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The risk of death associated with delayed coronary artery bypass surgery Sobolev, Boris G; Levy, Adrian R; Kuramoto, Lisa; Hayden, Robert; Brophy, James M; FitzGerald, J M Jul 5, 2006

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ralssBioMed CentBMC Health Services ResearchOpen AcceResearch articleThe risk of death associated with delayed coronary artery bypass surgeryBoris G Sobolev*1,2, Adrian R Levy1,3, Lisa Kuramoto2, Robert Hayden4, James M Brophy5 and J Mark FitzGerald2Address: 1Department of Health Care and Epidemiology, University of British Columbia, Vancouver, Canada, 2Centre for Clinical Epidemiology and Evaluation, Vancouver Coastal Health Research Institute, Vancouver, Canada, 3Centre for Health Evaluation and Outcome Sciences, St. Paul's Hospital, Vancouver, Canada, 4Department of Surgery, Royal Columbian Hospital, New Westminster, Canada and 5McGill University Health Centre, Montreal, CanadaEmail: Boris G Sobolev* - sobolev@interchange.ubc.ca; Adrian R Levy - alevy@cheos.ubc.ca; Lisa Kuramoto - lisa.kuramoto@vch.ca; Robert Hayden - erh@telus.net; James M Brophy - james.brophy@mcgill.ca  ; J Mark FitzGerald - markf@interchange.ubc.ca* Corresponding author    AbstractBackground: The detrimental effect of delaying surgical revascularization has been estimated inrandomized trials and observational studies. It has been argued that the Kaplan-Meier method used inquantifying the hazard of delayed treatment is not appropriate for summarizing the probability ofcompeting outcomes. Therefore, we sought to improve the estimates of the risk of death associated withdelayed surgical treatment of coronary artery disease.Methods: Population-based prospective study of 8,325 patients registered to undergo first time isolatedcoronary artery bypass grafting (CABG) in any of the four tertiary hospitals that provide cardiac care toadult residents of British Columbia, Canada. The cumulative incidence of pre-operative death, thecumulative incidence of surgery, and the probability that a patient, who may die or undergo surgery, diesif not   operated by certain times over the 52-week period after the decision for CABG were estimated.The risks were quantified separately in two groups: high-severity at presentation were patients with eitherpersistent unstable angina or stable angina and extensive coronary artery disease, and low-severity atpresentation were stable symptomatic patients with limited disease.Results: The median waiting time for surgery was 10 weeks (interquartile range [IQR] 15 weeks) in thehigh-severity group and 21 weeks (IQR 30 weeks) in the low-severity group. One percent of patients diedbefore surgery:   54 in the high-severity and 26 in the low-severity group. For 58 (72.5%) patients, deathwas related to CVD (acute coronary syndrome, 33; chronic CVD, 16; other CVD, 4; and sudden deaths,5). The overall death rate from all causes was 0.61 (95% CI 0.48-0.74) per 1,000 patient-weeks, varyingfrom 0.62 (95% CI 0.45-0.78) in the high-severity group to 0.59 (95% CI 0.37-0.82) in the low-severitygroup. After adjustment for age, sex, and comorbidity, the all-cause death rate in the low-severity groupwas similar to the high-severity group (OR = 1.02, 95% CI 0.64-1.62). The conditional probability of deathwas greater in the high-severity   group than in the low-severity group both for all-cause mortality (p =0.002) and cardiovascular deaths (p <0.001).Conclusion: The probability of death conditional on not having undergone a required CABG increasesPublished: 05 July 2006BMC Health Services Research 2006, 6:85 doi:10.1186/1472-6963-6-85Received: 13 January 2006Accepted: 05 July 2006This article is available from: http://www.biomedcentral.com/1472-6963/6/85© 2006 Sobolev et al; licensee BioMed Central Ltd.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Page 1 of 9(page number not for citation purposes)with time spent on wait lists.BMC Health Services Research 2006, 6:85 http://www.biomedcentral.com/1472-6963/6/85BackgroundCoronary-artery bypass grafting (CABG) is indicated forrevascularizing patients who have limiting angina thatpersists despite optimal medical treatment and suitablecoronary anatomy. In a meta-analysis of seven rand-omized controlled trials of immediate CABG versus med-ical therapy, surgery has been shown to improveprognosis in stable symptomatic patients with left maincoronary disease, triple vessel disease, or two vessel dis-ease involving a significant stenosis of the proximal leftanterior descending coronary artery [1]. It has beenargued that some of the survival benefits could be lost dueto additional deaths resulting from a longer wait forrequired revascularization [2]. Methodologically, notincluding pre-operative deaths implies that survival timebegins at procedure; and, therefore, treatment effect isimplicitly conditioned on surviving to treatment [3]. Also,when reporting mortality among patients who may die orundergo surgery special statistical techniques must beused to isolate the effect of competing risks of surgery anddeath [5]. The Kaplan-Meier method used in reports onthese trials is not appropriate for describing the probabil-ity of competing outcomes over time [4].The detrimental effect of delaying CABG surgery has beenestimated as well in observational studies of patientswhose treatment was delayed due to a rationing of accessto care. Population-based studies show that from 0.4 to1.3 percent of patients scheduled for CABG die preopera-tively [6-8]. Again, these proportions cannot be studied bythe Kaplan-Meier method as they are affected by the inci-dence of both surgery and death. Therefore, it is not clearwhether the low observed probabilities of death indicatea true low risk of death or appropriate timing of surgery.One measure suggested for summarizing the risk of deathover time in competing-risk setting is the probability ofdeath conditional on not having experienced the compet-ing event by a certain time [9,10]. Using this approach, wesought to improve the estimates of the risk of death asso-ciated with delayed coronary artery bypass surgery inpatients requiring and suitable for surgical revasculariza-tion. We, therefore, estimated the time-dependent proba-bility of death, given that CABG was not performed bycertain times, using data from a prospective database of alladult patients who were accepted for isolated first timecoronary artery surgery in British Columbia [BC], Canada.MethodsThe University of British Columbia Ethics Board approvedthe study protocol.Data sourcesdure, or removal from wait lists without surgery, for allpatients who have been accepted for surgical coronaryrevascularization in any of the four tertiary hospitals thatprovide cardiac care to adult residents of BC since 1991[11]. The reliability of demographic and clinical data inthe registry has been described elsewhere [12].The date and cause of death for the registry records wereobtained from BC Linked Health Database Deaths File for1990 through 2001 [13]. Causes of death were codedaccording to the International Classification of Diseases,9th revision (ICD-9) [14]. Cardiovascular deaths were allthose with ICD-9 codes 410–439 plus sudden deaths dueto unknown causes. Data on coexisting medical condi-tions were retrieved from the BC Linked Health DatabaseHospital Separations File using diagnoses reported in dis-charge abstracts created during the calendar year beforeregistration for CABG [15].PatientsWe studied records of patients for whom surgical revascu-larization was indicated at the time of consultation with acardiac surgeon. For this analysis, patients were dividedinto high-severity and low-severity at presentation groupsaccording to angiographic findings, symptom severity andleft ventricular dysfunction (ejection fraction less than50%) [16].The high-severity group consisted of patients with eitherpersistent unstable angina or stable angina and extensiveCAD (left-main stenosis more than 50%, triple-vessel dis-ease, or double-vessel disease with significant proximalleft anterior descending stenosis and impaired left ven-tricular function). The low-severity group consisted of sta-ble symptomatic patients with limited CAD (double-vessel disease with no lesion in the proximal left anteriordescending artery and normal left ventricular function orsingle-vessel disease with significant proximal left anteriordescending stenosis).There were 8,494 patients identified who required iso-lated (did not include a valve replacement procedure) firsttime coronary artery bypass surgery in these two groupsbetween January 1991 and December 2000. We excluded169 records of the patients who were removed on the reg-istration date (50), had missing operating room reports(4), or had immediate access to surgery (115). Of those,161 eventually underwent surgery; seven died; 75 becameunfit for surgery; 100 declined surgery; 16 were transferredto another surgeon or hospital; and 96 were removedfrom wait lists for other reasons. The baseline characteris-tics of patients are shown in Table 1. The remaining 8,325patients had either a surgery date or a date and reason forPage 2 of 9(page number not for citation purposes)A population-based cardiac registry contains the time ofregistration on wait lists for CABG and the time of proce-removal without surgery. The study period ended inDecember 2001, allowing only 52 weeks of follow-upBMC Health Services Research 2006, 6:85 http://www.biomedcentral.com/1472-6963/6/85after the last patients were added to the list. Therefore, werestricted the analysis to the first 52 weeks after registra-tion so that 455 (5.5%) patients remaining on the lists at12 months were censored. Statistical analysisThe primary outcomes were the occurrence of death fromall causes and death related to cardiovascular disease(CVD) while awaiting coronary artery surgery. The date ofthe operating room booking request from surgeon servedas the date of decision for surgery and registration on await list.In the participating hospitals, surgical wait lists are used tohold patient names until the surgery can be scheduled.Patients are also removed from the wait lists without sur-gery if they die, reconsider the decision to undergo sur-gery, accept surgery from another surgeon, move out ofthe province, or if their conditions deteriorate so that sur-gery is no longer possible. Details regarding the wait-listmanagement were published elsewhere [11].tional on not having undergone surgery by a certain timeafter the registration on a wait list for CABG. The condi-tional probability function (CPF) of death is interpretedas the cumulative incidence of deaths by a certain wait-listweek among cardiac surgery patients who had not yetundergone CABG by that time.To estimate CPF of death, we first estimated separately thecumulative incidence of death and the cumulative inci-dence of surgery over time while treating wait-list remov-als, other than surgery and death, as censoredobservations. The cumulative incidence function of anevent is defined as the integration over time of the productof the event rate and the probability of remaining on thelist [17]. The following section describes the estimationprocedure.Suppose the events of death and surgery occur at E dis-tinct, unevenly spaced, ordered times, ti, for i = 1,2,..., E,and define t0 = 0. Using Gooley's notation [5], let ei be thenumber of deaths at time ti, ri be the number of surgeriesat time ti, ci be the number of censored events at time ti,Table 1: Characteristics of 8,325 patients (6,405 in high-severity and 1,920 in low-severity) registered for isolated coronary artery bypass surgery in British Columbia, 1991–2000Characteristic All patients N (%) High-severity N (%) Low-severity N (%)Age group (y)<50 679 (8.2) 496 (7.7) 183 (9.5)50–59 1841 (22.1) 1397 (21.8) 444 (23.1)60–69 3167 (38.0) 2457 (38.4) 710 (37.0)70–79 2478 (29.8) 1933 (30.2) 545 (28.4)≥80 160 (1.9) 122 (1.9) 38 (2.0)SexWomen 1473 (17.7) 1102 (17.2) 371 (19.3)Men 6852 (82.3) 5303 (82.8) 1549 (80.7)Comorbidity at registrationMajor conditions* 1775 (21.3) 1358 (21.2) 417 (21.7)Other conditions † 2137 (25.7) 1723 (26.9) 414 (21.6)None 4413 (53.0) 3324 (51.9) 1089 (56.7)Coronary anatomyLeft-main stenosis 990 (11.9) 990 (15.5) 0 (0.0)Multi- vessel disease‡ 6672 (80.1) 4986 (77.8) 1686 (87.8)Limited disease§ 663 (8.0) 429 (6.7) 234 (12.2)*congestive heart failure, diabetes, chronic obstructive pulmonary disease, rheumatoid arthritis, cancer.†peripheral vascular disease, cerebrovascular disease, dementia, peptic ulcer disease, hemiplegia, renal disease, or liver disease.‡3 or 2-vessel disease with PLAD.§2-vessel disease with no PLAD or 1-vessel disease with PLADPage 3 of 9(page number not for citation purposes)The risk of death as a function of treatment delay isdescribed by the probability that a patient dies condi-and ni = ni-1 - (ei + ri + ci) be the number of patients stillwaiting beyond time ti, where n0 is the initial number ofBMC Health Services Research 2006, 6:85 http://www.biomedcentral.com/1472-6963/6/85patients at risk. As described by Kalbfleisch and Prentice,a non-parametric estimator for the cumulative incidenceof death at time t, F1(t), is given by the following formula[18]:Similarly, a non-parametric estimator for the cumulativeincidence of surgery at time t, F2(t), isThe formula for a Taylor series approximation of the vari-ance for the cumulative incidence of an event was devel-oped by Gaynor [19].The CPF of death, among those who remained untreated,is defined as the ratio of the cumulative incidence of deathand the complement of cumulative incidence of surgery[10]. We used the non-parametric estimator for the calcu-lation of the CPF of death [9]:Its variance was determined by Pepe in [9]. To estimatethe cumulative incidence of events, CPF of death, and thecorresponding confidence intervals, we used Matlab ver-sion 7.0.1 [see Additional file1]. A two-sample test wasused to compare the CPF between the study groups [9].The cumulative incidence of surgery was comparedbetween the two groups by the Gray's test [20].We used discrete-time survival regression models to eval-uate the combined effect of clinical factors that identifythe patient groups in this study on the death rate, whileadjusting for age, sex, and comorbidity [21]. The likeli-hood ratio test was used to assess whether the modelswere consistent with the data [22]. Existing literature sug-gest that age, sex and comorbidities may be potential con-founders. Elderly patients are more likely to undergorevascularization as an urgent procedure. The smaller cor-onary vessel diameters may account for higher risk ofadverse events in women. Co-existing medical conditionsmay delay scheduling surgery. All of these factors wereentered into the regression models. In particular, eachpatient was classified as 1) presenting with congestiveheart failure, diabetes, chronic obstructive pulmonary dis-ease, cancer or rheumatoid arthritis, 2) presenting withother co-existing chronic conditions as defined in [23], or3) presenting with no co-existing conditions.ResultsAt 52 weeks of follow-up, 7,155 (85.9%) patients under-went surgery, 80 (1.0%) died while awaiting surgery, 455(5.5%) patients were remaining on the lists, and 635(7.6%) dropped out during follow-up for various reasons:became unfit to surgery (166), declined surgery (181),transferred to another surgeon or hospital (93), receivedother surgery (21), or removed from the list due to otherreasons (174), Table 2. Over 10% of low-severity patientsand less than 5% of high-severity patients were stilluntreated at 52 weeks.The extent of disease was a major factor influencing timeto surgery. The median waiting time for surgery was 10weeks (interquartile range [IQR] 15 weeks) in the high-severity group and 21 weeks (IQR 30 weeks) in the low-severity group. The differences in the cumulative inci-dence of surgery were significant over time betweenˆ ( ) .{ | } { | }F tene rniii t tj jjj t ti j i11 11 11= −+⎛⎝⎜⎜⎞⎠⎟⎟ ( )−≤ −≤∑ ∏−ˆ ( ) .{ | } { | }F trne rniii t tj jjj t ti j i21 11 21= −+⎛⎝⎜⎜⎞⎠⎟⎟ ( )−≤ −≤∑ ∏−CP tF tF tm1 1213( )( )( ).=−( )Table 2: Number of patients (%) by 52-week outcome of registration for isolated coronary artery bypass surgeryOutcomes All patients N(%) High-severity N(%) Low-severity N(%)Underwent surgery 7155 (85.9) 5722 (89.3) 1433 (74.6)Removed without surgeryDied while waiting 80 (1.0) 54 (0.8) 26 (1.4)Became unfit for surgery 166 (2.0) 90 (1.4) 76 (4.0)Patient request 181 (2.2) 131 (2.0) 50 (2.6)Transferred or moved 93 (1.1) 62 (1.0) 31 (1.6)Other surgery 21 (0.3) 13 (0.2) 8 (0.4)Other reason 174 (2.1) 117 (1.8) 57 (3.0)Page 4 of 9(page number not for citation purposes)Still on wait list 455 (5.5) 216 (3.4) 239 (12.4)BMC Health Services Research 2006, 6:85 http://www.biomedcentral.com/1472-6963/6/85groups with higher incidence in the high-severity group,(Gray's two-sample test = 411.8, p < 0.001), Figure 1.A total of 5,722 surgeries over 87,674 patient-weeks in thehigh-severity and 1,433 surgeries over 43,817 patient-weeks in the low-severity group were done. The averagesurgery rate was 6.5 per 100 patients per week of delay inthe high-severity group compared to 3.3 in the low-sever-ity, the odds ratio (OR) = 0.50 (95% confidence interval[CI] 0.47–0.53), after adjustment for age, sex, and comor-bidity. The log-likelihood ratio test, 619.9, df = 5, p <0.001, does not support the global null hypothesis, sug-gesting that the model is consistent with data.One percent of patients died before surgery: 54 in thehigh-severity and 26 in the low-severity group. For 58(72.5%) patients, death was related to CVD (acute coro-nary syndrome, 33; chronic CVD, 16; other CVD, 4; andsudden deaths, 5).The overall death rate from all causes was 0.61 (95% CI0.48–0.74) per 1,000 patient-weeks, varying from 0.62(95% CI 0.45–0.78) in the high-severity group to 0.59(95% CI 0.37–0.82) in the low-severity group. Afteradjustment for age, sex, and comorbidity, the all-causedeath rate in the low-severity group was similar to thehigh-severity group (OR = 1.02, 95% CI 0.64–1.62). Thelog-likelihood ratio, 16.2, df = 5, p < 0.01, test does notsupport the global null hypothesis, suggesting that, atleast one regression coefficient differs from zero, andtherefore, the model is consistent with data.Figure 2 shows the relationship between wait time and theprobability of preoperative death from all causes by sever-ity group, which was estimated by non-parametric meth-ods as described in a previous section and also by theKapaln-Meier method. Although the all-cause death rate issimilar for the two groups, 0.62 versus 0.59 per 1,000patient-weeks, longer wait times contributed to a highercumulative incidence of death in the low-severity thanhigh-severity group [11]. The non-parametric cumulativeincidence function provides lower probabilities of deaththan the Kaplan-Meier method [24]. At 52 weeks sinceregistration, the Kaplan-Meier estimates are about 4 timesgreater (3.7% versus 0.9%) in the high-severity group, and2 times greater (3.4% versus 1.5%) in the low-severitygroup.To compare proportions of patients dying by a certaintime among those who had not undergone surgery by thattime, we calculated the conditional probability of death ineach group. The non-parametric estimate of the condi-tional probability of death was derived from the ratio ofthe cumulative incidence of death and the complement ofthe cumulative incidence of surgery. The conditionalprobability for death from all causes was greater in thehigh-severity group than in the low-severity group (Pepe'stwo-sample test = 2.8, p = 0.002), Figure 3. Amongpatients who had not undergone CABG by 8, 16, 32 and52 weeks, the probability to die from all causes was 0.6%(standard error [SE] 0.1), 1.8% (0.3), 6.8% (0.9) and14.9% (1.8) in the high-severity group, and 0.6% (0.2),1.2% (0.3), 3.6% (0.8) and 7.9% (1.5) in the low-severitygroup.The conditional probability for CVD death was greater inthe high-severity group than in the low-severity group(Pepe's two-sample test = 3.6, p = 0.0002), Figure 4.Among patients who had not undergone CABG by 8, 16,32 and 52 weeks, the probability to die from CVD was0.6% (0.1), 1.6% (0.3), 5.4% (0.8) and 12.1% (1.7) in thehigh-severity group, and 0.3% (0.1), 0.6% (0.2), 2.1%(0.6) and 4.7% (1.2) in the low-severity group.DiscussionIn this prospective study of 8,325 consecutive patients wehave reported outcomes of delaying coronary artery sur-gery in two groups of patients for whom isolated CABGwas indicated. The high-severity group included patientswith either persistent unstable angina or stable anginaand extensive CAD at presentation. The low-severitygroup included stable symptomatic patients with limitedEstimated cumulative incidence of surgery and 95% CIs by week since registratio  in high-severity (red) and low- ever-ity (blu ) group ; w -sample test = 411.8, p < 0.001Figure 1Estimated cumulative incidence of surgery and 95% CIs by week since registration in high-severity (red) and low-sever-1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 5200.250.50.751WEEK  SINCE  REGISTRATIONCUMULATIVE  INCIDENCE  OF  SURGERYPage 5 of 9(page number not for citation purposes)CAD.ity (blue) groups; two-sample test = 411.8, p < 0.001.BMC Health Services Research 2006, 6:85 http://www.biomedcentral.com/1472-6963/6/85Page 6 of 9(page number not for citation purposes)Estimated probabilities of preoperative death, as cumulative incidence function (blue) and Kaplan-Meier (red) and their stand-ard errors, by week since registration in hig -severity and low-severity groupFigu e 2Estimated probabilities of preoperative death, as cumulative incidence function (blue) and Kaplan-Meier (red) and their stand-ard errors, by week since registration in high-severity and low-severity group.0 4 8 12 16 20 24 28 32 36 40 44 48 5200.  SINCE  REGISTRATIONCUMULATIVE  PROBABILITY  OF  DEATHHIGH−SEVERITY0 4 8 12 16 20 24 28 32 36 40 44 48 5200.  SINCE  REGISTRATIONCUMULATIVE  PROBABILITY  OF  DEATHLOW−SEVERITYBMC Health Services Research 2006, 6:85 http://www.biomedcentral.com/1472-6963/6/85In each group, we have estimated the time-dependentconditional probability that a patient, who may die orundergo surgery, dies if not operated by certain times.These probabilities, which summarize competing risksdata on wait-lists, have not been previously reported foruntreated CAD patients for whom CABG was indicated.As noted by Pepe [9], the conditional probability functionis not a predicted probability and its interpretation doesnot require any implicit assumptions. It is simply the pro-portion of patients who have died among those whoremained untreated. We found that among patientsdelayed without treatment for 52 weeks, an estimated14.9% die in the high-severity group and 7.9% die in thelow-severity group from all causes. Similarly, an estimated12.1% and 4.7% die from CVD in these two groups.We report on all-cause and CVD mortality because theaccuracy of death certificate codes is a concern in this anal-ysis [25], whereas using all-cause mortality could not haveinduced any bias in the results. Some evidence that codingof CVD deaths is accurate comes from a Canadian studyin which the false positive rate was 2.1% and the false neg-ative rate was 0.4% for myocardial infarction coded as anunderlying cause of death [26]. We also argue that there isno reason to suspect that there would be differential cod-ing of death certificates according to urgency of treatmentas the physician completing the death certificate wouldIn quantifying the risk of preoperative death amongpatients needing CABG, the Kaplan-Meier method is com-monly used to estimate the cumulative probability ofdeath by certain times after registration for the operation[27-29]. It has been established, however, the Kaplan-Meier method is not appropriate for describing the prob-abilities of competing events since its complement overes-timates the proportion of events [4]. This methodproduces valid probability estimates only in a hypotheti-cal situation where all competing risks can be removedwithout altering the risk of death.Other investigators have reported the incidence of preop-erative death per time unit of waiting for CABG [6-8,27,29-31]. Although accurately describing the instanta-neous hazard, death rates can not be converted into prob-abilities of death without an unrealistic and unverifiableassumption that time to surgery and time to death areindependent [5]. Plomp and colleagues have reported onthe variation in time to deaths among those who diedbefore surgery [32], but the proportion of CABG candi-dates dying over follow-up could not be derived fromtheir figures.Methodologically, measuring risk of death as a function oftreatment delay in patients awaiting the treatment is sim-ilar to quantifying the risk of death during follow-up in aEstimated conditional probability for cardio-vascular death and 95% confi ence intervals, b  week since registration in high-severity (r d) and low- everity (blue) group ; tw -sam-ple tes  = 3.6, p < 0.001Fi ur 4Estimated conditional probability for cardio-vascular death and 95% confidence intervals, by week since registration in high-severity (red) and low-severity (blue) groups; two-sam-ple test = 3.6, p < 0.001.0 4 8 12 16 20 24 28 32 36 40 44 48 5200.  SINCE  REGISTRATIONCONDITIONAL  PROBABILITY  OF  CARDIAC  DEATHEstimated conditional probability for all-cause death and 95% confidence intervals, by week since egistration in igh-sever-ity (red) and low-severity groups (blue); two-sample te t = 3.1, p = 0.002Figur 3Estimated conditional probability for all-cause death and 95% confidence intervals, by week since registration in high-sever-ity (red) and low-severity groups (blue); two-sample test = 3.1, p = 0.002.0 4 8 12 16 20 24 28 32 36 40 44 48 5200.  SINCE  REGISTRATIONCONDITIONAL  PROBABILITY  OF  DEATHPage 7 of 9(page number not for citation purposes)not necessarily have been aware of the assigned urgency atregistration for CABG.population exposed to competing events [4]. Therefore,an alternative approach to summarize competing risksBMC Health Services Research 2006, 6:85 http://www.biomedcentral.com/1472-6963/6/85data is to estimate the proportion of patients dying by acertain time among those not receiving treatment by thattime [10]. We used the conditional probability functionsuggested as a method for summarizing multiple end-points in the competing-risks setting by Pepe [33].There were important limitations to our study. First, wehave not adjusted the CPF of death for available covariatesas the statistical methodology for that is yet to be devel-oped. Therefore, there is a concern that some other factorscan confound the difference between the two studygroups. However, in our data set both study groups weredistributed similarly over age, sex and comorbidity cate-gory and differed only by the extent of CAD. The numberof deaths observed does not permit the analysis acrossstrata. A new update of data in the future will perhapsallow us to report CPFs by important covariates, such assex and age. Also, our analysis lacks data on socioeco-nomic status. Given social class differences in access tohealthcare and mortality, socioeconomic status is a poten-tial confounding factor for the observed associationbetween time to CABG and the risk of death [34]. Oneimportant issue is preferential allocation of hospitalresources [35]. It remains unclear whether directly admit-ting patients of low priority is done to circumvent longwait lists, or to substitute for cancelations on the operat-ing room schedule [11].The quality of information on dates of registration andremoval is a concern in this analysis as well. Although weconsidered the date of the booking request as the date ofdecision for surgery, no audit was conducted to verify theaccuracy of coding dates in BCCR records.In conclusion, the contribution of this paper is the esti-mated conditional probabilities of death in relation to dif-ferent delays in the treatment of patients requiring andsuitable for CABG. These summary probabilities derivedfrom the population-based prospective database suggestthat the risk of death among those remaining untreatedincreases with time on wait lists.ConclusionOur findings have implications for policies related toaccess to elective cardiac surgery. First, in deciding on theduration of time that the treatment of elective patients canbe safely delayed, surgeons and policy makers should beaware that the probability of death among untreatedpatients does not remain constant over time. Second,implicit in priority wait lists is the perception of a low riskof pre-operative death in less severe patients. Our resultsdemonstrate that policy makers should be aware of an 8%risk of death in untreated patients with coronary arteryCompeting interestsThe author(s) declare that they have no competing inter-ests.Authors' contributionsBS conceived the study concept and design, participatedin analysis and interpretation, and drafted the manu-script. AL participated in data acquisition and criticallyrevised the manuscript. LK performed statistical analysisand drafted the manuscript. RH participated in dataacquisition. JB critically revised the manuscript. JMF criti-cally revised the manuscript and has been involved indrafting the manuscript. All authors read and approvedthe final manuscript.Additional materialAcknowledgementsThis research was supported by the Canada Research Chair Program (BS), the Michael Smith Foundation for Health Research Scholar Program (AL, JMF), grants from the Canadian Foundation for Innovation (BS, AL), and the CIHR Investigator Program (JMF).The following cardiac surgeons are contributors to the BCCR Surgical Research Committee: Drs. James Abel, Richard Brownlee, Larry Burr, Anson Cheung, James Dutton, Guy Fradet, Virginia Gudas, Robert Hayden, Eric Jamieson, Michael Janusz, Shahzad Karim, Tim Latham, Jacques LeBlanc, Sam Lichtenstein, Hilton Ling, John Ofiesh, Michael Perchinsky, Peter Skars-gard and Frank Tyers.The draft of the paper was presented at the Surgical Research Committee meeting on May 20, 2005. All useful comments from the participants have been incorporated into the manuscript. We are grateful to external review-ers, Drs. Anders Jeppsson and Wei-Ching Chang, for their thoughtful and useful suggestions.References1. Yusuf S, Zucker D, Peduzzi P, Fisher LD, Takaro T, Kennedy JW,Davis K, Killip T, Passamani E, Norris R: Effect of coronary arterybypass graft surgery on survival: overview of 10-year resultsfrom randomised trials by the Coronary Artery Bypass GraftSurgery Trialists Collaboration.  Lancet 1994, 344:563-570.2. Hannan EL, Racz MJ, Walford G, Jones RH, Ryan TJ, Bennett E, Culli-ford AT, Isom OW, Gold JP, Rose EA: Long-term outcomes ofcoronary-artery bypass grafting versus stent implantation.New England Journal of Medicine 2005, 352:2174-2183.3. DeLong ER, Nelson CL, Wong JB, Pryor DB, Peterson ED, Lee KL,Mark DB, Califf RM, Pauker SG: Using observational data to esti-mate prognosis: an example using a coronary artery diseaseregistry.  Statistics in Medicine 2001, 20:2505-2532.Additional File 1Appendix Matlab programs for non-parametric estimators of cumulative incidence and conditional probability functionsClick here for file[http://www.biomedcentral.com/content/supplementary/1472-6963-6-85-S1.pdf]Page 8 of 9(page number not for citation purposes)disease judged to be low-severity at presentation, if thereis a protracted delay before revascularization.4. 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