Variation in Mortality Risk Factors With Time After Coronary Artery Bypass Graft Operation

Transcription

1 CARDIOVASCULAR Variation in Mortality Risk Factors With Time After Coronary Artery Bypass Graft Operation Dexiang Gao, PhD, Gary K. Grunwald, PhD, John S. Rumsfeld, MD, PhD, Todd Mackenzie, PhD, Frederick L. Grover, MD, Jonathan B. Perlin, MD, PhD, Gerald O. McDonald, MD, and A. Laurie W. Shroyer, PhD Department of Veterans Affairs Medical Center and University of Colorado Health Sciences Center, Denver, Colorado, and Office of Quality and Performance and Office of Patient Care Services, Department of Veterans Affairs Central Office, Washington, DC Background. Differences in mortality risk factor sets during different time periods (eg, short-term versus intermediate-term) after coronary artery bypass grafting have been reported. However, little is known about the time-varying effects of mortality risk factors after the operation. Methods. We analyzed 11,815 veterans who had coronary artery bypass grafting at any of the 43 Veterans Affairs cardiac surgery centers from October 1997 to September Time-varying effects of 14 mortality risk factors during the 210 days after coronary artery bypass grafting were evaluated using Cox B-spline regression, which provides an estimate of risk for each variable for each day after operation. Results. Eight variables showed significant timevarying effects after operation. The effect of prior heart operation was very high immediately after operation, but disappeared within 1 week. Three other cardiac variables (prior myocardial infarction, preoperative intraaortic balloon pump, and Canadian Cardiovascular Society anginal class III or IV) also conferred the highest risk on the day of operation and decreased thereafter. In contrast, the four time-varying noncardiac risk variables (age, impaired functional status, chronic obstructive pulmonary disease, and renal dysfunction) showed little or no association with mortality immediately after operation, but had increasing impact during the several months after operation. Conclusions. A sizable number of mortality risk factors have time-varying effects after coronary artery bypass grafting. Several cardiac risk factors have peak impact immediately after operation but dissipate thereafter. Several noncardiac risk factors confer little risk immediately after operation, but these risks increase during several months. This information may help clinicians focus management strategies for patients during the 7 months after operation. (Ann Thorac Surg 2003;75:74 81) 2003 by The Society of Thoracic Surgeons Preoperative risk factors have been described for short-term ( 30 days), intermediate-term (31 to 210 days), and long-term ( 210 days) mortality after coronary artery bypass graft (CABG) operation [1 7]. Important differences in risk factor sets for these periods have been noted. For example, our research group has previously reported that cardiac factors appear to have a larger impact on short-term mortality, whereas noncardiac factors appear to have a larger impact on intermediate-term mortality [7]. However, the definitions of short-term and intermediate-term mortality in previous studies were somewhat arbitrary, and it is unclear exactly how individual risk factors vary as a function of time after CABG operation. For example, it is unknown whether changes in the effects of risk factors on mortality after CABG operation occur during very short periods (days or weeks) or during longer terms (months or longer), because in previous Accepted for publication Aug 1, Address reprint requests to Dr Shroyer, Cardiac Research, Department of Veterans Affairs Medical Center, 820 Clermont St (112R), Denver, CO 80220; laurie.shroyer@med.va.gov. analyses the risk was held constant within predetermined time periods (eg, 0 to 30 days). To explicitly evaluate the time-varying properties of risk factors after CABG operation, we used advanced statistical methods to estimate the effects of preoperative risk variables on mortality for each of the 210 days after the operation. Our goal was to help clinicians understand how risk factors for mortality after CABG operation vary as a function of time so that they can better counsel patients with regard to mortality risk for the 7-month period after the operation and better coordinate continuity of patient care after the operation. Material and Methods Study Population The Veterans Affairs (VA) Continuous Improvement in Cardiac Surgery Program has collected risk and outcome data on all subjects undergoing cardiac operation from the 43 VA cardiac surgical centers since 1987 [1, 2]. Subjects included in the present study were all VA patients who underwent CABG operation from October 1, 1997, through September 30, Only 8 patients were 2003 by The Society of Thoracic Surgeons /03/$30.00 Published by Elsevier Science Inc PII S (02)

2 Ann Thorac Surg GAO ET AL 2003;75:74 81 TIME-VARYING RISK AFTER CABG omitted because of missing outcome data, giving a total study population of 11,815 patients. Outcomes The goal of this study was to examine the details of the time-dependent impact of risk factors on survival of patients after CABG operation. The outcome was allcause mortality between the date of operation and 210 days after operation. We chose this period to cover both the initial recovery phase (usually taken to be around 30 days, and often labeled short-term ) plus an additional 6 months (which we call intermediate-term ). Mortality assessments were performed using both individual follow-up by VA personnel (including information from electronic medical records, cardiology clinics, and personal contact by VA Continuous Improvement in Cardiac Surgery Program surgical clinical nurse reviewers) and the VA Beneficiary Identification and Record Locator System (BIRLS). The BIRLS assessments have been shown to be comparable with the National Death Index for mortality assessment in a VA population [8]. The BIRLS was used for primary determination of mortality outcomes, with confirmation and determination of any deaths missed by the BIRLS by individual follow-up. Outcome assessment was complete for all 11,815 patients included in this study for at least 210 days after operation. Risk Variables We considered 24 candidate preoperative risk variables for mortality after CABG operation. In our previous less-detailed analysis [7] we noted that 10 of these 24 risk variables were not significantly associated with either 0- to 30-day or 31- to 210-day mortality, so because of the intensive nature of our present analyses we did not consider these variables in our primary analyses. We examined the remaining 14 risk variables (prior heart operation, Canadian Cardiovascular Society anginal class III or IV, prior myocardial infarction, preoperative intraaortic balloon pump, ST-segment depression on preoperative electrocardiogram, New York Heart Association functional class III or IV, left main coronary artery stenosis more than 50%, left ventricular ejection fraction, age, partially or totally dependent functional status, chronic obstructive pulmonary disease [COPD], peripheral vascular disease, cerebral vascular disease, and serum creatinine 1.5 mg/dl) in detail as described below. The 10 variables not found to be significantly associated with mortality in our previous analyses were male sex, body surface area, current smoker, diabetes, percutaneous transluminal coronary artery angioplasty 0 to 72 hours before operation, intravenous nitroglycerin 0 to 48 hours before operation, surgical priority, number of stenotic coronary arteries, preoperative digoxin use, and preoperative diuretic use. We examined these 10 variables less intensively by including each of them as a constant hazard predictor and with a linearly timevarying effect in our final multivariable survival model (described in the statistical analyses section below). None of these variables were significant in either form, so further results for these variables are not reported. Statistical Analyses Multivariable analyses were performed to evaluate the independent time-varying effects of each of the 14 preoperative risk variables on all-cause mortality. Cox regression (survival analysis) was used rather than the more traditional logistic regression because it is able to make use of the times of deaths, which are necessary to study the timing of effects of risk factors after operation, our goal. Two separate multivariable methods were used: (1) Cox proportional hazards regression with incorporation of B-spline functions of survival time after operation, and (2) standard Cox proportional hazard survival analysis. The comparison of B-spline models with the standard Cox model provides a test of the proportional hazards assumption (ie, is risk constant over time) and the B-spline regression is one approach for incorporating nonproportionality of risk (ie, varying risk over time when it is detected) [9]. All statistical analyses were conducted using SAS version 8 [10]. First, the time-dependent effect of each of the risk factors on survival was modeled using Cox proportional hazards regression methods with incorporation of B- spline functions of survival time after operation [11 13]. Spline functions are smoothly joined piecewise polynomials, allowing a flexible and smoothly varying hazard ratio as a function of time. This analysis provides an estimate of the hazard ratio (and a 95% confidence interval [CI]) at each day (0 to 210) after operation. The hazard ratio at a given day after operation is the ratio of the estimated hazard for those with a specific risk factor to the estimated hazard for those without the risk factor, controlling for other covariates. Generally, the hazard ratio may be thought of as the relative risk at a given point in time. As an example, suppose the hazard ratio for the variable prior heart operation is found to be 5 on day 2 after operation. This means that a patient who has survived to day 2 and has had a previous heart operation has 5 times the risk of a mortality event on day 2, as compared with a corresponding patient without a previous heart operation, controlling for all other risk factors. A hazard ratio of 1 at a given time indicates no increased risk at that time owing to the risk factor. The major advantage of this statistical method is that it allows investigation of the shape of the time dependence of predictors without requiring that the exact functional form first be specified. Details of these statistical analyses are described in the Appendix. For each of the risk variables found to be time-dependent, the results of these analyses are presented as a graph of the hazard ratio and a 95% CI at each day (0 to 210) after operation. Second, each variable was evaluated using standard Cox proportional hazard survival analysis for the total 210 day period, which dictates a constant hazard ratio (ie, constant risk over the time period of evaluation) for each variable [14, 15]. An overall final mortality model was selected using minimum Akaike information criterion (see Appendix for details) from both the time-dependent and time-constant hazard ratio models. Sample SAS programing code for the Cox B-spline 75 CARDIOVASCULAR

3 CARDIOVASCULAR 76 GAO ET AL Ann Thorac Surg TIME-VARYING RISK AFTER CABG 2003;75:74 81 Table 1. Characteristics Study Population (N 11,815) Variable Percent or Mean (SD) Demographic/Noncardiac Age (y) 64 (10) Functional status: partially or totally 15.2% dependent COPD 26.1% Peripheral vascular disease 25.7% Cerebral vascular disease 22.3% Serum creatinine level 1.5 mg/dl 15.3% Cardiac Prior heart operation 6.8% CCS anginal class III or IV 77.7% Prior myocardial infarction 57.3% Preoperative IABP 5.0% Preoperative ST-segment depression on 18.4% electrocardiogram NYHA functional class III or IV 16.4% Left main coronary artery stenosis 50% 27.5% Left ventricular ejection fraction % CCS Canadian Cardiovascular Society; COPD chronic obstructive pulmonary disease; IABP intraaortic balloon pump; NYHA New York Heart Association; SD standard deviation. regression and 95% CI is available on request to the corresponding author. Results Baseline Patient Characteristics Baseline patient characteristics for the 14 preoperative risk variables studied in detail are listed in Table 1. The average age of the study population was 64 years. A sizable proportion of patients had noncardiac comorbidities such as COPD (26%) and peripheral vascular disease (26%). More than half of the patients had a prior myocardial infarction, 7% had prior heart operation, and nearly half had a reduced left ventricular ejection fraction ( 0.55). Fig 1. Kaplan-Meier survival curve (solid line) and 95% confidence limits (dashed lines) after coronary artery bypass graft operation. their highest values on the day of operation and decreased thereafter (Figs 2 5). The hazard ratio for prior heart operation, after adjusting for other covariates, was 7.5 (95% CI, 4.9 to 11.3) on the day of operation, but rapidly decreased to become nonsignificant approximately 7 days after the operation. The hazard ratio for prior myocardial infarction was 1.43 (95% CI, 1.15 to 1.78) on the day of operation, and gradually dropped to become nonsignificant approximately 2 to 3 months later. The hazard ratio for Canadian Cardiovascular Society anginal class III or IV was 2.12 (95% CI, 1.15 to 3.34) on the day of operation and decreased thereafter, becoming nonsignificant approximately 1 month after the operation. The hazard ratio for preoperative intraaortic balloon pump was 2.34 (95% CI, 1.74 to 3.15) on the day of Outcome Overall mortality rate for the study population for the 210-day period was 6.3%. The cumulative survival curve for the study population is shown in Figure 1. Numbers of deaths in each of the 7 months were 393, 98, 62, 54, 41, 52, and 40, respectively. Time-Varying Risk Factors Eight of the 14 mortality risk variables considered in detail had significant time-dependence of the hazard ratio (ie, had significant time-varying effects after operation). Adjusted hazard ratios and 95% CI at each day (0 to 210) after operation for each of these time-varying risk factors are shown in Figures 2 9. For each of the four cardiac variables with time-varying risk (prior heart operation, prior myocardial infarction, Canadian Cardiovascular Society anginal class III or IV, and preoperative intraaortic balloon pump), the hazard ratios all started at Fig 2. Hazard ratio (HR, solid line) and 95% pointwise confidence bands (dashed lines) for time-dependent cardiac risk predictor prior heart operation at each day (0 to 210) after coronary artery bypass graft operation. A horizontal line at 1 would indicate no increased risk.

4 Ann Thorac Surg GAO ET AL 2003;75:74 81 TIME-VARYING RISK AFTER CABG 77 CARDIOVASCULAR Fig 3. Hazard ratio (HR, solid line) and 95% pointwise confidence bands (dashed lines) for time-dependent cardiac risk predictor prior myocardial infarction at each day (0 to 210) after coronary artery bypass graft operation. A horizontal line at 1 would indicate no increased risk. Fig 5. Hazard ratio (HR, solid line) and 95% pointwise confidence bands (dashed lines) for time-dependent cardiac risk predictor preoperative intraaortic balloon pump (IABP) at each day (0 to 210) after coronary artery bypass graft operation. A horizontal line at 1 would indicate no increased risk. operation and decreased steadily, becoming not significant after approximately 2 to 3 months. In contrast, the hazard ratios for the four time-varying noncardiac variables (age, COPD, renal dysfunction, and partially or totally dependent functional status) increased from a nonsignificant or nearly nonsignificant hazard ratio on the day of operation and reached a plateau at 2 to 4 months after operation (Figs 6 9). The hazard ratio for age per 10 years was 1.27 (95% CI, 1.11 to 1.47) on the day of operation and increased gradually, reaching a maximum hazard ratio of 1.81 (95% CI, 1.52 to 2.15) after approximately 2 months. The hazard ratio for COPD became significant at approximately 1 month after the operation. The hazard ratio for renal dysfunction became significant shortly after operation and increased steadily for approximately 3 months after CABG operation. The hazard ratio for partially or totally dependent functional status was not significant immediately after operation but increased steadily, becoming significant approximately 1 month after operation. For several of these variables, the function estimates show slight decreases in hazard toward the latter end of the period, but the wide confidence bands in those regions indicate that there is insufficient evidence to conclude that hazard decreases in those cases. Fig 4. Hazard ratio (HR, solid line) and 95% pointwise confidence bands (dashed lines) for time-dependent cardiac risk predictor Canadian Cardiovascular Society (CCS) anginal class III or IV at each day (0 to 210) after coronary artery bypass graft operation. A horizontal line at 1 would indicate no increased risk. Fig 6. Hazard ratio (HR, solid line) and 95% pointwise confidence bands (dashed lines) for time-dependent noncardiac risk predictor age per 10-years at each day (0 to 210) after coronary artery bypass graft operation. A horizontal line at 1 would indicate no increased risk.

5 CARDIOVASCULAR 78 GAO ET AL Ann Thorac Surg TIME-VARYING RISK AFTER CABG 2003;75:74 81 Fig 7. Hazard ratio (HR, solid line) and 95% pointwise confidence bands (dashed lines) for time-dependent noncardiac risk predictor chronic obstructive pulmonary disease (COPD) at each day (0 to 210) after coronary artery bypass graft operation. A horizontal line at 1 would indicate no increased risk. Fig 9. Hazard ratio (HR, solid line) and 95% pointwise confidence bands (dashed lines) for time-dependent noncardiac risk predictor totally or partially dependent functional status at each day (0 to 210) after coronary artery bypass graft operation. A horizontal line at 1 would indicate no increased risk. Time-Constant Risk Factors The remaining six mortality risk variables had significant time-constant hazard ratios during the entire study period, meaning that their effects on mortality did not significantly vary with time after the operation. These variables, with their overall hazard ratios and 95% CI for the 210-day period after CABG operation, are listed in Table 2. Comment The goal of this study was to examine the time-varying properties of mortality risk factors after CABG operation. We therefore evaluated the details of the impact of 14 preoperative risk factors on survival during the first 210 days after the operation using statistical methods capable of estimating differences in risk effects for each day after operation. We found that 8 of the 14 variables examined in detail had significant time-varying effects on mortality during the 7 months after the operation, including four cardiac risk variables and four noncardiac risk variables. Cardiac variables appear to drive much of the upfront risk with CABG operation, with the timing of some effects differing substantially. For example, we found that the magnitude of risk of prior heart operation was highest on the day of the operation (hazard ratio 7), but it was no longer a significant risk variable by approximately a week after the operation. This supports the clinical impression that the increased mortality risk from Table 2. Hazard Ratios (95% Confidence Intervals) and Probability Values for Risk Predictors Found To Have Time- Constant Hazards Variable Hazard Ratio (95% CI) p Value Fig 8. Hazard ratio (HR, solid line) and 95% pointwise confidence bands (dashed lines) for time-dependent noncardiac risk predictor creatinine 1.5 mg/dl at each day (0 to 210) after coronary artery bypass graft operation. A horizontal line at 1 would indicate no increased risk. Demographic/Noncardiac Peripheral vascular disease 1.30 ( ) Cerebral vascular disease 1.37 ( ) Cardiac Preoperative ST-segment 1.31 ( ) depression on electrocardiogram NYHA functional class III 1.51 ( ) or IV Left main coronary artery 1.23 ( ) stenosis 50% Left ventricular ejection fraction ( ) 0.01 NYHA New York Heart Association.

6 Ann Thorac Surg GAO ET AL 2003;75:74 81 TIME-VARYING RISK AFTER CABG prior heart operation is most likely directly related to the operation itself (eg, bleeding risk, risk of embolization from prior grafts). Prior heart operation has consistently been reported as a strong risk factor for short-term (30-day) mortality after CABG operation [2 7]. The present study suggests that previous analyses may have substantially underestimated the risk from prior heart operation in the first few days after operation and overestimated the risk after the first week. The other three cardiac risk factors with time-varying effects (elevated anginal class, previous myocardial infarction, and preoperative intraaortic balloon pump) also had peak effects immediately after operation, but these effects dissipated more than 1 to 3 months after the operation. On the other hand, noncardiac risk factors appear to have more pronounced effect on survival after the early postoperative period, and risks from these factors tend to increase during the first several months after operation. For example, a history of COPD does not appear to be a mortality risk factor for the operation during the early postoperative period, but predicts increased mortality starting at approximately 1 month after operation. Similar patterns were found for renal insufficiency and reduced preoperative functional status. These results suggest that there should be an increased focus on noncardiac comorbidity in the months after the early recovery phase from the operation to maximize outcomes. Often, patients are labeled as cardiac patients after bypass operation, but strong consideration should be given to more aggressive management of comorbidities by primary care physicians in the early months after the operation. Renal insufficiency (serum creatinine 1.5 mg/dl) was found to be a strong risk factor for intermediate mortality after CABG operation in this study. This risk factor can potentially be modified by more aggressive blood pressure control to meet JNC-VI (The Sixth Reports of the Joint National Committee on Prevention, Detection, Evaluation, and Treatment of High Blood Pressure) guideline recommendations, careful management of diabetes, and by the increased use of angiotensin-converting enzyme inhibitors, which appear to retard the progression of renal disease, especially in diabetic patients [16, 17]. Similarly, aggressive management of COPD in the months after CABG operation can potentially lead to improved outcomes. For a patient with severe COPD, a longer postoperative convalescence period with rehabilitation or enhanced primary care follow-up may be considered clinically appropriate. Finally, functional status has been associated with higher mortality in multiple patient populations, independent of specific medical diagnoses [18 20]. This may represent a measure of the overall severity, or impact, of disease on a given patient. Future research should focus on specific determinants of functional status with the goal of identifying potentially modifiable factors. In the meantime, consideration should be given to the continuation of cardiac rehabilitation, shown to improve functional status, throughout the intermediate period after CABG operation when possible. The findings of this study may also enhance preoperative counseling of patients, both by expanding the period of risk assessment to 7 months after the operation and by highlighting which factors confer time-varying versus constant risk after the operation. For example, a patient with prior heart operation and history of myocardial infarction, but lacking noncardiac risk factors, can be told their major risk is perioperatively within approximately the first 40 days after their operation. Alternatively, a patient lacking these cardiac risk variables but with renal dysfunction and COPD can be told that they may be at enhanced risk in the intermediate recovery period. Approximately half of the risk variables evaluated in this study, such as reduced left ventricular ejection fraction, a history of cerebral vascular disease, and a history of peripheral vascular disease, conferred constant risk for mortality from the time of operation across the 7-month period after CABG operation. Whereas previous studies have reported these variables as risk factors, most have focused on short-term (eg, 30-day) mortality. The results of this study therefore extend our understanding of the impact of these variables to the 7-month period after CABG operation. Strengths of this study included the use of a large, prospectively collected database with nearly complete preoperative and follow-up data on all patients who underwent CABG operation in the VA during the 2-year period analyzed. The statistical methods used in this study were unique in allowing explicit evaluation of the time-varying effects of mortality risk variables after CABG operation. In a previous study [7], we noted differences in risk factors between the periods 0 to 30 days and 31 to 210 days after operation, in which the cut-off of 30 days was fixed to correspond to the many previous studies of 30-day mortality. However, those analyses were by definition unable to provide more specific information about patterns of risk after operation. The present study used more sophisticated analyses, which provided detailed information about timing of effects of risk variables after CABG operation. In general, risk factors for cardiac procedures and diseases are discussed as fixed (ie, their effect is constant with regard to the procedure or disease). This is a reflection of standard statistical methods, which report a single magnitude of risk for each variable, thereby implying an all or nothing effect on the outcome. The results of this study suggest that a substantial proportion of CABG operation risk variables have time-varying effects related to clinical outcomes. Our study uses these particular statistical methods, allowing examination of the day-to-day variation of the impact of risk factors on mortality after CABG operation. These statistical methods may be useful for other cardiovascular procedures and diseases, as there may be important time-varying effects of risk variables in relation to procedures such as percutaneous coronary intervention or diseases such as acute coronary syndromes or congestive heart failure. Several potential limitations of this study should be addressed. First, the results may have limited generaliz- 79 CARDIOVASCULAR

7 CARDIOVASCULAR 80 GAO ET AL Ann Thorac Surg TIME-VARYING RISK AFTER CABG 2003;75:74 81 ability to non-va populations. Second, we noted minor discrepancies between the two methods of mortality assessment used (BIRLS and individual follow-up). However, reanalysis of data using only the BIRLS outcome did not alter the results. Third, we did not have specific information on cause of death. Fourth, our evaluation of a 6-month interval after the first 30 days after operation is somewhat arbitrary, and we cannot be certain of the time-varying impact of risk factors beyond 7 months after the operation. In summary, we found significant time-varying effects of a number of mortality risk variables after CABG operation. We found that several cardiac variables have primary impact immediately perioperatively, whereas noncardiac variables have increasing impact in the months after the operation. This suggests that noncardiac variables should be an important focus of care in the months after CABG operation. Future studies are needed to determine whether these risk factors can be modified, and the results of this study should not detract from a focus on secondary prevention of cardiac events or addressing cardiac risk factors indefinitely after CABG operation. Nonetheless, cardiothoracic surgeons and cardiologists should be aware of the time-varying properties of some mortality risk factors after CABG operation and should consider appropriate referral to address noncardiac issues early after the operation. Funding for this study was provided by VA Health Services Research and Development Grant IHY (ALWS), the VA Office of Quality and Performance at VA Headquarters, and the VA Office of Patient Care Services at VA Headquarters, Washington, DC. Dr Rumsfeld is supported by a VA Health Services Research and Development Research Career Development Award (RCD ). Dr Mackenzie is supported by Grant MO1 RR00069, General Clinical Research Centers Program, National Institutes of Health. References 1. Grover FL, Johnson R, Shroyer LW, Marshall G, Hammermeister KE. The Veterans Affairs continuous improvement in cardiac surgery study. Ann Thorac Surg 1994;58: Grover FL, Shroyer ALW, Hammermeister KE. Calculating risk and outcome: the Veterans Affairs database. Ann Thorac Surg 1996;62(Suppl):S Shroyer ALW, Plomondon ME, Grover FL, Edwards RH. The. coronary artery bypass risk model: The Society of Thoracic Surgeons Adult Cardiac National Database. Ann Thorac Surg 1999;1996:67: Risum O, Abdelnoor JL, Svennevig S, et al. Risk factors for early and late mortality in surgical treatment of coronary artery disease. Cardiovasc Surg 1995;3: Hannan EL, Kilburn H, O Donnell JF, Lukacik G, Shields EP. Adult open heart surgery in New York State: an analysis of risk factors and hospital mortality rates. JAMA 1990;264: Jones RH, Hannan EL, Hammermeister KE, et al. Identification of preoperative variables needed for risk adjustment of short-term mortality after coronary artery bypass graft surgery. J Am Coll Cardiol 1996;28: Gardner SC, Grunwald GK, Rumsfeld JS, et al. Risk factors for intermediate-term survival following coronary artery bypass graft surgery. Ann Thorac Surg 2001;72: Fisher SG, Weber L, Goldberg J, Davis F. Mortality ascertainment in the veteran population: alternatives to the National Death Index. Am J Epidemiol 1995;141: Durrleman S, Siman R. Flexible regression models with cubic spline. Stat Med 1989;8: SAS/STAT User s Guide, Version 8, SAS Institute, Cary, NC, Abrahamowicz M, MacKenzie T, Esdaile JM. Timedependent hazard ratio: modeling and hypothesis testing with application in lupus nephritis. J Am Stat Assoc 1996;91: MacKenzie T, Abrahamowicz M. B-splines without divided differences. Student 1996;1: Hess KR. Assessing time-by-covariate interactions in proportional hazards regression models using cubic spline functions. Stat Med 1994;13: Cox DR. Regression models and life tables. J R Stat Soc Series B 1972;34: Allison PD. Survival analysis using the SAS system. Cary, NC: SAS Institute Inc, 1995: The Sixth Report of the Joint National Committee on Prevention, Detection, Evaluation, and Treatment of High Blood Pressure. Available at: index.htm. Accessed 5/15/ Kshirsagar AV, Joy MS, Hogan SL, Falk RJ, Colindres RE. Effect of ACE inhibitors in diabetic and nondiabetic chronic renal disease: a systematic overview of randomized placebocontrolled trials. Am J Kidney Dis 2000;35: Davis RB, Iezzoni LI, Phillips RS, Reiley P, Coffman GA, Safran C. Predicting in-hospital mortality. The importance of functional status information. Med Care 1995;33: Inouye SK, Peduzzi PN, Robison JT, Hughes JS, Horwitz RI, Concato J. Importance of functional measures in predicting mortality among older hospitalized patients. J Am Med Assoc 1998;279: Mossey JM, Shapiro E. Self-rated health: a predictor of mortality among the elderly. Am J Public Health 1982;72: Appendix The Cox regression models with the incorporation of B-spline functions were estimated using SAS PROC PHREG, with time-varying covariates used to incorporate the spline functions of survival time [11 13]. For computational efficiency, the survival times (0 to 210 days) were grouped into 100 groups with each group containing 1% of total events. The median survival time was used as the group survival time for each group. Examination of specific cases showed no detectable effects of this slight approximation. Quadratic without knots or linear B-splines with a prior fixed maximum of three interior knots were used as the possible B-spline functions. The interior knots were placed at approximately 25% (7 days after operation), 50% (28 days after operation), and 75% (91 days after operation) of event (death) times. When a model contains one or two knots, those knots can be located at any combination of the three possible interior knot positions. In general, the results of these types of more-complex Cox spline regression modeling approaches have been noted not to be very sensitive to the location of the B-spline knots [9]. We conducted several sensitivity studies of effects of knot location and also experienced this insensitivity. In addition to the B-spline models for time-dependent effects,

8 Ann Thorac Surg GAO ET AL 2003;75:74 81 TIME-VARYING RISK AFTER CABG each of the 14 variables was also considered with a timeconstant hazard (the standard Cox proportional hazard survival analysis) [14, 15]. Thus, 10 different models were considered for each risk variable. We used the minimum Akaike information criterion to select the final model from this set [11, 13]. If the difference in the Akaike information criterion values was within 4, the model with the fewest degrees of freedom was selected as the final model. The 95% pointwise confidence bands were constructed following the approach described in Hess [13]. These reduce to the usual 95% CI for the hazard ratio in standard Cox regression. Owing to the computational complexity and the large number of possible spline models for each variable, selection of the order and number of knots of the spline function for each variable was performed assuming timeconstant effects for other variables. The final model was estimated with all time-varying spline functions included simultaneously. Results for the simultaneous estimation were very similar to those assuming only one timevarying risk factor. 81 CARDIOVASCULAR Notice From the American Board of Thoracic Surgery Regarding Trainees and Candidates for Certification Who Are Called to Military Service Related to the War on Terrorism The Board appreciates the concern of those who have received emergency calls to military service. They may be assured that the Board will exercise the same sympathetic consideration as was given to candidates in recognition of their special contributions to their country during the Vietnam conflict and the Persian Gulf conflict with regard to applications, examinations, and interruption of training. If you have any questions about how this might affect you, please call the Board office at (847) Peter C. Pairolero, MD Chairman The American Board of Thoracic Surgery 2003 by The Society of Thoracic Surgeons Ann Thorac Surg 2003;75: /03/$30.00 Published by Elsevier Science Inc