80 Samples v i i 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 of my committee, Dr. A l a n Martin, Dr. Robert Schutz and Dr. 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 in the anthropometry data collection and to Park for his assistance with statistics. I want to also extend my gratitude to Rob Langi l l and Dr. Rhodes from Buchanan Lab, and to Sonya Lumholst-Smith from the Changing Aging Program, for the use o f their equipment and facilities. Further acknowledgment goes to Dr. Gary Brodowicz and Dr . Richard Baumgartner for sharing their body composition data sets. Finally, I must thank my family and friends for their endless patience and encouragement. Vlll To my grandmothers, Irma Elizabeth Hamilton and Margaret Frances Dalton IX 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 of the disease and disability affecting the elderly today has been linked to age-related changes in body composition, which in turn, may largely be the result of sedentary lifestyle practices and poor nutrition (Baumgartner, Stauber, McHugh , Koehler, & Garry, 1995; Chumlea & Baumgartner, 1989; Evans & Cyr-Campbell, 1997; Going, Will iams, & Lohman, 1995; Shephard, 1997). Consequently, the measurement of body composition is becoming increasingly important in the assessment of health, nutritional and functional status o f the older adult population and in monitoring the effectiveness of exercise, diet and medical interventions. Women over the age o f 75 years comprise one of the fastest growing segments of the population (Canada, 1999; Donatelle & Davis, 1994), yet at present, no one method of body composition assessment appears to be both accurate and convenient for use in this more elderly population. Three major problems concern the measurement of 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; Keys & Brozek, 1953). The 2C model divides the body into fat mass (FM) and fat-free mass ( F F M ) components and assumes a constant density of 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 f f m ) is considerably lower and much more variable due to rapid bone loss associated with aging (Baumgartner, Heymsfield, Lichtman, Wang, & Pierson, 1991; Deurenberg, Weststrate, & van der Kooy, 1989; Going et a l , 1995; Lukaski, 1987; Mart in & 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 of 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 of these equations were derived from body density measurements from U W W and w i l l thus retain errors inherent to the 2C model (Baumgartner et al., 1991). Advances in body composition technology now allow quantification of previously unmeasureable fractions of 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 3C: 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). Four- compartment 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 of existing body composition prediction equations in a sample of 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 of 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 of people aged 65 years and older in Canada is expected to nearly double over the next thirty years and comprise more than 20% of the population as a result of 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% of 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 of 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 of body composition in the elderly has become an important focus in the growing body of 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 Den Heuvel, & Deurenberg, 1994). Women continue to outlive their male counterparts and thus make up the majority of seniors over the age of 75 years (Canada, 1999; Donatelle & Davis, 1994; Shephard, 1997). 5 Consequently, the specific health care needs of elderly women should be the focus of 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 in 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 of body composition and thus our understanding of the biological information. Recent investigations on aging and body composition have been primarily technical in nature as practical, accurate and reliable methods, requisite for epidemiological research and furthering our understanding of 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 in 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 in body fat, muscle, bone and water content have been documented in 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). With 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 in estrogen production, and fat stores tend to "migrate" to the trunk and visceral cavity (Ley, Lees, & Stevenson, 1992; Vogel & Friedl, 1992). The redistribution of fat appears to stabilize after age 65 (Baumgartner et al., 1995). Changes in 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, Robbins ,& Silbert, 1983; Vogel & Friedl, 1992). In more extreme cases of 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 in life and then begin to decline (Going et al., 1995). Recent data from a study of elderly people ages 65-85 years indicates that these'd'eclines continue into the ninth decade of life and an average of 6-7% o f these combined components may be lost over the 20 year span (Baumgartner et al., 1995). Wasting of appendicular skeletal muscle is the primary source of this decline, and accounts for approximately 60% of the lean tissue lost with aging (Baumgartner et al., 1998; Kirkendall & Garrett, 1998). Significant and rapid bone mineral loss associated with post- menopause can contribute an additional 11% to this decline in elderly women (Baumgartner et al., 1995; Voge l & Friedl, 1992). Disabili ty 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, in turn, can limit performance in activities of daily l iving 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 (TBW) decreases from 50% of total body weight in early adulthood to 45% in middle age (Going.et al., 1995), and a possible total loss of 4-6 litres by old age. At 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 of 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 of fat-free tissue with aging (Baumgartner et al., 1991). Together, these unfavourable changes in body composition greatly impact health and functioning in 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 in older age could be greatly reduced through regular exercise and proper nutrition. Consequently, the measurement of body composition has become increasingly important in the assessment and management of disease and disability among the elderly. 2.4 Conventional methods in body composition assessment The only true direct measures of body fat or other body constituents is through cadaver analysis (Brodie, 1988a; Clarys, Martin, & Drinkwater, 1984); thus, human body composition assessment relies on methods of 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 of 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 (FM) and fat-free mass (FFM) , based on the premise that F M is considerably less dense than all other components of the body (Heymsfield et al., 1989; Keys & 9 Brozek, 1953). The F M component contains all lipids in the body, both essential and non- essential, 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 of whole body density (D b ) is therefore dependent on the relative contribution of 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" in body composition against which most other methods are compared to (Brodie, 1988a; Clarys et al., 1984; Jebb & El ia , 1993; Lukaski, 1987). Using the principle of Archimedes and U W W , Db can be calculated from body volume, by subtracting body weight in water from body weight in 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 of the F M and F F M are unchanging and are of constant density, with values o f 0.9g/ml and l . l g / m l , respectively (Brodie, 1988a; Keys & Brozek, 1953). Other 2C 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 & El 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 of the skinfold thickness (SF), body circumferences, 10 breadths, height (HT), weight (WT) and body mass index (BMI) (Durnin & Rahaman, 1967; Durnin & Womersley, 1974; Heyward & Stolarczyk, 1996a; Keys & Brozek, 1953; Lohman, 1981; Mart in & 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 SF has been studied extensively in the body composition literature because of the strong relationship between the subcutaneous layer of adipose tissue, body density and percent body fat (Durnin & Womersley, 1974; Lohman, 1981). Using spring-loaded calipers, the thickness o f one or several SF sites (which contains two layers of 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 of body composition in 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 l imb circumferences are often added in combination with SF anthropometry in order to improve the prediction equation (Baumgartner et al., 1991; Dupler, 1997; Goran et al., 1997; Will iams, Going, Mi l l i ken , Ha l l , & Lohman, 1995). Anthropometric predictors of body fat must have strong statistical and biological support for their selection. Finally, equations specific to elderly women must reflect the uniqueness of the aging female body in the choice of predictor variables. The prediction of 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 of adipose tissue is presumed constant. Additionally, skin thickness and SF 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 When U W W and anthropometry are used to measure body composition in the elderly population, biological variations in the assumptions of the 2C 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 of F F M (dffm), to be unchanging. This is true among young and middle-age adults, but not the case for older adults whose muscle, bone and water fractions all change with aging. O f these, the density of the bone mineral content is the greatest, and therefore, variations in this fraction w i l l have the largest impact on the measurement of dffm. Significant bone mineral loss associated with aging lowers the overall density of the F F M , and thus, violates the assumptions of constant dffm and value o f l . l g / m l (Going et al., 1995; Shephard, 1997). A s a result, body fatness is overestimated in the elderly when Siri 's formula is applied (Martin & Drinkwater, 1991). This error is likely more drastic in elderly women who experience more rapid and significant bone demineralization (Vogel & Friedl, 1992). Several researchers have accounted for this by modifying Siri 's equation (Deurenberg et al., 1989); however, others have shown this to be unacceptable (Baumgartner et al., 1991; Will iams et al., 1995). Williams et al. (1995) have demonstrated that adjusted two-component models under and overestimate percentage body fat measured by a multi-component model by 6% and 14%, respectively. 12 A n additional concern is the U W W procedure itself. The process of 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 in further erroneous measurements o f total body density (Baumgartner et al., 1991; Brodie, 1988b; Jebb & Elia , 1993; Shephard, 1997). Measurement techniques and assumptions of the SF method may introduce further error. Many experts have questioned the reliability of the SF measurement in elderly populations as several studies have demonstrated greater error, in, the prediction of body fat from skinfold anthropometry with increasing age (Baumgartner et al., 1995; Will iams et al., 1995). Others suggest that age-related changes in the hydration affect the elasticity and compressibility of 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 of the SF as a result o f dehydration and reduced muscle tone have been implicated (Chumlea & Baumgartner, 1989). Finally, the inability o f the SF 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 SF 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 in 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 of compressibility on body fat predictions, and as all the subjects were older in age, it 13 is difficult to say whether variations in compressibility are age-related or due to individual differences. The effect of skin thickness on the prediction of body fatness was also examined in this study. It was proposed that in lean subjects a thicker layer o f skin would lead to greater measurement error. Women 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 in 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 in the prediction of body fat (Martin et al., 1992). Again, subjects were elderly, and hence, the independent factor of age on skin thickness was not clear. Finally, less reliable prediction of 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 of directness to the next, and consequently, prediction equations derived from U W W w i l l retain the systematic errors inherent to the 2C model (Baumgartner et al., 1991). (Heymsfield et al,, 1989). 2.6 Advances in body composition technology Advances in body composition technology now allow for quantification of previously unmeasureable tissue in vivo. With the development of dual-photon absorptiometry (DP A ) , and then dual-energy X-ray 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 2C model (Heymsfield et al., 1989; Mazess et al., 1990). 14 Both D P A and D E X A have been used in 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 of 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 of 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 of error associated with the use of 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 (Kel ly 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 4C measurements of 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 rem dose of 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 of 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 of 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 in 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 of soft-tissue. The mass attenuation coefficients o f bone mineral at the two beam energies are known constants whereas the ratio of the mass attenuation coefficient of soft-tissue (R s t ) is related to the fatty fraction and must be calculated from all the pixels that 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 in the measurement of percent fat (1.4%) and fat mass (1.0kg) in 12 young adult men and women. In another study using younger adults, the precision of two different manufacturers of 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 of D E X A measured percentage fat with far greater precision than the Lunar model as reflected by the coefficient of variation ( C V ) for Hologic (CV=1.3%) versus Lunar (CV=3-4%), and both were superior to U W W (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. Unt i l then, the validity o f 16 D E X A depends on its accurate measurement of known quantities of meat and lard, inanimate materials whose physical and chemical properties simulate that of humans, animal carcasses and 4C 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 of F M and F F M (Kohrt, 1998; Snead et al., 1993; V a n Loan & Maycl in , 1992; Wellens et al., 1994); however, results based on these studies are limited because of the unknown accuracy of other reference methods. Unt i l 1993, the validity and accuracy of D E X A had not been examined in vivo (Svendsen et al., 1993). Svendsen and colleagues (1991) measured whole body composition in 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 of %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 of lard were placed on the ventral side o f the bodies of six women, ages 24-49. The ability for D E X A to monitor change in body fat was confirmed in 10 young adults, age 28 years, with 1.51kg packets of lard using Hologic 1000W instrumentation (Kohrt, 1998). Several researchers have validated D E X A against 4C models. Prior and colleagues (1983) found D E X A fat and fat measured using a 4C 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 of densitometry (Prior et al., 1997). 17 Others have shown reasonable agreement between these two methods at the group level, but substantial error in 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 (Bergsma- Kadijk, 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 of D E X A exist (Lunar, Hologic and Norland), yet to date only a paucity o f information is available on the cross-calibration of 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 of 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 of D E X A thus far have been based on pencil-beam technology and cannot be assumed for the most recent model of 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 (Kel ly 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 in the assessment of limb fat mass (Kelly, 1998a). The precision for the fan beam in the measure of F M was 300 grams and 600 grams for the pencil beam. Due to superior spatial assessment, QDR-4500 has overcome some of 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 by the National Institute o f Health (NIH). The Health A B C Study and the N H A N E S IV (National Health and Nutrition Examination) w i l l provide large volumes of 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 in hydration may be problematic in the measurement of the elderly (Roubenoff et al., 1993). Small but systematic and predictable errors in soft tissue composition were noted with fluid balance changes in a recent study (Pietrobelli, Wang, Formica, & Heymsfield, 1998). Similarly, another group of researchers showed that an increase in lean tissue mass was correlated to fluid intake (Thomsen, Jensen, & Henriksen, 1998), while others found the density of F F M to be unaffected by declines in 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 by 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 of 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 in elderly. Therefore, the effect of hydration on the measurement of body composition remains unclear. A previous problem o f D E X A underestimating central regions of body fat was not found in this study and was attributed to improvements in software and instrumentation. Beam hardening may occur in large subjects in 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 in size to approximately 190 X 60cm; again, problematic for measuring large or obese persons (Jebb & El ia , 1993). Finally, little is known about the algorithms used for analysis, which seem to be in state of constant review (Gotfredsen et al., 1997; Jebb & El ia , 1993). ? Despite these possible limitations, D E X A has greater validity than U W W in the assessment of elderly body composition. Like U W W , however, D E X A instrumentation is not highly accessible outside of 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 in the elderly and warrants further attention. 2.10 Prediction equations Several prediction equations have now been developed for specific use in 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 of anthropometry and are discussed • further. One of the most widely used equations to assess body composition is that of 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 of these, only 37 females ages 50-68 years were included at the elderly end o f the spectrum. Furthermore, the SF 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 2C model. Dupler (1997) considered some of the previous limitations and used modified U W W procedures to develop new SF equations for the elderly. Again , a large sample was used and the average age was 70 years. Furthermore, age- related changes in fat patterning were considered and therefore only trunk SF sites were measured. However, this study still retains the problems with 2C model and Siri 's equation. Chapman and co-researchers (1998), predicted D E X A F F M (R2 = 0.96) from W T , H T and the thickness of the triceps (TRI) SF. However, the subcutaneous fat of the T R I is only weakly correlated to F F M , and was probably not the most appropriate choice of 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 of subscapular:triceps SF 's (SSTRI) and was based on D E X A (R2 =0.94). The sample size of women was small with an «=23, and again, this equation was not cross-validated. A s well , the ratio of the number of subjects to number of independent variables was just over 4:1, when the minimum recommended is 10:1 (Heyward & Stolarczyk, 1996b). In many of these studies', only T R I or the sum four skinfolds ( S U M 4 S F = biceps+triceps+suprailiac+subscapular) were the only SF's measured, therefore it was unclear whether other SF sites might have improved the prediction equation. Waist (WC) and hip (HC) 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 of 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). Only two studies to date have examined more practical techniques of body composition assessment against a 4C model. Will iams et al. (1995) found a lower S E E associated with bioelectric impedance analysis (BIA) regressed against F F M than for the sum of 10 SF's and F M and therefore developed new equations F F M based on B I A only. Individual SF'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 4C criterion body fat and to consider new equations for the elderly (Goran et al., 1997). Hip circumference, W T , B M I and the sum of 9 SF'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 of these 4C 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 QDR4500 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 of criterion body fat from indirect measurements by way of 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 of 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 of the criterion method must be demonstrated. Second, the measurement precision of 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 of the data may be necessary. This is often the case for the relationship between SF's and body density, and therefore, log transformations of 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 of a useful equation. Pearson product correlation coefficients (r) are used to describe the strength of 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 of 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 of 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 of the equation (Cohen & Cohen, 1975; Guo et al., 1996). 23 When the nature of the research is exploratory, the most common approaches are stepwise, forward, maximum R2, and all possible subsets regression procedures (Brodie, 1988a; 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 of both stepwise and all possible subsets procedures. The magnitude of the multiple regression coefficient of determination (R2) determines how much of the prediction of body fat can be explained by the predictor variables, and the standard error of the estimate (SEE) indicates how precise this prediction is. The use of Mal low 's statistic (C p ) has also been recommended when the sample size and number of predictor variables are small (Ott, 1984). The C p statistic is the ratio SEEp/s2 - ( N - 2p) where SEE/? is the residual sum o f squares for a model with p parameters, and s2 is the residual mean square based on the regression equation with all the independent variables. The lowest C p value corresponds to the subset of predictors with the highest R2 and lowest S E E ; however, a C p value that is close to equal the number of regression 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 of the equation, but not too many so that multicollinearity among independent variables becomes a problem and affects the stability of 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 of the sample required can be determined by power analysis. (Cohen & Cohen, 1975). To detect a difference in R2 = 0.05, with an alpha level of 0.05 and a power of 0.8, a 24 sample size of n = 222 is required, whereas an n = 46 wi l l detect a difference in R2 = 0.15 with a power of 0.6 when three predictor variables are used. A n alternative recommendation is to ensure a minimum of 10 to 20 subjects for each predictor variable (Heyward & Stolarczyk, 1996a). Nonetheless, a survey o f the literature demonstrates a range of 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). Many o f these studies have included men and women of several different ages in their sample; further inspection showed that very few investigations contained large numbers of 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 by 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 of the newly derived equation (Baumgartner et al., 1991; Guo et al., 1996). Using 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 in North America. In order to contribute to the successful aging of this older adult population, further research is needed to improve our understanding of 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 of large volumes of data requisite for epidemiological research. A s wel l , private health care and fitness facilities would benefit from the availability of simple assessment tools to evaluate body composition status and monitor the effectiveness of 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 in women 75-80 years; 2) to test the performance o f previously published equations in these women; 3) to determine the best anthropometric predictors of body fat in 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 of predictor variables, (ii) using D E X A as the criterion method, (iii) and using appropriate regression methods; 5) to test the performance of new prediction equations in independent samples (i) in similarly aged women (ii) and in younger women to evaluate the impact of age on equation development and performance. 26 3. Methods 3.1 Subjects The study sample consisted of 40 Caucasian women and 3 Asian women between the ages of 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 of a larger study that examined the effects of progressive resistance exercises on muscle strength, functional ability, bone mineral density and body composition in 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 IV) . Ethics approval was granted by the Research Ethics Board of the University o f British Columbia (Appendix V ) . Forty-six women participated in 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 Body composition was assessed by dual energy X-ray absorptiometry ( D E X A ) and anthropometry at the baseline of the "parent" strength training study, and by anthropometry only during the study and at the end. The purpose of collecting body composition data iri this "parent" study was to monitor the effects of strength training on body composition for a year- long period. Only the baseline data were used for this current research. D E X A (QDR-4500W; V8.20a:5; Hologic Inc., Waltham, M A ) was used to measure criterion body fat. The QDR-4500W 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 (FM) , total percent fat (%fat), regional trunk fat mass (TFM) 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 (WT) was measured with a digital scale to the nearest 0.1kg. Waist (WC) and hip (HC) circumferences were measured to the nearest 0.1cm using a non-expandable tape measure. The site of the W C was defined as the narrowest girth between the ribs and the iliac crest, while the H C was measured at the maximum 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 (TH) 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 of the body in rotational order, with the exception of 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 mm (or 10%). The final SF measurement was the average of the closest two SF values. Harpenden calipers were set at a constant pressure of 9.4g/mm 2 and calibrated regularly. Skinfold Direction of fold Anatomical site T R I vertical Midpoin t between the acromial process and olecranon process on the posterior aspect o f the arm. B I C vertical Same level as marked for the triceps but on the anterior aspect o f the arm. SS diagonal The inferior angle of the scapula along the natural cleavage line. M A vertical A l o n g the midaxillary line at the level o f the xiphoid process. SI oblique Superior to the iliac crest and anterior to the midaxillary line. A B D vertical 2 c m lateral to the umbilicus and at the level o f the umbilicus. T H vertical Midpoin t between the inguinal crease and the patella with the knee and hip flexed at right angles and the foot supported. C F vertical A t the level o f maximum calf circumference on the medial aspect o f the calf, again with the knee and hip at right angles. Anthropometric data were collected within one day of 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 in 75-80 year old women, 8 published equations (Appendix II) were selected from the literature and tested in this study sample. The literature was surveyed specifically for studies that derived prediction equations in elderly women using anthropometry and SF 's for the independent variables. Furthermore, studies were chosen for a range in dependent variables in order to examine equations based on two (2C), three 29 (3C) and four (4C) compartment models of body composition. Additionally, descriptive data provided in these studies were used as reference data with which to compare our current data. ' Finally, in order to test the application of 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 SF 's in young, middle-age and elderly women were sought out. A s a result of 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 Michael 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 of new equations, assumptions of the linear regression model were considered. Scatter plots and Pearson correlation analyses were used to determine the nature and strength of 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 of less than 1 were considered acceptable. The Pearson's correlation coefficient and the paired t-tests difference score for 30 repeated SF measures were used to determine the reliability of the SF measurement. Finally, the accuracy o f D E X A in the measurement of total mass was examined by regressing D E X A mass against standard body weight (WT). 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 of 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 of predictor variables included in 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 of the estimate (SEE) for the prediction of the dependent variable. However, in this study, the adjusted R2 (adj. R2) was used because of the relatively small sample 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, Ma l low ' s C p ; the subset with the lowest C p value is generally considered the best Overall model. However, when both sample size and the number of regression coefficients are small, the 31 most stable equation has a C p value approximately equal to the number of predictor variables (Ott, 1984). Height, W T , B M I , SF 's ( A B D , B I C , M A , SI, SS, TRI , C F and TH) , the sum of B I C , TRI , SI and SS ( S U M 4 S F ) , the ratio of SS and TRI SF 's (SSTRI,), and trunk girths (HC 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, SSTRI and W C were entered as predictor variables for T F M and % T F . The selection of the final regression equations was primarily based on the adj.R2, S E E , and C p criteria. However, strong biological associations for the individual predictors and body fatness, and each variable's significance in previously published equations were also considered (Guo et al., 1996). New 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 of trunk fat. Residual analyses were conducted/for the final regression equations to ensure homogeneity in the variance of predicted body fat for all values of the dependent variable (Dupler, 1997). A n independent group of women was not measured for the purpose of 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 of the new equations as conventional data splitting was not recommended for sample sizes of less than 100. The data was split into 10 almost equal groups (7 groups of n = 4, and 3 groups of n = 5). For each round of 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 of 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 of interest, the new equation for %Fat was applied to the independent databases of Brodowicz (1999) and Baumgartner (1999) which included D E X A %Fat, anthropometry and SF measurements for both similarly aged women and younger women. Unfortunately, the best model for the prediction of %Fat included the M A SF, which was not measured in either of the other studies. Modified equations were therefore developed, using only the variables measured in 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 2C equations selected from the literature are expected to overestimate D E X A fat in our sample o f women ages 75-80 years; while 3C and 4C 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 R2 values than those reported for 2C equations. 3. Due to changes in 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) in the independent sample of 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 in Table 4.1.1. Table 4.1.1: Descriptive Characteristics of the Study Sample Age H T (cm) W T (kg) BMI W C (cm) H C (cm) W H R Mean 77.4 158.1 66.4 26.6 87.4 101.4 0.86 s.d. 1.8 6.4 11.0 4.0 11.6 8.7 0.08 Skewness N/a 0.3 0.6 0.5 0.2 0.5 N/a Kurtosis N/a -0.7 0.2 -0.2 -1.1 -0.3 N/a A B D BIC C F M A SI SS T H TRI STJM4SF SSTRI Mean 32.1 20.0 26.1 23.2 19.5 21.4 36.5 27.6 143.7 0.76 s.d. 8.6 7.1 8.2 7.2 6.7 8.2 9.2 7.4 39.6 0.20 Skewness -0.8 0.3 0.2 -0.8 -0.1 -0.0 -0.5 0.1 -0.2 -0.1 Kurtosis 1.1 -0.3 -0.9 -0.3 -0.3 -0.7 -0.5 -0.4 -0.1 -0.4 S U M 4 S F = triceps + biceps + subscapular + suprailiac SSTRI = subscapular : triceps skinfold thickness ratio F M (kg) % Fat Trunk F M (kg) % Trunk Fat FFM(kg) Total Mass(kg) Mean 23.79 35.83 11.87 34.78 39.78 65.21 s.d. 7.03 5.27 4.08 6.7 4.5 10.88 Skewness 0.7 -0.0 0.3 -0.4 N/a N/a Kurtosis 0.3 -0.4 -0.2 -0.5 N/a N/a *n/a = not applicable The data were further analyzed to test for assumptions of the linear regression model. Scatter plots for independent and dependent variables demonstrated the existence of 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 BIC CALF SI MA SS TRI THIGH SUM4SF SUBTRI DEXA FM 0.65 0.92 0.63 0.65 0.62. • 0.78 0.83 0.54 0.88 0.34 DEXA %FAT 0.69 0.85 0.62 0.72 0.71 0.75 0.84 0.54 0.87 0.30 DEXA TRUNK FM 0.66 N /A N /A 0.71 0.68 0.81 N /A N /A 0.87 0.47 DEXA % TRUNK FAT 0.69 N /A N /A 0.75 0.76 0.79 N /A N /A 0.85 0.48 HT WT BMI WC HC DEXA FM 0.18 0.95 0.93 0.87 0.89 DEXA %FAT -0.08 0.75 0.86 0.77 0.76 DEXA TRUNK FM 0.15 0.89 0.89 0.92 0.79 DEXA % TRUNK FAT -0.08 0.70 0.81 • 0.83 0.64 * N / A - not applicable Figure 4.1.1: Fat mass vs. independent variables (a) FM vs. WT 40.00 30.00' in w ti E Q 20.00. 10.00. • • f I • • I 50.00 1 60.00 70.00 80.00 90.00 weight 35 (b) FM vs. BMI 40 .00 . TO 3D.00-1 J3 o 20.00 4 • • 10.00. 20.00 25.00 30.00 BMI 35.00 (c)FM vs. HC 01 30.00' J3 o 20.00 J 10.00 • • • I. • • • i 90:00 100.00 110.00 120.00 HC (cm) 36 (d) FM vs. WC 40.00. co 30.00' J3 o * ~ 20.00. 10.00. 1 • • • 1 1 • I I 1 I I B 1>. • B • I • 1 • 1 1 • • 1 70.00 80.00 90.00 WC (cm) 100.00 (e) FM vs. AB Skinfold 10.00 20.00 30.00 AB (mm) SO .00 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 CALF (mm) 40.00 38 (h)FM vs. MA Skinfold — i — 20.00 10.00 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 3 0 . 0 0 - u> E 2 0 . 0 0 - 5 10.00 - 10.00 20.00 S S (mm) 30.00 (QFM vs. TRI Skinfold 40.00. C 30.00' in £ - J3 20.00. a 10.00. I I 10.00 20.00 30.00 T R I (mm) 40.00 (m) FM vs. SUM4SF • • • t • • • — i — 50.00 25.00 75.00 100.00 125.00 SUM4SF (mm) (n) FM vs. SUBTRI 40.00 J S U B T R I 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 T 1 1 f- 60.00 70.00 80.00 90.00 Weight (kg) (b)%Fatvs. BMI 20.00 25.00 30.00 BMI '35.00 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' i r 40.00 50.00 ABD (mm) 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) 4 4 (g)%Fatvs. SUM4SF 45.00 A 40.00 35.00 H 30.00' 25.00H 25.00 1 r 50.00 75.00 100.00 r 125.00 SUM4SF (mm) (h)%Fatvs. SUBTRI 45.00 H 25.00 H SUBTRI 45 0)%Fatvs. SS Skinfold 45.00 40.00' rt U_ 35.00' 5 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 H T (cm) 170.00 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 Weight (kg) 90.00 47 (b) Trunk FM vs. BMI 20.00 25.00 30.00 BMI 35.00 (c) Trunk FM vs. MA Skinfold • • - • • i • • i — i — 30.00 10.00 20.00 MA (mm) 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 WC (cm) (e) Trunk FM vs. SI Skinfold 20.00. ca C 15.00. tn (A ft E *J «E c 3 10.00. 5.00. • • 10.00 20.00 30.00 SI (mm) 49 (f) Trunk FM vs. SS Skinfold — i 1 — 20.00 30.00 10.00 SS (mm) (g) Trunk FM vs. ABD Skinfold 20.00-1 0> 15.00-1 ra E c 3 10.00 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 3 • • 10.00 J 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 3 10.00-1 5.00 150.00 160.00 HT (cm) 170.00 51 Figure 4.1.4: %Trunk Fat vs. Independent Variables (a )%FatTrunk vs. BMI 2 D . 0 D H B M I (b)%Fat trunk vs.WC 40.00' u. S9 30.00 20.00 H . 70.00 T 1 T 80.00 90.00 100.00 W C (cm) 52 (c)%Trunk Fat vs. HT 40.00 H 30.00 20.00' • • 150.00 160.00 H T (cm) 170.00 (d)%Trunk Fatvs.WT 40.00• U- JC c 3 30.00 H 20.00 50.00 60.00 70.00 80.00 90.00 WT (kg) 53 Second, it is important that independent variables and particularly dependent variables are normally distributed in the sample population. Frequency distributions for the four dependent variables (Appendix VIII) and selected independent variables (Appendix IX) showed no major departures from normality and values of 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 of both the criterion methods and anthropometry methods used. Paired t-tests and correlations were used to test the reliability of the SF measurement (Table 4.1.3). The differences between repeated SF 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 of Sk in fo ld Measurements A B D B I C C F M A SI SS T R I T H T r i a l 1 31.82 20.07 26.20 23.28 19.47 21.47 27.84 36.76 T r i a l 2 31.90 19.87 25.94 22.88 19.44 21.31 27.53 .36.37 Difference -0.09 0.20 0.25 0.40 0.04 0.16 0.32 0.38 r 0.95 0.94 0.94 0.97 0.96 0.99 0.94 0.98 A l l significant at p < 0.05 Although testing the accuracy and reliability of D E X A were not specific objectives of this study (these have been documented previously in the literature review), it was of interest to see how closely D E X A total mass (TM) compared with body weight (WT) 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 DEXA Mass (kg) Table 4.1.4: Prediction of Total Body Mass from D E X A Comparison r Mean Diff. s.d.(mean) P(mean) Standard body mass - D E X A body mass .999 1.2kg 0.49 <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 of 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 n Age HT(cm) WT(kg) BMI WC(cm) HC(cm) WHR U.B.C. 43 77.4(1.8) 158.1 (6.4) 66.4(11.0) 26.6 (4.0) 87.4(11.6) 101.4(8.7) 0.86 (.08) BAUM(1999) 101 74.5 (5.6) 155.9(6.8) 64.8 (12.6) 26.7 (5.0) 91.9(11.7) 104.1 (11.4) 0.88 (.07) BATJM(1995) 82 71-80 158.3(6.2) 63.1 (10.9) 25.1 (3.6) 87.8 (9.8) 101.5(8.6) 0.87 (.06) BROD(1999) 31 71.1 (4.6) 161.3 (6.2) 65.1 (10.1) 25.0(3.5) N/A N/A N/A VISSER(1994) 128 70.2 (5.3) 161.6(6.1) 68.1 (9.5) 26.1 (3.6) N/A N/A N/A SVEND(1991) 23 75(0) 158.9 (6.9) 65.5(11.6) 25.9(4.3) N/A N/A 0.84 (.08) n SS(mm) SI(mm) BlC(mm) TRI(mm) FM(kg) % F A T Trunk FM(kg) U.B.C. 43 21.4 (8.2) 19.5 (6.7) 20.0 (7.1) 27.6 (7.4) 23.8 (7.0) 35.8(5.3) 11.9(4.8) BAUM(1999) 101 20.7 (9.6) N / A . N / A 22.6 (8.3) 26.4 (9.3) 39.6(7.5) N / A BAUM(1995) 82 21.9(9.9) N / A N / A N / A 24.5 (8.2) 38.0 (6.8) 11.8(4.2) BROD(1999) 31 19.5 (7.0) 19.8(7.3) 10.7 (3.9) 20.8 (5.3) 25.8 (7.0) 39.1 (5.6) N / A VISSER(1994) 128 19.8(7.5) 19.8(8.0) 11.8(4.5) 19.8(5.1) N / A 43.3 (6.1) N / A SVEND(1991) 23 N / A N / A N / A N / A 21.7(8.8) 33.7 (9.9) N / A *N/A-no 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. Not 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 etal . (1998). Table 4.2.2: Summary of Current and Previously Published Correlations for Anthropometry and Criterion Body Fat Dependent Variable SS TRI BIC A B D M A SUM4SF U.B.C. D E X A F M (Hologic) 0.78 0.83 0.92 0.65 0.62 0.88 BAUM(1999) D E X A F M (Lunar) 0.77 0.75 N / A N / A N / A N / A BROD(1999) D E X A F M (Lunar) 0.65 0.60 0.61 N / A N / A N / A GORAN(1997) F M (4C model) 0.61 0.68 N / A 0.67 0.72 N / A BAUM(1995) D E X A F M (Lunar) N / A 0.68 N / A N / A N / A N / A VISSER(1994) B o d y Density -0.39 -0.28 -0.27 N / A N / A -0.4 56 Table 4.2.2 (cont'd) Dependent Variable W T BMI W C H C U.B.C. D E X A F M (Hologic) 0.95 0.93 0.87 0.89 BAUM(1999) D E X A F M (Lunar) 0.96 0.91 0.85 0.93 BROD(1999) D E X A F M (Lunar) 0.90 0.86 N/A N/A GORAN(1997) F M (4C model) 0.88 0.85 0.72 0.83 BAUM(1995) D E X A F M (Lunar) N / A 0.93 N/A 0.93 VISSER(1994) Body Density N / A -0.61 N/A 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 in our sample of elderly women. These equations have been referred to previously (Appendix II) and are summarized here in Table 4.3.1. Table 4.3.1: Previously Published Equations Selected for Analyses Author Equation Chapman et al. (1998) FFM(kg) = 0.582(WT) - 0.397(TRI) + 0.392(HT) - 48.956 Dupler(1997) (a)%Fat = 0.1688(BMI) + 0.542(HC) - 0.1639(WT) - 7.9498 Dupler(1997) (b)FM = 0.2449(WT) + 0.5218(HC) - 0.076(TC) - 37.8619 Durnin & Womersley (1974) D b = 1.1339 - 0.0645 [log (BIC + TRI + SI + SS)] *for elderly women Goran etal. (1997) F M = 0.31(HC) + 0.22(CALF) + 0.31(WT)-31.33 Svendsen et al. (1991) F M = 0 .63(TRI)+4.47(BMI)+9.32(SUBTRI)+1.35(WT)+1.04(HT) -192.48 Visser etal. (1994) (a) D b=-0.0356riog(BIC +TRI + SI+ SS)1 +1.0688 Visser et al. (1994) (b) D b=-0.0022(BMI)+ 1.0605 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 of the Svendsen equation, which significantly underestimated body fat. 57 Table 4.3.2: Prediction of F M from Published Equations Comparison r Mean Diff. S.D. t P C H A P M A N E Q N - D E X A F M 0.92 1.92 2.72 4.64 <0.001 D U P L E R E Q N a - D E X A F M 0.92 4.05 2.53 10.27 O . 0 0 1 G O R A N E Q N - D E X A F M 0.94 2.63 2.48 6.96 <0.001 S V E N D S E N E Q N - D E X A F M 0.97 -3.30 3.51 -6.17 <0.001 Table 4.3.3: Prediction of %Fa t from Published Equations Comparison r Mean Diff. S.D. t p D U P L E R E Q N b - D E X A % F A T 0.76 4.77 3.47 9.03 O . 0 0 1 D & W E Q N - D E X A % F A T 0.84 4.38 2.87 10.03 <0.001 V I S S E R E Q N a - D E X A % F A T 0.84 9.02 3.35 17.64 O . 0 0 1 V I S S E R E Q N b - D E X A % F A T 0.86 8.20 2.68 20.07 O . 0 0 1 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 of F M (.92-.97) than for %Fat (.76-.86). However, further analysis of four of 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 of body fat but were reasonable accurate at high body fat levels. The corresponding limits of 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 in the current sample of women 75-80 years of age. 58 Figure 4.3.1: Agreement Between Predicted and Measured Fat from Published Equations 10.00 < 7.60' 5.00 4 (a) Chapman Equation «5 2.50 U - c — 0.00 H o £ 0> -2.50 • Q -5.00' -10.00' 10.00 1 20.00 * Mean = 1.92 7* — I — 30.00 Average FM (kg) Mean 40.00 (b) Goran Equation Mean 20.00 Average FM (kg) 59 (c) Dupler Equation (ii) 35.00 Average %Fat Mean (d) Durnin & Womersely Equation U_ 5.00. — 2.50. at o c <u D.DOJ S -2-50. •7.50 J •10.00. • Mean = 4*38 . • • • " m 25.00 1 — 30.00 35.00 40.00 1 — .45.00" Average %Fat Mean 60 Table 4.3.4: Limits of Agreement for Previously Published Equations and D E X A Comparison Difference s.d. (diff) d +/- 2 X SD C H A P M A N E Q N vs. D E X A F M 1.92kg 2.72kg -3.52 to 7.36 G O R A N E Q N vs. D E X A F M 2.63kg 2.48kg -2.33 to 7.59 D U P L E R E Q N b vs. D E X A % F A T 4.77% 3.47% -2.17 to 11.71 D & W E Q N vs. D E X A % F A T 4.38% 2.87% -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, SF sites o f the limbs (BIC, TRI , C F and T H ) did not significantly contribute to the explanation of body fatness in elderly women and were not entered in 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./?2 and minimum S E E criteria (Appendix XI) . Fol lowing this, all possible subsets regression analyses were used to evaluate other possible prediction models that might be more stable (appropriate C P), practical and biologically meaningful (Appendix XII) . Equations for F M and %Fat using only SF 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, SS, 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, SS, SSTRI and W C were entered'into the.TFM and % T F regression analyses. A set of 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 of the dependent variables: F M (EQN1), %Fat (EQN2), T F M (EQN3) and % T F (EQN4) (Table 4.4.2). Table 4.4.1: New Regression Models for the Prediction of Body Fat D E X A Predictor Variables Adj. R 2 C p SEE C V F M W T , H T , M A 0.95 4.46 1.53kg 6.4% W T , H T , M A , S S T R I 0.96 1.77 1.46kg 6.1% W T , H T , M A , H C 0.96 3.78 1.50kg 6.3% W T , H T , M A , W C 0.95 4.20 1.51kg 6.3% % F A T B M I , M A 0.84 4.25 2.14% 6.0% H T , W T , M A 0.84 4.61 2.12% 5.9% B M I , M A , S S T R I 0.85 1.63 2.04% 5.7% B M I , M A , W C 0.84 3.74 2.10% 5.9% T F M W T , H T , M A , W C 0.90 3.77 1.27kg 10.7% W T , B M I , M A , W C 0.90 4.54 1.28kg 10.8% % T F H T , M A , W C 0.83 3.9 2.76% 7.9% H T , M A , W C , A B D 0.84 3.99 2.72% 7.8% Table 4.4.2: Best New Prediction Equations for Body Fat Eqn New Prediction Equations Adj. R 2 C p SEE C V 1 F M = 0.611(WT) - .231(HT) + .143(MA) + 16.462 0.95 4.46 1.53kg 6.4% 2 %Fat = 0.341 ( W T ) -- .339(HT) + .285(MA) + 60.122 0.84 4.61 2.12% 5.9% 3 T F M = 0 .185(WT)- .008(HT) + .112(MA) + .136(WC) - 2.072 0.90 3.77 1.27kg 10.7% 4 % T F = 0 .387(MA) • - .227(HT) + .356(WC) + 30.659 0.83 3.9 2.76% 7.9% Table 4.4.3: New Skinfold Equations for Total Body Fat D E X A Predictor Variables Regression method Adj. R 2 Cp SEE C V F M T R I , B I C , C A L F , A B D A l l poss. subsets 0.87 5.04 2.56kg 10.8% F M B I C , C A L F Stepwise 0.86 2.66kg 11.2% % F A T M A , C A L F , S U M 4 S F A l l poss. subsets 0.77 2.93 2.52% 7.0% % F A T S U M 4 S F , C A L F Stepwise 0.77 2.51% 7.0% A l l regression models included the M A skinfold and some combination of HT, W T or B M I , which together, explained 70% or more of the variation in body fat. Additionally, measures of central fat (HC, W C and SSTRI) were important in the prediction of F M ; however, 62 H C and W C were not statistically significant. The model which included H T , W T , M A and SSTRI involved the measurement of 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 p =1.77). Thus, the model with H T , W T and M A was chosen for F M . Similarly, for %Fat, the contribution from SSTRI was significant but not for W C . The equation with B M I , M A and SSTRI, again, involved the measurement of 5 predictor variables and was ruled out. The combination of H T , W T and M A was marginally better (smaller SEE) 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 of the A B D SF 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 by a tighter clustering o f residual data (Svendsen et al., 1991). No excessive trends in the residuals were apparent (ie.homogeneity of variance was not violated). However, the magnetude of 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 of Residuals Dependent Variable: FM 161 ; 1 14' i 1 12 10 -2.50 -1.50 -.50 .50 1.50 2.50 -2.00 -1.00 0.00 1.00 2.00 Regression Standardized Residual 64 (c) Scatter plot of residuals vs. predicted F M •g <u CC In (/> <u a> (D Q T J <U N "E <D " D 55 Dependent Variable: FM 2? - 2 a? O J a? -3 ° • a rf3 a • • • • - 3 - 2 - 1 0 1 2 Regression Standardized Predicted Value (d) Partial regression plot for F M and Height Dependent Variable: FM • D B • • D • • • a o a -6 -10 HEIGHT 20 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: %FAT 4 & C 0) 2 Std. Dev'= .96 Mean = 0.00 N = 43.00 V -2.50 -1.50 -.50 .50 1.50 2.50 -2.00 -1.00 0.00 1.00 2.00 3.00 Regression Standardized Residual (b) Normal P-P plot of regression standardized residual Dependent Variable: %FAT 1.00 .50 JD Q QL B O 25 •o <D 13 <1> Q . U J o.oo 0.00 /  a / • A u u u U D / • / D / .25 .50 Observed Cum Prob 67 (c) Scatter plot of residuals vs. predicted %Fat Dependent Variable: %FAT Regression Standardized Predicted Value (d) Partial regression plot for %Fa t and Height Dependent Variable: %FAT 2 0 -2 • • a a B d? • • • a • ° D O a • o • o J a • D • o • • % • o • -10 0 10 20 HEIGHT 68 (e) Partial regression plot for %Fa t and Weight Dependent Variable: %FAT a a Bo ° • • -20 -10 WEIGHT 30 (f) Partial regression plot for %Fa t and M A Skinfold Dependent Variable: %FAT 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 -.50 0.00 .50 1.00 1.50 2.00 -1.75 -1.25 -.75 -.25 .25 .75 1.25 1.75 2.25 Regression Standardized Residual (b) Normal P-P plot of regression standardized residual Dependent Variable: TFM 0.00 .25 .50 .75 1.00 Observed CumProb 70 (c) Scatter plot of residuals vs. predicted T F M Dependent Variable: TFM 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: TFM 2 L L o g °S • • • 9 10 20 WT 71 (e) Partial regression plot for, T F M and H T Dependent Variable: TFM • ff ° a • tfP -10 HT 10 (f) Partial regression plot for T F M and M A Dependent Variable: TFM • B • • • t a n -10 MA 72 (g) Partial regression plot for T F M and W C Dependent Variable: TFM Figure 4.4.4: Residual Analyses for the New % T F Equation (a) Histogram of residuals Dependent Variable: %TF 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: %TF CD U J 0.00 0.00 .25 .50 Observed Cum Prob (c) Scatter plot of residuals vs. predicted % T F Dependent Variable: %TF 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: %TF L L I- -6 3° ° -10 MA (e) Partial regression plot for % T F and W C Dependent Variable: %TF . 20 10 % TF •10 • • g a a ° "a a cn • -20 W C -10 10 20 30 75 (g) P a r t i a l regression plot for % T F and H T Dependent Variable: %TF -20 HT • a • ° ° " 10 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?2 value and the coefficient of variance (C.V.) , and met the guidelines for acceptable prediction equations (SEE < 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?2 and larger SEE) to those that included a combination of skinfolds and anthropometry. Equations for F M and T F M explained more of the variance in body fat (adj./?2 = .95 and .90, respectively) than the corresponding %Fat and % T F equations (adj.i?2 = .84, .83). However, the precision of the percent fat equations (C.V.%Fat = 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 of S E E and C . V . were more important in the selection and comparison of prediction equations than that of maximum or adj J? . In light of this, the %Fat equation would be recommended over the F M equation. Moreover, %Fat is the measure of 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 of subjects. Averages for the 10 rounds o f regression analysis are summarized in Table 4.5.2. The smaller and closer the error of the residuals is to the S E E of 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 %Fa t Equation Round Mean Diff. b/w Jackknifed Estimate of %Fa t and" D E X A % F a t s.d. (diff) n t P 1 • i ;• 0.096 2.406 4 0.080 0.941 2 1.326 3.395 4 0.781 0.492 3 ' . ' - ' 0.320 . 0.641 4 0.999 0.392 4 -1.211 2.675 4 -0.905 0.432 5 -0.146 1.993 4 -0.146 0.893 6 1.531 0.848 5 4.038 0.016 7 -0.888 2.149 4 -0.826 0.469 8 -1.698 2.767 5 -1.372 0.242 9 -0.173 0.312 5 -1.106 0.349 10 0.659 2.352 4 0.627 0.565 77 Table 4.5.2: J a c k k n i f e d Est imates (average of 10 predic t ion equations and res idual analyses) Pred ic t ion E q n . A d i . R 2 S E E Res idua l Analys i s Dif f . s.d. % F a t 0.835 2.14 % F a t 0.184% 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?2 , minimum SEE and appropriate C p criteria. Regression outcomes are appended (Appendix XIY) . Table 4.6.1: M o d i f i e d P red ic t i on Equat ions Eqn# P red ic t i on E q u a t i o n A d j . R 2 C p S E E C V 5 % F a t = 9.819 + .162(SUM4SF) + .652(BMI) - .261(SS) 0.82 n/a 2.21 6.2% 6 % F a t = 9.198 + .696(BMI)+ .295(TRI) 0.80 n/a 2.37 6.6% 78 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 in both groups o f elderly women, yet accurately predicted %Fat in the younger women. Residual graphs (Figure 4.6.1) indicated that the error in the prediction of %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 of 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 n r Mean Diff. S.D. C V t P % F a t ( B R O D [ ) - E Q N 5 31 .727 6.63 3.91 % F a t ( B A U M ) - E Q N 6 100 .805 5.12 4.45 9.99 11.25 9.44 11.52 <0.001 <0.001 Table 4.6.3: Paired T-Test Comparisons for Younger Women Comparison n r Mean Diff. S.D. C V t p % F a t ( B R O D 2 ) - EC/N5 33 .887 -0.717 5.43 18.37 -0.76 0.454 Table 4.6.4: Limits of Agreement for Modified Equations and D E X A Comparison Difference SD d +/- 2 X SD % F a t ( B R O D , ) - %Fat(Eqn5) 6.63 3.91 -1.19 to 14.45 % F a t ( B A U M ) - %Fat(Eqn6) 5.12 4.45 -4.20 to 14.02 % F a t ( B R O D 2 ) - %Fat(Eqn5) -0.717 5.43 -11.58 to 10.14 79 Figure 4.6.1: Agreement Between Predicted and Measured %Fa t (a) Brodowicz elderly women data -f • — /• Mean =6.63 -10.00 J 1 1 1 1 — 20.00 25.00 30.00 35.00 40.00 Average %Fat 80 (b) Baumgartner data 15.00. 10.00 5.00 H 4V c w. 0.00' -5.00. -10.00. 1 •» • 1 » • • . % « . • >. • . • . » M e a n = 5 . 1 2 ~7 • «• • t • 20.00 30.00 40.00 Average %Fat — i — 50.00 Mean (c) Brodowicz younger women data 10.00. 0> c I 5.00. 0.00. -5.00. -10.00. 20.00 25.00 30.00 35.00 40.00 Average %Fat Mean 81 5. Discussion A review o f the literature indicated that existing anthropometry prediction equations may not be valid for estimating body composition in women 75 years and older. The intent of 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 of age. 5.1 New prediction equations for women 75-80 years A l l but one of 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 of our data, however, revealed strong correlations between anthropometry and D E X A fat and thus supported the development of 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 of anthropometric variables surfaced as the best predictors of body fat: H T , W T , B M I , M A , SSBTRI , W C , and H C (Table 4.4.1). O f these, the M A SF was common to all . A n important finding of 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?2 and S E E values for the new equations were comparable to and in some cases better than those for reported for published equations. Within the current sample of edlerly women, the goodness of fit was better for F M (adj./?2 = 0.95) than for %Fat (adj./?2 = 0.84) due to slightly lower correlations for anthropometry and %Fat than for 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 l ikely 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 of 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 of the corresponding jackknifed equation indicated good internal validity for the %Fat equation (Table 4.5.2). Several factors affect the development and performance of 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 of these is discussed further to help explain differences between our new equations and published equations, and why 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 of 75 and 80 years. A l l subjects were considered healthy and were l iving independently in the community. Although the demographics of this sample may not be representative of 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 of different ethnic and cultural background. The average age of our participants exceeded most other studies in which equations were derived by approximately 7 years (Table 4.2.1). This was an important distinction as one of 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 by Baumgartner (1995), then it would be reasonable to expect that equations carefully derived in 60 year old women would not perform as well when applied to women in the their 70's and 80's. This could explain why the Goran equation (4C), derived in women of average age 68, did not predict body fat adequately in 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 in our sample. This study had a relatively small n of 17, thus limiting the precision and accuracy of the prediction equation. A l l four equations showed a similar lack of agreement with D E X A body fat measurements (Figure 4.3.1). Therefore, it was difficult to isolate and comment on the effects of age. To our knowledge, the only other database involving a large group of women over the age of 75 where D E X A (or 4C model) was used to measure body composition is that of Baumgartner et al. (Baumgartner et al., 1995); however, no equations were derived for this group. 5.3 Predictor variables Predictor variables measured in 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 of robust prediction equations. A range of SF '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 of existing equations indicated that HT , W T , B M I , S U M 4 S F , TRI , C A L F , SSTRI and H C are the most common predictors of body fat in elderly women. The best individual predictors of.body fat in 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 in any other equation perhaps because it is not often measured in body composition studies. The M A SF was not as strongly correlated to body fat as some of the other skinfolds, yet significantly contributed to the explanation in 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 of M A . Moreover, the M A SF may be related to the internalization of body fat which was not explained by B I C or TRI . Clearly, the M A skinfold should be considered a useful predictor of body fat in elderly women in the future. Other studies have shown that SF'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 of 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 in %Fat and F M , respectively in this study sample. However W T and H T together seemed to explain the variation in 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 of the SF in the elderly because of changes in compressibility and elasticity of the SF, reduced muscle tone, and the internalization of body fat (Baumgartner et al., 1995). Repeated measures tests for the various SF ' s (Table 4.1.4), and scatter plots with body fat indicated that SF's are reliable and useful measures for body composition prediction in elderly women. Moreover, there is no evidence that this relationship diminishes with age in our sample. Perhaps the problems associated with U W W have contributed to earlier observations of poor agreement between anthropometry and body fat in the elderly. 5.4 Criterion body fat The measurement of body composition in the elderly has been a topic of great debate in the literature. Clearly, 3C and 4C 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; Will iams et al., 1995). Reference body fat was measured by D E X A (QDR-4500W; Hologic, Inc.) in this study and, therefore, not subject to the measurement errors associated with U W W and the 2C model. The fan-beam technology o f the QDR-4500 is considered more accurate than pencil- beam scanners in the assessment of body composition due to superior sampling techniques, and has demonstrated high accuracy when compared to 4C measures o f F M and F F M in elderly persons (Ke l ly et al., 1997; Visser et al., 1998). Additionally, the QDR-4500 has demonstrated low measurement error (300g) for F M (Kelly, 1998a). Existing equations standardized to D E X A used earlier models of D E X A as wel l as different manufacturers (Chapman et al., 1998; Svendsen et al., 1991), and therefore it is l ikely that the new equations are an improvement over these. Equations based on 4C 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; Wil l iams et al., 1995). However, where accuracy is gained in the 4C model, precision may be lost due to an accumulation of error associated with the use o f multiple assessment techniques (Guo et al., 1996). A final advantage in using the QDR-4500 instrumentation in our study is the connection to epidemiological research. The National Institute of 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 in their study on health, aging and body composition (Health A B C ) (Kel ly , 1999). Body composition predicted by 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 in 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 3C and 4C models compared more closely to current D E X A F M than did published 2C %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 in the literature that U W W , together with Siri 's formula, erroneously overestimates fatness in the elderly. Two studies seemed to be outside the range of 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 in measuring trunk fat (Kohrt, 1998; Snead et al. , 1993). This could also explain the poor performance of the Svendsen equation in our sample despite other similarities in the methodology of these two studies. Will iams and colleagues (1995) used 4C methods to measure body composition in older adults (49-80 yrs) and reported average fat values of 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 of 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 of total body mass may be related to an error in the measurement of the F F M component and may not affect the measure o f F M . D E X A ' s accuracy in the measurement of 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 of 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./?2, min. S E E and appropriate C p criteria when selecting the final equations. To my knowledge, the only other studies that used all possible subsets regression procedures were those of Dupler (1997) and Durnin and Womersley (1974). 89 Based on these statistical criteria, there were little differences between the best subsets described in Table 4.4.1. The recommended number o f prediction variables for a sample of 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 of the variance in body fatness. The addition of the central fat measure did not markedly improve the precision or predictability of the F M or %Fat equations. However, H C was important in the prediction of body fat in both the Goran and Dupler equations. A s expected, central fat measurements contributed significantly to the prediction and precision of 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, in the younger .sample, %Fat was significantly predicted but not F M . This was unexpected. Further analysis showed that the limits of agreement for predicted and measured fat were much wider in the younger sample than for the samples of elderly women. These results emphasize the importance of examining the agreement between two methods recommended by Bland and Altman (1986) and of 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 in external samples. One, the best predictors of body fat in elderly women were not measured in these independent samples and therefore a lesser equation was tested. Two, M A and H C may become increasingly important in the prediction of body fat in elderly women. Three, inter-rater differences in the measurement of 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 DEXA. 5.7 Summary and recommendations An 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 3C model for criterion fat in elderly women and the first study to use the QDR-4500 version of D E X A . The use o f QDR-4500 in two future national surveys conducted by the N I H w i l l enable the comparison of body fat predicted by the new equation to a large normative database related to health, body composition and aging. 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 D E X A and anthropometry in elderly women. 92 6. References 1. Baumgartner, R., Koehler, K . , Gallagher, D . , Romero, L . , Heymsfield, S., Ross, R., Garry, P., & Lindeman, R. (1998). 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Appendices 101 > u « 3 cu 6J5 C co l < cu , M l \< a ct s b O N I vo S 3 CQ CO CQ O N H fe SI 2 s S oo V O fe oo 0 £ U oo V O l i f vn vo b C N o oo O S \v~> vo 3 fe" ffl OO £ u CQ s § H Q. >- Q > fe fe fe fe s .2 "O E 2 U £ u U s leg m 2 Q •* •* O N O N O N O N 1—1 »—' ca ca ( U U t-l u <D V is  V is O N O N icB O N O N o ca t-i \S vo O N O N ca -»-» 102 cv  N/ A  2. 5%  4. 0%  0. 8%  N /A  os 1. 1% ' 1. 0%  S E E  i 1. 95  k g 0. 92 8  1. 09  0. 00 82  N /A  2. 43  0. 01 13  0. 01 00  0. 96  0. 62 6 0. 84 1 N /A  oo ©' 0. 58  0. 67  Z, t-» r- >/-> r-- m ro (N oo fN .—H oo CN A ge  r an ge  76 -9 5 (m = 82 ) 65 -8 1 (m = 70 ) 65 -8 1 (m = 70 ) 50 -6 8 68 .2  I/O 60 -8 7 (m = 70 .2 ) 60 -8 7 (m = 70 .2 ) E qu at io n F F M (k g)  =  0 .5 82 (W T ) - 0. 39 7( T R I)  +  0 .3 92 (H T ) - 48 .9 56  . FM  =  W T  -  F F M  (a )% F at  =  0 .1 68 8( B M I)  +  0 .5 42 (H C ) - 0. 16 39 (W T ) - 7. 94 98  (b )F M  =  0 .2 44 9( W T ) +  0 .5 21 8( H C ) - 0. 07 6( T C ) - 37 .8 61 9 D b =  1 .1 33 9 - 0. 06 45  [ lo g (B IC  +  T R I +  S I +  S S )]  % Fa t =  4 95 /D b - 45 0 FM  =  0 .3 1( H C ) +  0 .2 2( C A L F ) +  0 .3 1( W T ) - 31 .3 3 FM  =  0  . 63 (T R I) + 4. 47 (B M I) + 9. 32 (S U B T R I) + 1. 35 (W T )+ 1. 04 (H T ) -1 92 .4 8 (a ) D b =  -  0 .0 35 6[ lo g( B IC  +  T R I +  S I +  S S )]  + 1 .0 6 8 8 ' % F at  =  4 95 /D b - 45 0 o SO © + ST © (N j= o <n 9 $ II I Q £ N= A ut ho r C ha pm an , 19 98  D up le r,  1 99 7 D up le r,  1 99 7 D ur ni n &  W om er sl ey , 19 74  G or an , 19 97  S ve nd se n et  a l. , 19 91  V is se r et  a l. , 19 94  V is se r et al .,  1 99 4 103 Appendix III: Med ica l Clearance UBC Department of Family Practice and the Seniors inter Action Society March 25th, 1998 Dear Doctor: Your 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. Your 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 of 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 of the twelve weeks, participants w i l l continue their exercises independently either at U B C or a fitness centre of 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 of 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 of this investigation is to examine the effects of a progressive strength training program on measures of 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 of a short (12 week) and long term (1 year) progressive resistance exercise program on muscular strength and endurance of the large muscles of the body; 2. To assess the effect of a one-year resistance exercise program on the maintenance of bone mineral density; 3. To determine changes in body composition (body fatness) following a short and long term resistance exercise program; 4. To assess the impact of short (12 week) and long term resistance training on balance and functional abilities; 5. To evaluate the relationship between strength gains and improvements in functional status 6. To explore the influence of a regular exercise program on the quality of life and psychological health in older adult women; 7. To assess exercise compliance in this population. 105 Y o u w i l l perform tests of 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 of tests and experiment wi l l ingly and may withdraw at any time. Additionally, your identity and test results w i l l be kept in confidence andSwill become the property of the above investigators. For safety, exercise trainers w i l l have acqess to your personal and medical information. 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. C O N S E N T Date: Subject: Witness: (print) (print) (signature) (signature) 106 Appendix VI: L i s t of Contact Authors Authors Wattanapenpaiboon N . , Lukito W. , Strauss B . J . , Hsu-Hage B . H . , Wahlqvist M . L . and Stroud D . B . Institution Monash University Department of Medicine, Monash medical Centre, Melbourne, Australia Title Agreement o f skinfold measurement and bioelectrical impedance analysis (BIA) methods with dual energy X-ray absorptiometry ( D E X A ) in estimating total body fat in Anglo-Celtic Australians Source International Journal of 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 . , McClung M . R . and Althoff S.A. Institution Dep. Public Health Education, Portland State University, Portland, Oregon Title Measurement o f body composition in 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 of body-composition techniques and models for detecting change in soft tissue with strength training. Source American Journal of Cl inical Nutrition 63(5). 1996. 678-686. Subjects 39 women ages 50-70 years. 108 Related Methods Body 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 of measurement of 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 of Medicine, University of New Mexico . Source Journal o f Gerontology: Medical Sciences. 1995. 50A(6), M307-M316. Title Cross-sectional age differences in body composition in persons 60+ years o f age. Subjects 181 women ages 60-95 years Related methods Body composition was quantified using D E X A and anthropometry (4 skinfold sites) Authors Hansen N . J . , Lohman T .G. , Going S.B., Ha l l M . C . , Pamenter R . W . , Bare L . A . , Boyden T.W. and Houtkooper L . B . Institution Departments of Exercise and Sport Sciences and of Nutrition and Food Science, University of Arizona and Department of Veterans Affairs Medical Center, Tucson, Arizona Source Journal o f Appl ied Physiology. 1993. 75(4), 1637-41. Subjects 100 women ages 28-39 years Related methods Body composition was assessed using D E X A and anthropometry (9 skinfold sites) 109 Appendix VII: Letter of Request for Data To Whom It M a y Concern: I am a graduate student in the School of Human Kinetics at the University of British Columbia and currently working on my thesis for a Masters o f Science degree under the supervision of Dr . A l a n D . Martin. The primary objective of my research is to examine the relationship between anthropometry and body composition measured by dual-energy x-ray absorptiometry in 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 of elderly women w i l l help us to evaluate its stability and accuracy. Additionally, applying our equation to data bases of 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 of 75 years. In order to pursue the secondary purpose of my research, requests for additional data bases are necessary. Recent work conducted by you and your colleagues (reference) is of interest to me and I would greatly appreciate your permission to access this data for secondary analysis. The intended use of 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. We 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: Abdominal SF Thickness Figure 2: Biceps SF Thickness 5.0 15.0 25.0 35.0 45.0 10.0 20.0 30.0 40.0 50.0 5.0 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 3: C a l f SF Thickness Figure 4: Midaxilary SF Thickness 12.5 17.5 22.5 27.5 32.5 37.5 15.0 20.0 25.0 30.0 35.0 40.0 J7 Nl Ml N N 5.0 10.0 15.0 20.0 25.0 30.0 35.0 7.5 12.5 17.5 22.5 27.5 32.5 37.5 112 Figure 5: Suprailiac SF Thickness Figure 6: Subscapular SF Thickness 2.5 7.5 12.5 17.5 22.5 27.5 32.5 5.0 10.0 15.0 20.0 25.0 30.0 35.0 5.0 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 7: Thigh 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 Figure 8: Triceps SF Thickness 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 Figure 10: SSTRI Ratio 20.0 40.0 60.0 80.0 100.0 120.0 140.0 .38 .50 .63 .75 .88 1.00 1.13 1.25 30.0 50.0 70.0 90.0 110.0 130.0 .44 .56 .69 .81 ' .94 1.06 1.19 113 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 Variables Entered/Removed3 Regression for F M Model Variables Entered Variables Removed Method 1 WEIGHT Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). 2 HEIGHT Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). 3 MIDAX1 Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). 4 subscap/tric eps sf ratio Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). a. Dependent Variable: total fat mass in kg 115 Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .948a .898 .895 2.2763 2 .970b .941 .938 1.7558 3 .978° .956 .953 1.5326 4 .980d .961 .957 1.4565 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 ANOVAe Model Sum of Squares df Mean Square F Sig. 1 Regression 1865.484 1 1865.484 360.013 .000a Residual 212.450 41 5.182 Total 2077.934 42 2 Regression 1954.617 2 977.309 317.008 .000b Residual 123.317 40 3.083 Total 2077.934 42 3 Regression 1986.324 3 662.108 281.870 .000° Residual 91.610 39 2.349 Total 2077.934 42 4 Regression 1997.325 4 499.331 235.389 .000d Residual 80.609 38 2.121 Total 2077.934 42 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 e. Dependent Variable: total fat mass in kg 116 Coefficients 3 Standardiz ed Unstandardized Coefficient Coefficients s Model B Std. Error Beta t Sig. 1 (Constant) -16.509 2.152 -7.672 .000 WEIGHT ^607 .032 .948 18.974 .000 2 (Constant) 18.731 6.761 2.771 .008 WEIGHT .664 .027 1.037 24.721 .000 HEIGHT -.247 .046 -.225 -5.377 .000 3 (Constant) 16.462 5.934 2.774 .008 WEIGHT .611 .028 .953 22.156 .000 HEIGHT -.231 .040 -.211 -5.735 .000 MIDAX1 .143 .039 .146 3.674 .001 4 (Constant) 18.295 5.696 3.212 .003 WEIGHT .624 .027 .974 23.247 .000 HEIGHT -.238 .038 -.217 -6.193 .000 MIDAX1 .166 .038 .170 4.328 .000 subscap/triceps sf ratio -2.854 1.253 -.082 -2.277 .028 a. Dependent Variable: total fat mass in kg Excluded Variables 6 Model Beta In t Sig. Partial Correlation Collinearity Statistics Tolerance 1 HEIGHT -.225a -5.377 .000 -.648 .844 BMI .423a 5.320 .000 .644 .237 TRISF1 .293a 4.949 .000 .616 .451 SUBSCAP1 .185a 2.736 .009 .397 .472 MIDAX1 .171 a 3.213 .003 .453 .720 BICEP1 .373 a 4.396 .000 .571 .239 ILIAC1 .163a 2.925 .006 .420 .676 ABD1 ,131a 2.218 .032 .331 .651 THIGHSF1 .1>30a. 2.461 .018 .363 .790 CALFSF1 .Q99a 1.623 .112 .249 .642 SUM4SF .321a " 4.751 .000 .601 .357 WAISTG1 .180a 1.791 .081 .272 .234 HIPG1 .215a 1.951 .058 .295 .193 WHR .029a .528 .600 .083 .827 subscap/triceps sf ratio -.018a -.324 .748 -.051 .858 117 Excluded Variables 6 Collinearity Partial Statistics Model Beta In t Sig. Correlation Tolerance 2 BMI .084b .149 .883 .024 4.806E-03 TRISF1 .187b 3.141 .003 .449 .342 SUBSCAP1 .050b .781 .440 .124 .361 MIDAX1 .146b 3.674 .001 .507 .712 BICEP1 .257b 3.444 .001 .483 .210 I LI AC 1 .105b 2.285 .028 .344 .631 ABD1 '.085b 1.807 .078 .278 .628 THIGHSF1 .045b .963 .341 .152 .667 CALFSF1 .066b 1.369 .179 .214 .630 SUM4SF .200b 2.951 .005 .427 .272 WAISTG1 -.017b -.185 .854 -.030 .186 HIPG1 .149b .1 -722 .093 .266 .189 WHR -.037b -.844 .404 -.134 .762 subscap/triceps sf ratio -.041b -.982 .332 -.155 .849 3 BMI -.232c -.467 .643 -.076 4.661E-03 TRISF1 .113° 1.795 .081 .280 -.268 SUBSCAP1 -.059° -.935 .356 -.150 .281 BICEP1 .158° 1.885 .067 .292 .151 ILIAC1 .013° .243 .809 .039 .384 ABD1 .012° .246 .807 .040 .478 THIGHSF1 .039 c .939 .354 .151 .666 CALFSF1 .025° .568 .573 .092 .583 SUM4SF .073 c .838 .407 .135 .149 WAISTG1 -.123° -1.519 .137 -.239 .166 HIPG1 .127 c 1.665 .104 .261 .187 WHR -.071° -1.862 .070 -.289 .726 subscap/triceps sf ratio -.082° -2.277 .028 -.347 .791 4 BMI .074d .149 .882 .025 4.291 E-03 TRISF1 .070d 1.048 .301 .170 .229 SUBSCAP1 .118d 1.249 .220 .201 .112 BICEP1 .152d 1.902 .065 .298 .151 ILIAC1 .018d .342 .734 .056 .384 ABD1 .022d .474 .638 .078 .473 THIGHSF1 .014d .328 .745 .054 .608 CALFSF1 .008d .190 .851 .031 .564 SUM4SF .114d 1.359 .182 .218 .143 WAISTG1 -.041d -.436 .666 -.071 .120 HIPG1 .092d 1.219 .231 .196 .177 WHR -.040d -.955 .346 -.155 .571 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 Appendix XI: Stepwise Multiple Regression Analyses (a) Equation development for F M Variables Entered/Removed3 Model Variables Entered Variables Removed Method 1 WT Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). 2 HT Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). 3 MA Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). 4 subscap/tric eps sf ratio Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). a. Dependent Variable: total fat mass in kg 119 Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .948 a .898 .895 2.2763 2 .970b .941 .938 1.7558 3 .978 c .956 .953 1.5326 4 .980d .961 .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 ANOVAe Sum of Mean Model Squares df Square F Sig. 1 Regression 1865.484 1 1865.484 360.013 .000a Residual 212.450 41 5.182 Total 2077.934 42 2 Regression 1954.617 2 977.309 317.008 .000b Residual 123.317 40 3.083 Total 2077.934 42 3 Regression 1986.324 3 662.108 281.870 .000 c Residual 91.610 39 2.349 Total 2077.934 42 4 Regression 1997.325 4 499.331 235.389 .000d Residual 80.609 38 2.121 Total 2077.934 42 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 e. Dependent Variable: total fat mass in kg 120 Coefficients 3 Unstandardized Coefficients Standardiz ed Coefficient s Model B Std. Error Beta t Sig. 1 (Constant) -16.509 2.152 -7.672 .000 WT .607 .032 .948 18.974 .000 2 (Constant) 18.731 6.761 2.771 .008 WT .664 .027 1.037 24.721 .000 HT -.247 .046 -.225 -5.377 .000 3 (Constant) 16.462 5.934 2.774 .008 WT .611 .028 .953 22.156 .000 HT -.231 .040 -.211 -5.735 .000 MA .143 .039 .146 3.674 .001 4 (Constant) 18.295 5.696 3.212 .003 WT .624 .027 .974 23.247 .000 HT -.238 .038 -.217 -6.193 .000 MA .166 .038 .170 4.328 .000 subscap/triceps sf ratio -2.854 1.253 -.082 -2.277 .028 a. Dependent Variable: total fat mass in kg 121 Excluded Variables' Partial Collinearity Statistics Model Beta In t Sig. Correlation Tolerance 1 HT -.225a -5.377 .000 -.648 .844 BMI .423a 5.320 .000 .644 .237 ABD .131 a 2.218 .032 .331 .651 MA . .171 a 3.213 .003 .453 .720 SI :163 a 2.925 .006 .420 .676 SS .185a 2.736 .009 .397 .472 SUM4SF .321 a 4.751 .000 .601 .357 subscap/triceps sf ratio '- ;018a -.324 .748 -.051 .858 WC .180a 1.791 .081 .272 .234 HC .215a 1.951 .058 .295 .193 2 BMI .084b .149 .883 .024 4.806E-03 ABD .085b 1.807 .078 .278 .628 MA .146b 3.674 .001 .507 .712 SI .105b 2.285 .028 .344 .631 SS .050b .781 .440 .124 .361 SUM4SF .200b 2.951 .005 .427 .272 subscap/triceps sf ratio -.041b -.982 .332 -.155 .849 WC -.017b -.185 .854 -.030 .186 HC .149b 1.722 .093 .266 .189 3 BMI -.232° -.467 .643 -.076 4.661 E-03 ABD .012 c .246 .807 .040 .478 SI .013C .243 .809 .039 .384 SS -.059° -.935 .356 -.150 .281 SUM4SF .073 c .838 .407 .135 .149 subscap/triceps sf ratio -.082° -2.277 .028 -.347 .791 WC -.123° -1.519 .137 -.239 .166 HC .127 c 1.665 .104 .261 .187 4 BMI .074d .149 .882 .025 4.291 E-03 ABD .022d .474 .638 .078 .473 SI .018d .342 .734 . .056 .384 SS .118d 1.249 .220 .201 .112 SUM4SF .114d 1.359 .182 .218 .143 WC -.041d -.436 .666 -.071 .120 HC .092d 1.219 .231 .196 .177 a. Predictors in the Model: (Constant), WT 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 Variables Entered/Removed3 Model Variables Entered Variables Removed Method 1 SUM4SF Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). 2 BMI Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). 3 MA • Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). 4 SUM4SF Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). 5 subscap/tric eps sf ratio Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). a. Dependent Variable: PCFAT 123 Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .867 a .751 .745 2.6606 2 .901 b .811 .802 2.3474 3 .920 c .847 .835 2.1396 4 .918d .843 .835 2.1385 5 .928 e .861 .851 2.0382 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 f Sum of Mean Model Squares df Square F Sig. 1 Regression 876.879 1 876.879 123.873 .000a Residual 290.232 41 7.079 Total 1167.111 42 2 Regression 946.696 2 473.348 85.901 .000b Residual 220.415 40 5.510 Total 1167.111 42 3 Regression 988.565 3 329.522 71.978 .000c Residual 178.546 39 4.578 Total 1167.111 42 4 Regression 984.181 2 492.091 107.602 .000d Residual 182.929 40 4.573 Total 1167.111 42 5 Regression 1005.099 3 335.033 80.650 .000e Residual 162.011 39 4.154 Total 1167.111 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: PCFAT 124 Coefficients 3 Unstandardized Coefficients Standardiz ed Coefficient s Model B Std. Error Beta t Sig. 1 (Constant) 20.711 1.418 14.608 .000 SUM4SF .171 .015 .867 11.130 .000 2 (Constant) 11.548 2.862 4.035 .000 SUM4SF 9.503E-02 .025 .481 3.755 .001 BMI .598 .168 .456 3.560 .001 3 (Constant) 7.950 2.867 2.773 .008 SUM4SF 3.070E-02 .031 .156 .979 .334 BMI .755 .162 .576 4.670 .000 MA .220 .073 .301 3.024 .004 4 (Constant) 6.157 2.204 2.794 .008 BMI .882 .096 .674 9.220 .000 MA .268 .053 .367 5.019 .000 5 (Constant) 7.139 2.146 3.327 .002 BMI .932 .094 .711 9.931 .000 MA .300 .053 .410 5.672 .000 subscap/triceps sf ratio -3.949 1.760 -.151 -2.244 .031 a. Dependent Variable: PCFAT Excluded Variables' Partial Collinearity Statistics Model Beta In .> t Sig. Correlation Tolerance 1 HT ,-.125a -1.637 .109 -.251 .998 WT .166a 1.286 .206 .199 .357 BM| . .456a 3.560 .001 .490 .287 ABD ... .015a .113 .911 .018 .376 MA .151 a 1.304 .200 .202 .442 SI -.122a -.780 .440 -.122 .249 SS -.314a -1.641 .109 -.251 .159 subscap/triceps sf ratio -.153a -1.764 .085 -.269 .769 WC .157a 1.125 .267 .175 .309 HC .185a 1.459 .152 .225 .366 2 HT -.066b -.929 .359 -.147 .931 WT -.136b -.934 .356 -.148 .222 ABD .101b .880 .384 .140 .360 MA .301b 3.024 .004 .436 .397 SI .133b .851 .400 .135 .196 SS -.405b -2.473 .018 -.368 .156 subscap/triceps sf ratio -.147b -1.937 .060 -.296 .769 WC -.160b -1.045 .302 -.165 .201 HC .013b .105 .917 .017 .298 125 Excluded Variables' Partial Collinearity Statistics Model Beta In t Sig. Correlation Tolerance 3 HT : ... -.078° -1.202 .237 -.191 .928 WT -.148° -1.120 .270 -.179 .222 ABD • .071° .675 .504 .109 .357 SI .068c .471 .640 .076 .191 SS ' . -.368c -2.456 .019 -.370 .155 subscap/triceps sf ratio -167 c -2.484 .018 -.374 .763 WC -.246° -1.774 .084 -.277 .194 HC .041 c .352 .727 .057 .296 4 HT -.067d -1.042 .304 -.165 .948 WT -.123d -.939 .354 -.149 .228 ABD .098d 1.085 .285 .171 .480 SI .104d 1.030 .309 .163 .383 SS -.128d -1.080 .287 -.170 .277 subscap/triceps sf ratio -.151d -2.244 .031 -.338 .785 WC -.219d -1.590 .120 -.247 .198 HC .071d .642 .525 .102 .329 SUM4SF .156d .979 .334 .155 .155 5 HT -.059e -.963 .342 -.154 .945 WT -.117e -.935 .356 -.150 .228 ABD .116 e 1.355 .183 .215 .476 SI .110 e 1.146 .259 .183 .383 SS .155 e .884 .382 .142 .117 WC -.100e -.651 .519 -.105 .154 HC .033 e .306 .761 .050 .320 SUM4SF .218e 1.442 .158 .228 .151 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: PCFAT (c) Equat ion development for T F M 126 Variables Entered/Removed3 Model Variables Entered Variables Removed Method 1 WC Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). 2 WT Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). 3 SI Stepwise (Criteria: Probability- of-F-to-ent er<= .050, Probability- of-F-to-rem ove >= .100). a. Dependent Variable: trunk fat mass in kg Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .922 a .850 .846 1.6034 2 .937 b .879 .873 1.4581 3 .951 c .904 .896 1.3163 a. Predictors: (Constant), WC b. Predictors: (Constant), WC, WT c. Predictors: (Constant), WC, WT, SI 127 ANOVAd Sum of Mean Model Squares df Square F Sig. 1 Regression 595.217 1 595.217 231.519 .000a Residual 105.408 41 2.571 Total 700.624 42 2 Regression 615.581 2 307.790 144.768 .000b Residual 85.044 40 2.126 Total 700.624 42 3 Regression 633.054 3 211.018 121.794 .000° Residual 67.571 39 1.733 Total 700.624 42 a. Predictors: (Constant), WC b. Predictors: (Constant), WC, WT c. Predictors: (Constant), WC, WT, SI d. Dependent Variable: trunk fat mass in kg Coefficients 3 Unstandardized Coefficients Standardiz ed Coefficient s Model B Std. Error Beta t Sig. 1 (Constant) -16.594 1.886 -8.797 .000 WC .326 .021 .922 15.216 .000 2 (Constant) -15.772 1.736 -9.086 .000 WC .217 .040 .613 5.383 .000 WT .131 .042 .353 3.095 .004 3 (Constant) -14.317 1.633 -8.769 .000 WC .178 .038 .504 4.648 .000 WT .124 .038 .333 3.230 .003 SI .124 .039 .203 3.176 .003 a. Dependent Variable: trunk fat mass in kg 128 Excluded Variables'1 Partial Collinearity Statistics Model Beta In t Sig. Correlation Tolerance 1 HT .016a .258 .798 .041 .979 WT .353 a 3.095 .004 .440 .234 BMI .329 a 2.800 .008 .405 .228 ABD .142a 1.899 .065 .288 .620 MA .192a 2.721 .010 .395 .638 SI .215 a 3.038 .004 .433 .610 SS .123 a 1.092 .281 .170 .287 subscap/triceps sf ratio -.094a -1.283 .207 -.199 .669 2 HT -.117b -1.795 .080 -.276 .672 BMI .210b 1.660 .105 .257 .181 ABD .115b 1.660 .105 .257 .609 MA .190b 3.030 .004 .437 .638 SI .203b 3.176 .003 .453 .608 SS .139b 1.367 .179 .214 .286 subscap/triceps sf ratio -.031b -.427 .672 -.068 .600 3 HT -.093c -1.547 .130 -.243 .659 BMI .159° 1.357 .183 .215 .177 ABD -.041° -.469 .641 -.076 .330 MA .114° 1.508 .140 .238 .421 SS .004° .040 .968 .007 .225 subscap/triceps sf ratio -.040° -.625 .536 -.101 .599 a. Predictors in the Model: (Constant), WC b. Predictors in the Model: (Constant), WC, WT c. Predictors in the Model: (Constant), WC, WT; SI' d. Dependent Variable: trunk fat mass in kg (d) Equation development for % T F 129 Variables Entered/Removed3 Variables Variables Model Entered Removed Method 1 Stepwise (Criteria: Probability- of-F-to-ent WC er <= .050, Probability- of-F-to-rem ove >= .100). 2 Stepwise (Criteria: Probability- of-F-to-ent MA er <= .050, Probability- of-F-to-rem ove >= .100). 3 Stepwise (Criteria: Probability- of-F-to-ent HT er <= .050, Probability- I of-F-to-rem I ove >= | .100). a. Dependent Variable: PCTRUNK Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .832a .693 .686 3.7574 2 .892b .796 .786 3.0987 3 .918° .843 .831 2.7574 a. Predictors: (Constant), WC b. Predictors: (Constant), WC, MA c. Predictors: (Constant), WC, MA, HT 130 ANOVAd Model Sum of Squares df Mean Square F Sig. 1 Regression 1306.671 1 1306.671 92.554 .000a Residual 578.834 41 14.118 Total 1885.505 42 2 Regression 1501.422 2 750.711 78.182 .000b Residual 384.083 40 9.602 Total 1885.505 42 3 Regression 1588.977 3 529.659 69.662 .000c Residual 296.528 39 7.603 Total 1885.505 42 a. Predictors: (Constant), WC b. Predictors: (Constant), WC, MA c. Predictors: (Constant), WC, MA, HT d. Dependent Variable: PCTRUNK Coefficients 3 Unstandardized Coefficients Standardiz ed Coefficient s Model B Std. Error Beta t Sig. 1 (Constant) -7.388 4.421 -1.671 .102 WC .482 .050 .832 9.621 .000 2 (Constant) - -3.812 3.731 -1.022 .313 WC .342 .052 .591 6.611 .000 MA .374 .083 .402 4.504 .000 3 (Constant) 30.659 10.687 2.869 .007 WC .356 .046 .614 7.697 .000 MA .387 .074 .416 5.222 .000 HT -.227 .067 -.218 -3.393 .002 a. Dependent Variable: PCTRUNK 131 Excluded Variables'1 Partial Collinearity Statistics Model Beta In t Sig. Correlation Tolerance 1 HT -.202a -2.440 .019 -.360 .979 WT -.112a -.619 .539 -.097 .234 BMI .328a 1.862 .070 .282 .228 ABD ,288a 2.837 .007 .409 .620 MA .402a 4.504 .000 .580 .638 SI .384a 4.078 .000 .542 .610 SS .314a 2.012 .051 .303 .287 subscap/triceps sf ratio .004a .034 .973 .005 .669 2 HT -.218b -3.393 .002 -.477 .977 WT -.116b -.784 .438 -.125 .234 BMI .350b 2.490 .017 .370 .228 ABD .131b 1.303 .200 .204 .495 SI .219b 2.020 .050 .308 .403 SS .125b .882 .383 .140 .254 subscap/triceps sf ratio -.036b -.409 .685 -.065 .662 3 WT .195 c 1.237 .224 .197 .160 BMI .175 c 1.165 .251 .186 .177 ABD .125° 1.400 .170 .221 .495 SI .177 c 1.807 .079 .281 .396 SS -.005c -.035 .973 -.006 .231 subscap/triceps sf ratio -.045° -.570 .572 -.092 .662 a. Predictors in the Model: (Constant), WC b. Predictors in the Model: (Constant), WC, MA c. Predictors in the Model: (Constant), WC, MA, HT d. Dependent Variable: PCTRUNK ^ > (e) Equation development for F M using SF's only 132 Variables Entered/Removed3 Model Variables Entered Variables Removed Method 1 BICEP1 Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). 2 CALFSF1 Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). a. Dependent Variable: total fat mass in kg Model Summary ' Std. Error of 1 J Adjusted R the Model R R Square ,• Square Estimate j 1 I .916 a .839 .835 2.8602 I 2 1 .930b .864 .857 2.6572 I a. Predictors: (Constant), BICEP1 b. Predictors: (Constant), BICEP1, CALFSF1 ANOVA c Sum of Mean Model Squares df Square F Sig. 1 Regression 1742.512 1 1742.512 212.995 .000a Residual 335.422 41 8.181 Total 2077.934 42 2 Regression 1795.508 2 897.754 127.149 .000b Residual 282.426 40 7.061 Total 2077.934 42 a. Predictors: (Constant), BICEP1 b. Predictors: (Constant), BICEP1, CALFSF1 c. Dependent Variable: total fat mass in kg 133 Coefficients' Unstandardized Coefficients Standardiz ed Coefficient s Model B Std. Error Beta t Sig. 1 (Constant) 5.578 1.322 4.221 .000 BICEP1 .912 .063 .916 14.594 .000 2 (Constant) 3.379 1.467 2.304 .027 BICEP1 .810 .069 .813 11.712 .000 CALFSF1 .163 .060 .190 2.740 .009 a. Dependent Variable: total fat mass in kg Excluded Variables 0 Partial Collinearity Statistics Model Beta In t Sig. Correlation Tolerance 1 ABD .007a .083 .934 .013 .510 MA -.001a -.013 .990 -.002 .534 SI -.003a -.039 .969 -.006 .494 SS .119 a 1.138 .262 .177 .359 TRISF1 .221 a 1.980 .055 .299 .294 CALFSF1 .190a 2.740 .009 .397 .706 THIGHSF1 .056a .751 .457 .118 .705 SUM4SF .204a 1.270 .211 .197 .151 2 ABD -.068b -.784 .438 -.125 .462 MA -.053b -.644 .523 -.103 .507 SI -.035b -.411 .684 -.066 .485 SS .111b 1.141 .261 .180 .359 TRISF1 .188b 1.779 .083 .274 .290 THIGHSF1 -.028b -.357 .723 -.057 .583 SUM4SF .155b 1.026 .311 .162 .149 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 Variables Entered/Removed3 Model Variables Entered Variables Removed Method 1 SUM4SF Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). 2 CALFSF1 Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). a. Dependent Variable: PCFAT Model Summary Std. Error of Adjusted R the Model R R Square Square Estimate 1 .867 a .751 .745 2.6606 2 .885b .783 .772 2.5189 a. Predictors: (Constant), SUM4SF b. Predictors: (Constant), SUM4SF, CALFSF1 ANOVA c Sum of Mean Model Squares df Square F Sig. 1 Regression 876.879 1 876.879 123.873 .000a Residual 290.232 41 7.079 Total 1167.111 42 2 Regression 913.324 2 456.662 71.976 .000b Residual 253.786 40 6.345 Total 1167.111 42 a. Predictors: (Constant), SUM4SF , b. Predictors: (Constant), SUM4SF, CALFSF1 c. Dependent Variable: PCFAT 135 *> Coefficients1 Unstandardized Coefficients Standardiz ed Coefficient s Model B Std. Error Beta t Sig. 1 (Constant) 20.711 1.418 14.608 .000 SUM4SF .171 .015 .867 11.130 .000 2 (Constant) 19.172 1.488 12.885 .000 SUM4SF .149 .017 .753 8.599 .000 CALFSF1 .135 .056 .210 2.397 .021 a. Dependent Variable: PC FAT Excluded Variables 0 Partial Collinearity Statistics Model Beta In t Sig. Correlation Tolerance 1 ABD .015a .113 .911 .018 .376 MA .151 a 1.304 .200 .202 .442 SI -.122a -.780 .440 -.122 .249 SS -.314a -1.641 .109 -.251 .159 TRISF1 .250a 1.194 .240 .185 .137 BICEP1 .336a 1.718 .093 .262 .151 CALFSF1 .210a 2.397 .021 .354 .708 THIGHSF1 .058a .604 .550 .095 .671 2 ABD -.06'7b -.530 .599 -.085 .350 MA .105b .930 .358 .147 .427 SI -.120b -.809 .424 -.128 .249 SS -.259b -1.402 .169 -.219 .156 TRISF1 .234b ' '1.182 .245 .186 .137 BICEP1 ; .280b 1.4.81 ' .147 .231 .148 THIGHSF1 -.035b -.352 .727 -.056 .561 a. Predictors in the Model: (Constant), SUM4SF b. Predictors in the Model: (Constant), SUM4SF, CALFSF1 c. Dependent Variable: PCFAT 136 Appendix XII: AH Possible Subsets Regression Analyses (a) Equation development for F M BMDP9R - ALL POSSIBLE SUBSETS REGRESSION /INPUT TITLE IS 'REGRESSION FOR BODY COMPOSITION". FILE=' A:\BDYCMP2.DAT' . VARIABLES =31. 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 20 HIPG 16 SUBTRI 3 HEIGHT 4 WEIGHT BMI 17 SUM4SF MIDAXSF 7 .10 11 SUBSCPSF ILIACSF ABDSF 26 TOTFAT 1 81 50 99 00 0 83 166 60 64 50 23 24 72 00 17 20 19 00 14 20 34 40 18461 00 2 88 00 101 40 1 25 165 70 66 20 24 11 94. 20 28 00 28 20 19 70 27 60 22630 00 3 98 00 107 80 0 69 164 00 75 40 28 03 111. 00 31 20 24 90 17 60 39 80 31082 10 4 107 50 108 20 0 93 154 70 78 40 32 76 121. 00 26 50 32 20 26 80 41 00 32286 80 5 86 70 101 00 0 78 163 90 66 60 24 79 89. 60 20 70 19 10 23 10 40 00 22763 00 6 102 20 114 00 0 97 158 10 78 50 31 41 131. 00 28 10 36 30 27 90 45 50 28038 20 7 86 50 96 50 0 69 156 80 60 20 24 49 77. 30 25 00 17 00 19 60 28 00 19610 10 CASE 19 20 16 3 4 5 17 8 NO. WAISTG HIPG SUBTRI HEIGHT WEIGHT BMI SUM4SF MIDAXSF 7 10 11 26 SUBSCPSF ILIACSF ABDSF TOTFAT 8 72 50 95 50 0 58 162 40 61 20 23 20 64 05 13 40 11 30 17 90 26 60 17296 30 9 87 40 105 00 0 98 174 10 70 30 23 19 83 40 29 70 19 70 26 00 37 90 22712 90 10 103 50 119 00 0 71 161 90 91 40 34 87 139 50 35 40 32 20 27 50 36 80 39753 60 NUMBER OF CASES READ. 44 137 CASES WITH DATA MISSING OR BEYOND LIMITS REMAINING NUMBER OF CASES 1 43 SUMMARY STATISTICS FOR EACH VARIABLE STANDARD COEFFICIENT SMALLEST LARGEST VARIABLE MEAN DEVIATION OF VARIATION VALUE VALUE 19 WAISTG 87 42558 20 HIPG 101 38605 16 SUBTRI 0 76442 3 HEIGHT 158 05814 4 WEIGHT 66 40581 5 BMI 26 57000 17 STJM4SF 88 37791 8 MIDAXSF 23 20000 7 SUBSCPSF 21 38023 10 ILIACSF 19 45349 11 ABDSF 32 10233 26 TOTFAT 23785 85813 CORRELATIONS 11 .56382 0 .132270 8 .66178 0 .085434 0 .20099 0 262931 . 6 .42240 0 040633 10 .98312 0 165394 ' 4 .02438 0 151463 26 70828 0 302205 7 20305 0 310476 8 19030 0 383078 6 69173 " 0 343986 8 54925 0 266313 7033 81977 0 295714 66 .20000 108 .00000 87 90000 123 .70000 0 39000 1 25000 147 50000 174 10001 47 00000 96 00000 18 83000 35 77000 23 50000 139 50000 6 10000 38 60000 4 60000 36 30000 3 50000 35 30000 5 40000 48 60000 11076 50000 42201 50000 WAISTG 19 WAISTG 19 1 000 HIPG 20 0 720 SUBTRI 16 0 576 HEIGHT 3 0 145 WEIGHT 4 0 875 BMI 5 0 879 SUM4SF 17 0 831 MIDAXSF 8 0 601 SUBSCPSF 7 0 845 ILIACSF 10 0 624 ABDSF 11 0 616 TOTFAT 26 0 871 HIPG SUBTRI HEIGHT 20 16 3 1 000 0 265 1 000 0 296 0 060 1 000 0 899 0 378 0 395 0 812 0 397 -0 097 0 796 0 481 0 049 0 511 0 411 0 126 0 663 0 740 -0 019 0 630 0 375 0 031 0 641 0 392 0 093 0 893 0 344 0 184 WEIGHT BMI SUM4SF 4 5 17 1 000 0 874 1 000 0 802 0 844 1 000 0 529 0 516 0 747 0 727 0 803 0 917 0 569 0 608 0 867 0 590 0 599 0 790 0 948 0 928 0 875 MIDAXSF SUBSCPSF ILIACSF ABDSF TOTFAT 8 7 10 11 MIDAXSF 8 1 000 SUBSCPSF 7 0 653 1 000 ILIACSF 10 0 739 0 718 1 000 ABDSF 11 0 653 0 685 0 802 1 000 TOTFAT 26 0 624 0 776 0 650 0 645 FIRST DIGITS OF CORRELATIONS 19 WAISTG 20 HIPG 4 WEIGHT 26 TOTFAT 5 BMI 17 SUM4SF 7 SUBSCPSF 10 ILIACSF 11 ABDSF 8 MIDAXSF 16 SUBTRI 3 HEIGHT 7* 88* 889* 8889* 87888* 867789* 6656687* 66565768* 655657676* 5233347334* 1231 1 * SUBSETS WITH 1 VARIABLES 138 R-SQUARED 0.897759 0.860936 0.796944 0.764781 0.759458 0.601565 0.422324 0.415886 0.389721 0.118139 ADJUSTED R-SQUARED 0.895265 0.857544 0.791991 0.759044 0.753591 0.591847 0.408234 0.401639 0.374836 0.096630 CP 52.51 85 .47 142.74 171.53 176.30 317.62 478.05 483.81 507.23 750.30 WEIGHT BMI HIPG SUM4SF WAISTG SUBSCPSF ILIACSF ABDSF MIDAXSF SUBTRI SUBSETS WITH 2 VARIABLES R-SQUARED 0.940654 0.940080 0.936936 0.934637 0.918738 0.917868 0.915778 0.913875 0.908957 0.906644 ADJUSTED R-SQUARED 0.937687 0.937084 0.933783 0.931368 0.914675 0.913762 0.911567 0.909568 0.904405 0.901976 CP 16.12 16.63 19.45 21.50 35.73 36.51 38.38 40.09 44.49 46.56 HEIGHT WEIGHT HEIGHT WEIGHT WEIGHT HIPG WEIGHT WEIGHT WEIGHT HIPG WEIGHT BMI BMI SUM4SF MIDAXSF BMI ILIACSF SUBSCPSF ABDSF WEIGHT SUBSETS WITH 3 VARIABLES R-SQUARED 0.955913 0.954274 0.951488 0.950879 0.950258 0.948117 0.947659 0.946559 ADJUSTED R-SQUARED 0.952522 0.950757 0.947757 0.947100 0.946431 0.944126 0.943633 0.942448 CP 4.46 HEIGHT 5.93 WEIGHT 8.42 HEIGHT 8.97 WEIGHT 9.52 HEIGHT 11.44 HEIGHT 11.85 HEIGHT 12.83 WEIGHT WEIGHT MIDAXSF BMI MIDAXSF WEIGHT SUM4SF BMI SUM4SF BMI MIDAXSF BMI SUM4SF WEIGHT ILIACSF BMI*' ILIACSF 139 0.945239 0.941027 0.944845 0.940603 14.01 14.37 HEIGHT WEIGHT ABDSF HIPG HEIGHT WEIGHT SUBSETS WITH 4 VARIABLES ADJUSTED R-SQUARED R-SQUARED 0.961151 0.957061 0.960639 0.956495 0.958910 0.958435 0.958098 0.957782 0.957309 0.957262 0.957025 0.957007 0.954585 0.954060 0.953687 0.953338 0.952815 0.952763 0.952502 0.952482 CP 1.77 VARIABLE 16 SUBTRI 3 HEIGHT 4 WEIGHT 8 MIDAXSF INTERCEPT 2.23 VARIABLE 16 SUBTRI 4 WEIGHT 5 BMI 8 MIDAXSF INTERCEPT 3.78 HIPG 4.20 WAISTG 4.50 SUBTRI 4.79 HIPG 5.21 SUBTRI 5.25 WAISTG 5.46 HEIGHT 5.4 8 WEIGHT HEIGHT HEIGHT HEIGHT WEIGHT WEIGHT WEIGHT WEIGHT BMI COEFFICIENT -2849.16 -238.172 624.126 165.516 18323.2 COEFFICIENT -3153.26 342.465 717.670 162.583 -19385.8 WEIGHT WEIGHT BMI BMI BMI BMI SUM4SF SUM4SF T-STATISTIC -2.26 -6.19 23 .22 4.32 T-STATISTIC -2.48 7.94 6.11 4.21 MIDAXSF MIDAXSF MIDAXSF MIDAXSF SUM4SF MIDAXSF SUBSCPSF SUBSCPSF SUBSETS WITH 5 VARIABLES ADJUSTED R-SQUARED R-SQUARED CP 0.962983 0.957980 2.13 VARIABLE 16 SUBTRI 3 HEIGHT 4 WEIGHT 17 SUM4SF 8 MIDAXSF INTERCEPT COEFFICIENT T-STATISTIC -3174.70 -204.646 575.594 29.7873 122.154 14869.3 -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 T-STATISTIC -4730.78 -200.727 582.406 142.450 99.8403 15014.0 -2.39 -4.10 13 .47 3.35 1.23 140 0.962666 0.957621 0.962623 0.957572 0.962364 0.957278 0.961424 0.956211 0.961394 0.956177 0.961356 0.956134 0.961271 0.956037 2.42 HIPG SUBTRI HEIGHT 2.45 SUBTRI WEIGHT BMI 2.69 HIPG SUBTRI WEIGHT 3.53 HEIGHT WEIGHT SUM4SF 3.55 SUBTRI HEIGHT WEIGHT 3.59 WAISTG SUBTRI HEIGHT 3.66 SUBTRI HEIGHT WEIGHT WEIGHT MIDAXSF MIDAXSF SUBSCPSF BMI MIDAXSF MIDAXSF SUBSCPSF MIDAXSF ABDSF WEIGHT MIDAXSF 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 *** 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. VARIABLE NO. NAME INTERCEPT 16 SUBTRI 3 HEIGHT 4 WEIGHT 8 MIDAXSF REGRESSION COEFFICIENT 18323.2 -2849.16 -238.172 624.126 165.516 STANDARD ERROR 5702.46 1258.76 38.4637 26.8804 38.3240 CONTRI- STAND. T- 2TAIL TOL- BUTION COEF. STAT. SIG. ERANCE TO R-SQ 2.605 3.21 0.003 -0.081 -2.26 0.029 0.790229 0.00524 -0.217 -6.19 0.000 0.828870 0.03920 0.975 23.22 0.000 0.580311 0.55116 0.169 4.32 0.000 0.663755 0.01907 (b) Equation development for %Fat BMDP9R - ALL POSSIBLE SUBSETS REGRESSION /INPUT TITLE IS 'REGRESSION FOR BODY COMPOSITION' . FILE='A:\BDYCMP2.DAT'. VARIABLES =31. 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, MIDAXSF, SUBSCPSF, WAISTG, HIPG, SUBTRI, SUM4SF. /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 MEAN STANDARD COEFFICIENT SMALLEST DEVIATION OF VARIATION VALUE LARGEST VALUE 30 TOTPCFAT 35.83023 5.27147 0.147123 24.50000 46.70000 CORRELATIONS HEIGHT WEIGHT 3 4 BMI 5 ILIACSF ABDSF MIDAXSF SUBSCPSF 10 11 8 7 TOTPCFAT 30 -0.083 0.754 0.863 0.721 0.690 0.714 0.745 WAISTG HIPG SUBTRI SUM4SF TOTPCFAT 19 20 16 17 30 TOTPCFAT 30 0.769 0.758 0.301 0.867 1.000 SUBSETS WITH 1 VARIABLES R-SQUARED 0.751324 0.744395 0.591202 0.574301 0.569190 0.555044 0.519526 0.510147 0.476218 0.090573 ADJUSTED R-SQUARED 0.745259 0.738161 0.581232 0.563918 0.558682 0.544191 0.507807 0.498199 0.463443 0.068392 CP 26.38 SUM4SF 28.20 BMI 68.47 WAISTG 72.92 HIPG 74.26 WEIGHT 77.98 SUBSCPSF 87.32 ILIACSF 89.78 MIDAXSF 98.70 ABDSF 200.09 SUBTRI 142 SUBSETS WITH 2 VARIABLES R-SQUARED 0.843104 0.811053 0.805450 0.791234 0.768728 0.767009 0.766944 0.763897 0.761465 0.761204 ADJUSTED R-SQUARED 0.835259 0.801606 0.795723 0.780796 0.757165 0.755359 0.755291 0.752092 0.749538 0.749265 CP 4.25 12.67 14.15 17.88 23.80 24.25 24.27 25.07 25.71 25.78 BMI BMI BMI BMI SUBTRI SUBSCPSF HEIGHT HIPG MIDAXSF WEIGHT MIDAXSF SUM4SF ILIACSF ABDSF SUM4SF SUM4SF SUM4SF SUM4SF SUM4SF SUM4SF SUBSETS WITH 3 VARIABLES ADJUSTED R-SQUARED R-SQUARED 0.860686 0.849969 0.852639 0.849348 0.847717 0.847646 0.847360 0.847280 0.846887 0.846557 0.844753 0.841304 0.837759 0.836002 0.835926 0.835618 0.835533 0.835109 0.834753 0.832811 CP 1.63 VARIABLE 5 BMI 8 MIDAXSF 16 SUBTRI INTERCEPT COEFFICIENT T-STATISTIC 0.931890 0.299125 -3.92679 7.13194 3.74 BMI 4.61 HEIGHT 5.04 BMI 5.05 BMI 5.13 HEIGHT 5.15 BMI 5.25 BMI 5.34 WEIGHT 5.81 BMI MIDAXSF WAISTG WEIGHT MIDAXSF ABDSF MIDAXSF MIDAXSF SUBSCPSF BMI MIDAXSF ILIACSF MIDAXSF MIDAXSF SUM4SF BMI MIDAXSF MIDAXSF HIPG 9.91 5.65 -2.22 SUBSETS WITH 4 VARIABLES ADJUSTED R-SQUARED R-SQUARED 0.867866 0.853957 CP 1.'74 VARIABLE 5 BMI '-• '8 MIDAXSF 7 SUBSCPSF 17 SUM4SF ' INTERCEPT COEFFICIENT 0.793308 0.205923 -0.236875 0.0953064 6.61611 -STATISTIC 5.18 2.99 -2.46 2.41 0.867853 0.853943 1.74 VARIABLE COEFFICIENT T-STATISTIC 143 0.867183 0.865320 0.864025 0.863819 0.863306 0.862904 0.862277 0.861045 0.853202 0.851143 0.849712 0.849484 0.848917 0.848472 0.847780 0.846418 5 BMI 8 MIDAXSF 16 SUBTRI 17 SUM4SF INTERCEPT 1.92 BMI 2.41 BMI 2.75 HEIGHT 2.80 WEIGHT 2.94 BMI ABDSF ILIACSF BMI BMI MIDAXSF 3.04 HEIGHT WEIGHT 3.21 BMI 3.53 BMI MIDAXSF MIDAXSF 0.758689 0.234806 -4.34828 0.0430038 9.74766 MIDAXSF MIDAXSF MIDAXSF MIDAXSF SUBSCPSF MIDAXSF WAISTG HIPG 4.98 3 .41 -2.46 1.44 SUBTRI SUBTRI SUBTRI SUBTRI SUBTRI SUBTRI SUBTRI SUBTRI (c) Equat ion development for T F M BMDP9R - ALL POSSIBLE SUBSETS REGRESSION /INPUT TITLE IS 'REGRESSION FOR BODY COMPOSITION'. FILE='A:\BDYCMP2.DAT'. VARIABLES =31. CASES=44. FORMAT='3.1F8.2' . /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= TRUNKFAT, MIDAXSF, SUBSCPSF, ABDSF, ILIACSF, HEIGHT, WEIGHT, BMI, SUBTRI, WAISTG. /REGRESS DEPENDENT= TRUNKFAT. INDEPENDENT = MIDAXSF, SUBSCPSF, ABDSF, ILIACSF, HEIGHT, WEIGHT, BMI, SUBTRI, WAISTG. /END. NUMBER OF CASES READ 44 CASES WITH DATA MISSING OR BEYOND LIMITS . . 1 REMAINING NUMBER OF CASES 43 SUMMARY STATISTICS FOR EACH VARIABLE STANDARD COEFFICIENT SMALLEST VARIABLE MEAN DEVIATION OF VARIATION VALUE LARGEST VALUE 23 TRUNKFAT 11866.58840 4084.30318 0.344185 4009.00000 22012.0000 144 CORRELATIONS MIDAXSF SUBSCPSF ABDSF ILIACSF HEIGHT WEIGHT BMI 8 7 11 10 3 4 5 TRUNKFAT 23 0.677 0.814 0.656 0.707 0.150 0.889 0.885 SUBTRI WAISTG TRUNKFAT 16 19 23 TRUNKFAT 23 0.468 0.922 1.000 SUBSETS WITH 1 VARIABLES ADJUSTED R-SQUARED R-SQUARED 0.849552 0.790695 0.782746 0.662285 0.499487 0.458117 0.430259 0.219307 0.022363 0.845882. 0.785590 0.777447 0.654048 0.487279 0.444901 0.416363 0.200266 -0.001482 .24.39 WAISTG 49.19 WEIGHT 52.54 BMI 103.29 SUBSCPSF 171.88 ILIACSF 189.31 MIDAXSF 201.05 ABDSF 289.93 SUBTRI 372.91 HEIGHT SUBSETS WITH 2 VARIABLES R-SQUARED 0.878617 0.877753 0.874179 0.873047 0.861994 0.855503 0.853911 0.850315 0.850134 0.849813 ADJUSTED R-SQUARED 0.872548 0.871641 0.867888 0.866699 0.855094 0.848279 0.846606 0.842831 0.842641 0.842304 CP 14 .14 14.51 16 .01 16.49 21.15 23 .88 24.55 26.07 26.14 26.28 WEIGHT ILIACSF BMI MIDAXSF ABDSF SUBTRI SUBSCPSF SUBSCPSF ILIACSF MIDAXSF WAISTG WAISTG WAISTG WAISTG WAISTG WAISTG WAISTG WEIGHT WEIGHT WEIGHT SUBSETS WITH 3 VARIABLES 145 R-SQUARED 0.903556 0.901751 0.899309 0.895142 0.887882 0.887876 0.886631 0.886609 0.886593 0.884749 ADJUSTED R-SQUARED 0.896138 0.894194 0.891563 0.887076 0.879258 0.879251 0.877910 0.877887 0.877870 0.875883 CP 5.63 6.40, ' 7.42 9.18 12 .24 12 .24 12.77 12.78 12.78 13.56 ILIACSF ,MIDAXSF MIDAXSF ILIACSF HEIGHT MIDAXSF ABDSF WEIGHT MIDAXSF HEIGHT WEIGHT WEIGHT BMI BMI "WEIGHT HEIGHT WEIGHT BMI WEIGHT BMI WAISTG WAISTG WAISTG WAISTG WAISTG WEIGHT WAISTG WAISTG BMI WAISTG SUBSETS WITH 4 VARIABLES ADJUSTED R-SQUARED R-SQUARED 0.912721 0.903534 0.910894 0.901515 0.909271 0.899721 0.909000 0.899421 0.908682 0.899070 0.908009 0.898325 0.905787 0.895869 0.904524 0.894474 0.904112 0.894019 0.903561 0.893409 CP 3.77 VARIABLE 8 MIDAXSF 3 HEIGHT 4 WEIGHT 19 WAISTG INTERCEPT 4.54 VARIABLE 8 MIDAXSF 4 WEIGHT 5 BMI 19 WAISTG INTERCEPT COEFFICIENT 112.034 -81.4047 184.823 136.490 -2071.93 COEFFICIENT 110.701 92.8691 228.082 137.129 -14917.5 T-STATISTIC 3 .29 -2.19 4.15 3 .29 T-STATISTIC 3.22 2.22 1.97 3 .22 5.23 ILIACSF HEIGHT WEIGHT WAISTG 5.34 MIDAXSF ILIACSF WEIGHT WAISTG 5.47 MIDAXSF HEIGHT BMI WAISTG 5.76 ILIACSF WEIGHT BMI WAISTG 6.70 ILIACSF HEIGHT BMI WAISTG 7.23 ILIACSF WEIGHT SUBTRI WAISTG 7.40 ABDSF ILIACSF WEIGHT WAISTG 7.63 SUBSCPSF ILIACSF WEIGHT WAISTG STATISTICS FOR 'BEST' SUBSET MALLOWS' CP 3.77 SQUARED MULTIPLE CORRELATION 0.91272 MULTIPLE CORRELATION 0.9553 6 ADJUSTED SQUARED MULT. CORR. 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 REGRESSION NO. NAME COEFFICIENT INTERCEPT -2071.93 8 MIDAXSF 112.034 3 HEIGHT -81.4047 4 WEIGHT 184.823 19 WAISTG 136.490 STANDARD STAND. T- ERROR COEF. STAT. 6001.15 -0 507 -0 35 34.0674 0 198 3 29 37.2480 -0 128 -2 19 44.5079 0 497 4 15 41.4993 0 386 3 29 CONTRI- 2 TAIL TOL- BUTION SIG. ERANCE TO R-SQ 0.732 0.002 0.636279 0.02484 0.035 0.669514 0.01097 0.000 0.160337 0.03961 0.002 0.166370 0.02485 (d) Equation development for % T F BMDP9R - ALL POSSIBLE SUBSETS REGRESSION /INPUT TITLE IS 1 REGRESSION FOR BODY COMPOSITION'. FILE='A:\BDYCMP2.DAT'. VARIABLES = 31. 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= 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 44 CASES WITH DATA MISSING OR BEYOND LIMITS . . 1 REMAINING NUMBER OF CASES '. 43 SUMMARY STATISTICS FOR EACH VARIABLE STANDARD COEFFICIENT SMALLEST LARGEST 147 VARIABLE MEAN DEVIATION OF VARIATION VALUE VALUE 24 PCTRUNK 34.78140 6.70022 0.192638 18.80000 45.70000 CORRELATIONS HEIGHT WEIGHT BMI ILIACSF ABDSF MIDAXSF SUBSCPSF 3 4 5 10 11 8 7 PCTRUNK 24 -0.076 0.703 0.806 0.754 0.692 0.757 0.793 WAISTG PCTRUNK 19 24 PCTRUNK 24 0.832 1.000 SUBSETS WITH 1 VARIABLES ADJUSTED R-SQUARED R-SQUARED 0.693008 0.685521 0.649656 0.641111 0.628911 0.619860 0.573753 0.563356 0.569096 0.558586 0.493573 0.481221 0.478375 0.465653 0.005829 -0.018419 CP. • „>••., ' v̂ - •>. 36.93 -.VARIABLE:' ,19 WAISTG INTERCEPT 47.66 BMI '. '52.79 SUBSCPSF 66.43 MIDAXSF 67.58 ILIACSF 86.26 WEIGHT 90.02 ABDSF 206.90 HEIGHT COEFFICIENT T-STATISTIC 0.482344 9.62 -7.38783 SUBSETS WITH 2 VARIABLES ADJUSTED R-SQUARED R-SQUARED 0.808713 0.799148 0.796297 0.786112 0.783175 0.772334 0.760479 0.748503 0.744417 0.731638 0.732768 0.719407 0.729205 0.715665 0.721231 0.707293 CP 10.31 VARIABLE 5 BMI 8 MIDAXSF INTERCEPT COEFFICIENT T-STATISTIC 0.942066 0.433055 -0.296173 7.01 5.77 13.39 MIDAXSF WAISTG 16.63 ILIACSF WAISTG 22.24 BMI ILIACSF 26.22 ABDSF WAISTG 29.10 HEIGHT WAISTG 29.98 MIDAXSF SUBSCPSF 31.95 SUBSCPSF WAISTG 148 0.717691 0.703576 0.717429 0.703300 32.83 BMI 32.89 BMI ABDSF WAISTG SUBSETS WITH 3 VARIABLES ADJUSTED R-SQUARED R-SQUARED 0.842733 0.830635 0.824160 0.810634 8 0.820099 0.806261'^ . • '9' 0.815597 0.801412'., 10 0.815497 0.801304 .... 10 0.815144 0.800924 10 0.815080 0.800855 10 0.814341 0.800060 10 0.813634 0.799298 11 0.813038 0.798657 11 CP .90 VARIABLE 3 HEIGHT 8 MIDAXSF 19 WAISTG INTERCEPT COEFFICIENT T-STATISTIC -0.227498 -3.39 0.386580 0.355864 30.6591 MIDAXSF WAISTG ILIACSF MIDAXSF .49 BMI :50 BMI .61 ILIACSF MIDAXSF WAISTG .64 HEIGHT BMI MIDAXSF .72 HEIGHT WEIGHT MIDAXSF .74 WEIGHT • BMI MIDAXSF 92 HEIGHT 10 BMI 24 BMI ILIACSF WAISTG ABDSF MIDAXSF MIDAXSF SUBSCPSF 5.22 7.70 SUBSETS WITH 4 VARIABLES ADJUSTED R-SQUARED R-SQUARED 0.855181 0.839937 0.850447 0.834704 0.848821 0.832908 0.848122 0.832135 0.846067 0.829864 CP 2.82 VARIABLE 3 HEIGHT 10 ILIACSF 8 MIDAXSF 19 WAISTG INTERCEPT 3.99 HEIGHT 4.3 9 HEIGHT 4.57 HEIGHT 5.07 WEIGHT COEFFICIENT T-STATISTIC -0.211881 -3.22 0.177608 1.81 0.291657 3.27 0.325986 6.81 29.5499 ABDSF MIDAXSF WAISTG WEIGHT MIDAXSF WAISTG BMI MIDAXSF WAISTG BMI MIDAXSF WAISTG STATISTICS FOR '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 VARIABLE NO. NAME REGRESSION COEFFICIENT STANDARD -ERROR STAND. COEF. T- STAT. 2 TAIL SIG. TOL- CONTRI- BUTION ERANCE TO R-SQ INTERCEPT 29.5499 ; 10.4076 4 410 2 84 0 007 3 HEIGHT -0.211881 . 0" 0657440 -0 203 -3 22 0 003 0 959651 10 ILIACSF 0.177608 0 0982729 0 177 1 81 0 079 0 395619 8 MIDAXSF 0.291657 0. 0890948 0 314 3 27 0 002 0 415416 19 WAISTG 0.325986 o". 0478898 0 563 6 81 0 000 0 557870 0.01245 0.04084 0.17659 (e) Equation development for F M using SF's only BMDP9R - ALL POSSIBLE SUBSETS REGRESSION /INPUT TITLE 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, SUM4SF, TRISF, BICEPSF, THIGHSF, CALFSF. /END. NUMBER OF CASES READ 44 CASES WITH DATA MISSING OR BEYOND LIMITS . . 1 REMAINING NUMBER OF CASES 43 SUMMARY STATISTICS FOR EACH VARIABLE STANDARD COEFFICIENT SMALLEST LARGEST VARIABLE MEAN DEVIATION OF VARIATION VALUE VALUE 8 MIDAXSF 23 20000 7 20305 0 310476 6 10000 38 60000 7 SUBSCPSF 21 38023 8 19030 0 383078 4 60000 36 30000 10 ILIACSF 19 45349 6 69173 0 343986 3 50000 35 30000 11 ABDSF 32 10233 8 54925 0 266313 5 40000 48 60000 17 SUM4SF 88 37791 26 70828 0 302205 23 50000 139 50000 6 TRISF 27 58605 7 41837 0 268917 11 00000 45 20000 9 BICEPSF 19 95814 7 06035 0 353758 4 40000 34 60000 12 THIGHSF 36 52791 9 16677 0 250953 14 80000 53 00000 13 CALFSF 26 05000 8 19786 0 314697 11 30000 41 20000 26 TOTFAT 23785 85813 7033 81977 0 295714 11076 50000 42201 50000 150 CORRELATIONS MIDAXSF SUBSCPSF ILIACSF ABDSF SUM4SF TRISF BICEPSF 8 7 10 11 17 6 9 MIDAXSF 8 1 000 SUBSCPSF 7 0 653 1 000 ILIACSF 10 0 739 0 718 1 000 ABDSF 11 0 653 0 685 0 802 1 000 SUM4SF 17 0 747 0 917 0 867 0 790 1 000 TRISF 6 0 652 0 788 0 748 0 698 0 929 1 000 BICEPSF 9 0 682 0 800 0 712 0 700 0 921 0 840 1 000 THIGHSF 12 0 305 0 460 0 451 0 448 0 574 0 635 0 543 CALFSF 13 0 509 0 450 0 466 0 564 0 540 0 512 0 542 TOTFAT 26 0 624 0 776 0 650 0 645 0 875 0 834 0 916 THIGHSF CALFSF TOTFAT 12 13 26 THIGHSF 12 1.000 CALFSF 13 0.588 1.000 TOTFAT 26 0.537 0.631 1.000 *** ERROR *** 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 TITLE 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 . . 1 REMAINING NUMBER OF CASES . . . . . . . . 43 SUMMARY STATISTICS FOR EACH VARIABLE STANDARD COEFFICIENT SMALLEST LARGEST VARIABLE MEAN DEVIATION OF VARIATION VALUE VALUE 8 MIDAXSF 23 20000 7 20305 0 310476 6 10000 38 60000 7 SUBSCPSF 21 38023 8 19030 0 383078 4 60000 36 30000 11 ABDSF. 32 10233 8 54925 0 266313 5 40000 48 60000 17 SUM4SF 88 37791 26 70828 0 302205 23 50000 139 50000 6 TRISF 27 58605 7 41837 0 268917 11 00000 45 20000 9 BICEPSF 19 95814 7 06035 0 353758 4 40000 34 60000 12 THIGHSF 36 52791 9 16677 0 250953 14 80000 53 00000 13 CALFSF 26 05000 8 19786 0 314697 11 30000 41 20000 26 TOTFAT 23785 85813 7033 81977 0 295714 11076 50000 42201 50000 CORRELATIONS MIDAXSF SUBSCPSF A B D S F S U M 4 S F TRISF BICEPSF THIGHSF 8 7 11' 17 6 9 12 MIDAXSF 8 1 000 . SUBSCPSF 7 0 653 1 000 ABDSF 11 0 653 0 685 1 000 SUM4SF 17 0 747 0 917 0 790 1 000 TRISF 6 0 652 1 0 788 ' 0 698 0 929 1 000'" BICEPSF 9 0 682 0 800 0 700 0 921 0 840 1 000 THIGHSF 12 0 305 0 460 0 448 0 574 0 635 0 543 1 000 CALFSF 13 0 509 0 450 0 564 0 540 0 512 0 542 0 588 TOTFAT 26 0 624 0 776 0 645 0 875 0 834 0 916 0 537 CALFSF 13 TOTFAT 26 CALFSF TOTFAT 13 26 1.000 0.631 1.000 SUBSETS WITH 1 VARIABLES ADJUSTED R-SQUARED R-SQUARED 0.838579 0.834642 0.764781 0.759044 0.696306 0.688899 0.601565 0.591847 0.415886 0.401639 0.397992 0.383309 0.389721 0.374836 0.288299 0.270940 CP 12.11 BICEPSF 35.48 SUM4SF 57.16 TRISF 87.16 SUBSCPSF 145.95 ABDSF 151.62 CALFSF 154.23 MIDAXSF 186.35 THIGHSF SUBSETS WITH 2 VARIABLES 152 R-SQUARED 0.864083 0.852984 0.844835 0.843644 0.840826 0.838607 0.838580 0.800234 0.770366 0.769173 ADJUSTED R-SQUARED 0.857287 0.845633 0.837077 0.835826 0.832868 0.830538 0.830509 0.790246 " 0.758884 0.757632 CP 6.04 9.55 12.13 12.51 13.40 14.10 14.11 26.25 35.71 36.09 BICEPSF TRISF SUM4SF SUBSCPSF BICEPSF ABDSF MIDAXSF SUM4SF ABDSF SUBSCPSF CALFSF BICEPSF BICEPSF BICEPSF THIGHSF BICEPSF BICEPSF CALFSF SUM4SF SUM4SF SUBSETS WITH 3 VARIABLES ADJUSTED R-SQUARED R-SQUARED 0.874285 0.864615 0.868471 0.867657 0.866193 0.865513 0.864527 0.853908 0.853881 0.853608 0.853165 0.858354 0.857477 0.855900 0.855167 0.854106 0.842670 0.842641 0.842347 0.841870 CP 4.81 VARIABLE 6 TRISF 9 BICEPSF 13 CALFSF INTERCEPT COEFFICIENT T-STATISTIC 177.953 660.606 150.217 1779.24 6.65 SUBSCPSF BICEPSF CALFSF 6.90 SUM4SF BICEPSF CALFSF 7.37 ABDSF BICEPSF CALFSF 7.58 MIDAXSF BICEPSF CALFSF 7.90 BICEPSF THIGHSF CALFSF 11.26 SUBSCPSF TRISF BICEPSF 11.27 ABDSF TRISF BICEPSF 11.35 MIDAXSF TRISF BICEPSF 11.49 SUM4SF TRISF BICEPSF 1.78 6.15 2.57 SUBSETS WITH 4 VARIABLES ADJUSTED R-SQUARED R-SQUARED 0.879872 0.867226 0.878405 0.865605 CP 5.04 VARIABLE 11 ABDSF 6 TRISF 9 BICEPSF 13 CALFSF INTERCEPT 5.50 VARIABLE 6 TRISF 9 BICEPSF 12 THIGHSF 13 CALFSF COEFFICIENT T-STATISTIC -93.7022 213.383 694.333 173.133 2539.80 -1.33 2.08 6.35 2 .87 COEFFICIENT T-STATISTIC 224.316 2.08 650.480 6.06 -69.7242 -1.13 179.341 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 TRISF 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 THIGHSF CALFSF SUBSETS WITH 5 VARIABLES ADJUSTED R-SQUARED R-SQUARED 0.885418 0.869934 0.885025 0.869488 CP 5.28 VARIABLE 11 ABDSF 6 TRISF 9 BICEPSF 12 THIGHSF 13 CALFSF INTERCEPT 5.40 VARIABLE 8 MIDAXSF 6 TRISF 9 BICEPSF 12 THIGHSF 13 CALFSF INTERCEPT COEFFICIENT -105.875 272.235 686.867 -81.5849 210.189 3470.91 COEFFICIENT -119.684 271.249 693.861 -99.7542 210.579 3389.92 T-STATISTIC -1.50 2.46 6.34 -1.34 3.19 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 CONTRI- VARIABLE REGRESSION STANDARD STAND. T- 2TAIL TOL- BUTION NO. NAME COEFFICIENT ERROR COEF. STAT. SIG. ERANCE TO R-SQ INTERCEPT 1779.24 1688.23 0 253 1 05 0 298 6 TRISF 177.953 100.027 0 188 1 78 0 083 0 289635 0 9 BICEPSF 660.606 107.447 0 663 6 15 0 000 0 277114 0 13 CALFSF 150.217 58.4348 0 175 2 57 0 014 0 694960 0 154 Appendix XIII: Regression Outputs for Final Prediction Equations (a) E Q N 1 - F M Variables Entered/Removedb Model Variables Entered Variables Removed Method 1 MA, HT, WT a Enter a. All requested variables entered. b. Dependent Variable: total fat mass in kg Model Summary Std. Error of I Adjusted R the Model R R Square Square Estimate 1 .978 a .956 .953 1.5326 I a. Predictors: (Constant), MA, HT, WT ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 1986.324 3 662.108 281.870 .000a Residual 91.610 39 2.349 Total 2077.934 42 a. Predictors: (Constant), MA, HT, WT b. Dependent Variable: total fat mass in kg j Coefficients3 Model . Uristandardized Coefficients Standardiz ed Coefficient s t Sig. •B . Std. Error Beta 1 (Constant) 16.462 5.934 2.774 .008 HT -.231 .040 -.211 -5.735 .000 WT .611 .028 .953 22.156 .000 MA .143 .039 .146 3.674 .001 a. Dependent Variable: total fat mass in kg (b) EQN2-%Fat 155 Variables Entered/Removed13 Model Variables Entered Variables Removed Method 1 MA, HT, WT 3 Enter a. All requested variables entered. b. Dependent Variable: PCFAT Model Summary Std. Error of Adjusted R the Model R R Square Square Estimate 1 .922 a .849 .838 2.1233 a. Predictors: (Constant), MA, HT, WT ANOVAb Sum of Mean Sig. Model Squares df Square F 1 Regression 991.283 3 330.428 73.292 .000 a Residual 175.827 39 4.508 Total 1167.111 42 a. Predictors: (Constant), MA, HT, WT b. Dependent Variable: PCFAT Coefficients3 Model Unstandardized Coefficients Standardiz ed Coefficient s t Sig. B Std. Error Beta 1 (Constant) 60.122 8.220 7.314 .000 HT -.339 .056 -.413 -6.070 .000 WT .341 .038 .711 8.942 .000 MA .285 .054 .390 5.294 .000 a. Dependent Variable: PCFAT (c) E Q N 3 - T F M 156 Variables Entered/Removed13 Model Variables Entered Variables Removed Method 1 WC, HT a MA. WT Enter a. All requested variables entered. b. Dependent Variable: trunk fat mass in kg Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .955a .913 .904 1.2685 a. Predictors: (Constant), WC, HT, MA, WT ANOVA b Sum of Mean Model Squares df Square F Sig. 1 Regression 639.475 4 159.869 99.347 .000a Residual 61.149 38 1.609 Total 700.624 42 a. Predictors: (Constant), WC, HT, MA, WT b. Dependent Variable: trunk fat mass in kg Coefficients 3 Model Unstandardized Coefficients Standardiz ed Coefficient s t Sig. B Std. Error Beta 1 (Constant) -2.072 6.001 -.345 .732 HT -8.140E-02 .037 -.128 -2.185 .035 WT .185 .045 .497 4.153 .000 MA .112 .034 .198 3.289 .002 WC .136 .041 .386 3.289 .002 a. Dependent Variable: trunk fat mass in kg (d) EQN4-%TF 157 Variables Entered/Removed 1 3, Model Variables Entered Variables Removed Method 1 WC, HT, MA a Enter a. All requested variables entered. b. Dependent Variable: PCTRUNK Model Summary Std. Error of Adjusted R the Model R R Square Square Estimate 1 .918 a .843 .831 . 2.7574 a. Predictors: (Constant), WC, HT, MA ANOVA b Sum of Mean Model Squares df Square F Sig. 1 Regression 1588.977 3 529.659 69.662 .000 a Residual 296.528 39 7.603 Total 1885.505 42 a. Predictors: (Constant), WC, HT, MA b. Dependent Variable: PCTRUNK Coefficients' Model Unstandardized Coefficients Standardiz ed Coefficient s t Sig. B Std. Error Beta 1 (Constant) 30.659 10.687 2.869 .007 HT -.227 .067 -.218 -3.393 .002 MA .387 .074 .416 5.222 .000 WC .356 .046 .614 7.697 .000 a. Dependent Variable: PCTRUNK 158 Appendix XIV: Descriptive Summaries for Independent Databases Baumgartner Data for Elderly Women (n=100) ( B A U M ) AGE WT HT BMI TRI SS WAIST HIP THIGH TOTFAT(g) %FAT M e a n 74.47 64.84 155.92 26.66 22.62 20.68 91.87 104.05 47.83 26429.19 39.57 S D 5.59 12.63 6.81 5.03 8.35 9.60 11.66 11.41 5.61 9294.52 7.47 Brodowicz Data for Elderly Women (n=31) ( B R O D i ) AGE HT WT TRI BIC SI SS %FAt TOTFAT(g) Mean 71.13 1.61 65.08 20.76 10.73 19.82 19.50 39.13 25813.87 S D 4.62 0.06 10.13 5.25 3.89 7.29 7.00 5.64 7005.63 Brodowicz Data for Younger Women (n=33) (BROD2) A g e H T W T T R I B I C SI SS %Fat T O T F A T ( g ) M e a n 33.39 1.66 63.48 19.61 7.80 15.73 15.18 29.56 19276.67 S D 4.72 0.07 9.35; .8.84 4.83 7.80 8.65 8.95 8145.80 159 Appendix X V : Stepwise Multiple Regression for Modified %Fat Eqn (a) using variables from Brodowicz study Variables Entered/Removed3 Model Variables Entered Variables Removed Method 1 SUM4SF Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). 2 BMI Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). 3 SS Stepwise (Criteria: Probability- of-F-to-ent er <= .050, Probability- of-F-to-rem ove >= .100). a. Dependent Variable: PCFAT Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .867a .751 .745 2.6606 2 .901b .811 .802 2.3474 3 .915° .837 .824 2.2103 a. Predictors: (Constant), SUM4SF b. Predictors: (Constant), SUM4SF, BMI c. Predictors: (Constant), SUM4SF, BMI, SS 160 ANOVAd Sum of , Mean Model Squares df Square F Sig. 1 Regression 876.879 1 876.879 123.873 .000 a Residual 290.232 41 7.079 Total 1167.111 42 2 Regression 946.696 2 473.348 85.901 .000 b Residual " ^220.415 40 5.510 Total .1167.111 42 3 Regression 976.575 3 325.525 66.631 .000° Residual .190.535 39 4.886 Total 1167.111 42 a. Predictors: (Constant), SUM4SF b. Predictors: (Constant), SUM4SF, BMI c. Predictors: (Constant), SUM4SF, BMI, SS d. Dependent Variable: PCFAT Coefficients 3 Unstandardized Coefficients Standardiz ed Coefficient s Model B Std. Error Beta t Sig. 1 (Constant) 20.711 1.418 14.608 .000 SUM4SF .171 .015 .867 11.130 .000 2 (Constant) 11.548 2.862 4.035 .000 SUM4SF 9.503E-02 .025 .481 3.755 .001 BMI .598 .168 .456 3.560 .001 3 (Constant) 9.819 2.784 3.527 .001 SUM4SF .162 .036 .818 4.496 .000 BMI .652 .160 .497 4.082 .000 SS -.261 .105 -.405 -2.473 .018 a. Dependent Variable: PCFAT 161 Excluded Variables'1 Partial Collinearity Statistics Model Beta In t Sig. Correlation Tolerance 1 HT -.125 a -1.637 .109 -.251 .998 WT .166 a 1.286 .206 .199 .357 BMI .456 a 3.560 .001 .490 .287 TRI .250 a 1.194 .240 .185 .137 SS -.314 a -1.641 .109 -.251 .159 BIC .336 a 1.718 .093 .262 .151 SI -.122 a -.780 .440 -.122 .249 subscap/triceps sf ratio -.153 a -1.764 .085 -.269 .769 2 HT -.066b -.929 .359 -.147 .931 WT -.136b -.934 .356 -.148 .222 TRI .204b 1.101 .278 .174 .136 SS -.405 b -2.473 .018 -.368 .156 BIC .145 b .767 .447 .122 .135 SI ,133 b .851 .400 .135 .196 subscap/triceps sf ratio -.147 b -1.937 .060 -.296 .769 3 HT -.089 c -1.336 .189 -.212 .915 WT -.193° -1.410 .167 -.223 .217 TRI .013° .067 .947 .011 .109 BIC -.013C -.065 .948 -.011 .117 SI .000° -.002 .999 .000 .169 subscap/triceps sf ratio .046° .309 .759 .050 .191 a. Predictors in the Model: (Constant), SUM4SF b. Predictors in the Model: (Constant), SUM4SF, BMI c. Predictors in the Model: (Constant), SUM4SF, BMI, SS d. Dependent Variable: PCFAT (b) using variables from Baumgartner study 162 Variables Entered/Removed3 Variables Variables Model Entered Removed Method 1 Stepwise (Criteria: Probability- of-F-to-ent BMI er <= .050, Probability- of-F-to-rem ove >= .100). 2 Stepwise (Criteria: Probability- of-F-to-ent TRI er <= .050, Probability- of-F-to-rem ove >= .100). a. Dependent Variable: PCFAT Model Summary Std. Error of Adjusted R the Model R R Square Square Estimate 1 .863 a .745 .738 2.6965 2 .898 b .807 .797 2.3722 a. Predictors: (Constant), BMI b. Predictors: (Constant),'-BMI, TRI ANOVA c Sum of Mean Model Squares df Square F Sig. 1 Regression 868.996 1 868.996 119.514 .000a Residual 298.115 41 7.271 Total 1167.111 42 2 Regression 942.009 2 471.005 83.696 .000b Residual 225.102 40 5.628 Total 1167.111 42 a. Predictors: (Constant), BMI b. Predictors: (Constant), BMI, TRI c. Dependent Variable: PCFAT 163 Coefficients 3 Unstandardized Coefficients Standardiz ed Coefficient s Model B Std. Error Beta t Sig. 1 (Constant) 5.800 2.778 2.088 .043 BMI 1.130 .103 .863 10.932 .000 2 (Constant) 9.198 2.619 3.511 .001 BMI .696 .151 .531 4.608 .000 TRI .295 .082 .415 3.602 .001 a. Dependent Variable: PCFAT ' ' '• :- Excluded Variables 0 Partial Collinearity Statistics Model Beta, In t Sig. Correlation Tolerance 1 HT .001 a .016 .987 .003 .991 WT .003a .017 .986 .003 .237 TRI .415a 3.602 .001 .495 .363 SS .146a 1.105 .276 .172 .355 subscap/triceps sf ratio -.050a -.579 .566 -.091 .844 WC .048a .286 .777 .045 .228 HC .168a 1.249 .219 .194 .341 2 HT -.027b -.386 .701 -.062 .978 WT -.075b -.518 .608 -.083 .232 SS -.031b -.241 .811 -.039 .295 subscap/triceps sf ratio .007b .085 .933 .014 .807 WC .022b .150 .881 .024 .228 HC .043b .341 .735 .055 .310 a. Predictors in the Model: (Constant), BMI b. Predictors in the Model: (Constant), BMI, TRI c. Dependent Variable: PCFAT 164

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