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J Thorac Cardiovasc Surg 2000;119:1221-1232
© 2000 The American Association for Thoracic Surgery
SURGERY FOR ACQUIRED CARDIOVASCULAR DISEASE |
From the Department of Thoracic and Cardiovascular Surgerya and the Department of Biostatistics and Epidemiology,b The Cleveland Clinic Foundation, Cleveland, Ohio.
Address for reprints: Eugene H. Blackstone, MD, Department of Thoracic and Cardiovascular Surgery, 9500 Euclid Ave, Desk F25, Cleveland, OH 44195 (E-mail: blackse{at}ccf.org ).
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Abstract |
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 Top Abstract IntroductionPatients and methods Results Discussion Limitations Appendix: Discussion References |
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Introduction |
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TopAbstractIntroductionPatients and methods Results Discussion Limitations Appendix: Discussion References |
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1 Are the benefits of bilateral ITA grafting on reintervention nullified in high-risk patients?
Reinterventions after bilateral ITA grafting are fewer in the elderly. 1-3 Does the decreased incidence of reintervention in the elderly simply reflect passive attrition by death?
The benefits of different interventions, such as bilateral versus single ITA grafting, are commonly expressed in terms of event-free survival. However, because reintervention is prominent in the young and death in the elderly, a young patient and an old patient may have similar event-free survival estimates. Can event-free survival be presented in a less counterintuitive format?
To answer these questions, we need to adjust potential long-term benefits for attrition by death. Competing risks analysis can accomplish this. 4,5 Therefore, we re-examined the outcome of patients after elective primary isolated coronary revascularization using one or two ITA grafts in light of three competing time-related events—death, reoperation, and percutaneous transluminal coronary angioplasty (PTCA)—which together constitute event-free survival.
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Patients and methods |
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TopAbstractIntroductionPatients and methods Results Discussion Limitations Appendix: Discussion References |
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1
Patients receiving bilateral ITA grafts differed in many respects from those receiving single ITA grafts. 1 Therefore, nonparsimonious propensity matching on known variables was used to formulate a well-matched, comparable group of 1975 patients undergoing bilateral ITA grafting and 4147 undergoing single ITA grafting. 1 These patients were the basis for the competing risks analyses in the present study.
Event-free survival and competing risks
Construction of an event-free survival curve and conduct of a competing risks analysis begin identically. The earliest occurrence of one of three mutually exclusive events was considered: (1) death, (2) cardiac reoperation, and (3) PTCA. The common analysis interval was the interval between operation and the earliest occurrence of one of these events. Freedom from all events (alive without reintervention) is termed event-free survival .
Freedom from each event was estimated by the nonparametric product-limit method (formula 4.4.2 of Andersen and associates 6). Variances of the estimates were based on the Greenwood formula (formula 4.4.19 of Andersen and associates 6). Asymmetric confidence limits were calculated with the use of these variances and formula 6E-6 in Kirklin and Barratt-Boyes. 7 The instantaneous risk (hazard function) for each competing event was estimated by a parametric method* that resolved the number of hazard phases, identified the shape of the hazard function, and estimated its parameters. 8 The width of the confidence limits for estimates calculated from the resulting equations were consistent in width with those for nonparametric estimates.
Multivariable analyses
Variables examined multivariably for each event were listed previously. 1 Multivariable analyses were conducted independently in the multiphase hazard function domain 8 for each of the three competing events to generate parsimonious equations. Regression coefficients are presented plus or minus one standard error. These are presented rather than hazard ratios because the models, and the underlying data, were not proportional hazards across time.
Because the mode of reintervention changed across calendar time, multivariable logistic analysis was performed of reintervention by PTCA versus reoperation (Appendix I).
Synthesis of information
Consequences of the independent, simultaneously operative, migration rates (hazard functions) from the category alive without reintervention (event-free survival) into each of the event categories were obtained by integration with the use of the parametric equations (Appendix II). This was supplemented, in some instances, with a comparison of the corresponding probability of the reintervention, obtained from the same multivariable equations, with its competing risks counterpart. The familiar probability of reintervention applies to patients who are alive and have not yet experienced the event. It represents their potential risk of reintervention were the competing risk of death not present. Thus, two different presentations are possible from the identical hazard functions: potential, from reintervention probability estimates, and actual, from the percent of patients expected to experience reintervention in the context of multiple hazard functions operating simultaneously. 9,10
These analyses were the substrate used to address the questions posed in the introduction. The question sequence will be altered to more easily describe the methods used for answering them.
Can event-free survival be presented in a less counterintuitive format?
Event-free survival is a composite time-related entity representing the aggregate occurrences of several dissimilar events. In this study, event-free survival decreases across time, commensurate with the percent of patients who have died, undergone reoperation, or experienced a PTCA increase across time. From one type of patient to another, and across time, the magnitude of event-free survival may be dominated by a different event. We propose that the simultaneous display of all components of event-free survival clarifies which events dominate and when, permitting clear interpretation of what may be otherwise counterintuitive aspects of event-free survival.
Are the benefits of bilateral ITA grafting on reintervention nullified in high-risk patients?
Both potential and actual expected benefits of two versus one ITA graft were compared for each patient. To accomplish this, we solved the multivariable equations for each patient (1) as if single ITA grafting had been performed and (2) again as if bilateral ITA grafting had been performed. For these calculations, the date of operation was artificially set to January 1, 1990, because of the prominent influence of calendar date on type of outcome (Appendix I). The difference between having one or two ITA grafts in the probability of each event (potential ) and again in the proportion of events (actual ) is presented at 12 years postoperatively.
Does the decreased incidence of reintervention in the elderly simply reflect passive attrition by death?
To investigate this question, we performed a competing risks simulation. Multivariable equations for reoperation and for PTCA were generated exactly as will be presented in Tables II and III, except the age association was ignored. Three independent uniform random number generators were used to generate a separate probability of death, reoperation, and PTCA for each simulated patient. The interval from operation to the time of each generated probability was calculated from the inverse of the multivariable equations. If the simulated interval to an event exceeded 12 years, the time was censored. A common interval to the earliest of simulated death, reoperation, or PTCA was generated. Finally, multivariable analyses of reoperation and PTCA were performed on these artificial events and intervals (with actual patient values being used for all risk factors) to determine if the coefficients for age in the reintervention analyses were different from the anticipated value of zero. A negative coefficient would be evidence that the risk factor analyses of reintervention were influenced spuriously by passive attrition from death of old patients.
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Results |
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TopAbstractIntroductionPatients and methods Results Discussion Limitations Appendix: Discussion References |
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and 3 were identical, Fig 1 depicts the pure probability of events among living patients, whereas Fig 3 depicts the end result of accounting for events simultaneously as they remove patients from risk. Thus, at 12 years the probability of each event among living patients (Fig 1) versus the percent of patients that will experience the event before experiencing any other (Fig 3) were 28.7% versus 26.6% for death, 8.6% versus 6.8% for reoperation, and 10.1% versus 8.1% for PTCA.
Multivariable analyses
The overall competing risks analysis has little intrinsic value because the transition rates are modulated importantly by patient variables (risk factors). The risk factors were summarized qualitatively and discussed previously 1 but are presented quantitatively in Tables I through III.
Single ITA grafting was associated with a greater probability of death, reoperation, and PTCA than was bilateral ITA grafting. However, the risk factors for death, in contrast to those for reoperation or PTCA, included a strong relation to old rather than young age at operation, to greater left ventricular dysfunction than less, and to several comorbidities rather than none. It was the opposing direction of influence of risk factors and the presence of different risk factors for different events that made estimates of event-free survival counterintuitive.
Can event-free survival be presented in a less counterintuitive format?
Yes.
Fig 4 contrasts event-free survival and the individual competing risk components between bilateral and single ITA grafting in a quite young (age 35 years), but otherwise median-risk, patient. Death was unlikely, regardless of surgical strategy. Thus, the dominant event determining event-free survival was reintervention.
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, B ) event-free survival was identical for a 30-year-old patient and a 66-year-old patient.
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Are the benefits of bilateral ITA grafting on reintervention nullified in high-risk patients?
No.
Across all ages, fewer patients were predicted to undergo reintervention with bilateral rather than single ITA grafting. 1 However, at old age, death prominently reduced the percent of patients who potentially might have required reintervention. Therefore, the potential probability of reintervention among surviving older patients was higher than the actual percent of older patients expected to experience a reintervention because many died before that point (Fig 6). This progressively narrowed the predicted benefit of two versus one ITA graft as age increased.
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These considerations permit us to summarize not just the potential benefit of bilateral ITA versus single ITA grafting, but the actual benefit in terms of fewer reinterventions before death (Fig 7). The actual benefit was positive, but uniformly smaller than that expected on the basis of differences in probability because the attrition of patients by death increasingly dominated nonfatal events as age increased.
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Simulated competing risks analyses that assumed no age effect related to reintervention still demonstrated that fewer older patients would survive to experience either reoperation or PTCA. However, multivariable risk factor analysis of simulated reintervention did not identify age as a risk factor and, more specifically, did not identify it as a negative risk factor. It yielded a coefficient of nearly zero (–0.0094 in the early hazard phase and 0.0049 in the late hazard phase for reoperation and 0.00057 for PTCA). Thus, attrition by death, precluding reintervention in many patients, did not confound risk factor identification and quantification of independent nonfatal events.
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Discussion |
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TopAbstractIntroductionPatients and methods Results Discussion Limitations Appendix: Discussion References |
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Are the benefits of bilateral ITA grafting on reintervention nullified in high-risk patients?
No.
The actual long-term benefit of bilateral versus single ITA grafting on freedom from reintervention was considerably less for some patients, such as the elderly, than those calculated from differences in reintervention probabilities . Thus, despite the fact that the actual number of reinterventions in the elderly will be fewer than the potential number were survival not the issue, bilateral ITA grafting still decreases the actual number of reinterventions in the elderly compared with single ITA grafting. This observation of decreased realized long-term benefit by factors that importantly reduce the likelihood of long-term survival was emphasized by Sergeant, Blackstone, and Meyns 12 for vein grafts versus use of the ITA.
Rates of migration from event-free survival to death, reoperation, or PTCA were influenced by both patient-related and operation-related variables; however, age was the most important patient-related variable and the easiest to portray. It was not the only one. Thus, it is important to assess the influence of multiple patient-related variables that determine the difference between the potential and the actual benefit of different surgical strategies for both individuals and groups of patients.
The inevitable question arises as to whether one should concentrate on individual event estimates, as is true of conventional analyses, or on competing risks estimates that are emphasized in this study. We believe both have a complementary and different role in patient-physician decision making, generation of new knowledge, and understanding of heart disease and its treatment. Conventional individual event analyses isolate the effects of single end points, removing the confounding influence of other events so as to reveal the nature of the disease or treatment on a specific event. In contrast, the competing risks analysis uses this same information, the same hazard functions, and the same risk factor analyses to reveal the consequences of these events operating simultaneously.
Does the decreased incidence of reintervention in the elderly simply reflect passive attrition by death?
No.
The depletion by death of patients at risk of reintervention does not result in spurious risk factor analyses and interpretation so long as the competing events are reasonably independent. Thus, young age is a true risk factor for reintervention, not the spurious, passive result of attrition by death of older patients. This finding is important because a risk factor always depletes the pool of high-risk patients as time evolves, thereby changing the prevalence of that factor in the remaining patient population. 2 However, so long as a sufficient number of high-risk patients remain to permit risk factor identification, attrition by one event, such as death, does not unwittingly affect the analysis of another.
Reoperation and PTCA are outcomes after coronary bypass surgery whose occurrences are related to return of ischemic symptoms, decreased by attrition from death, and influenced by patients’ decisions and physician recommendations when symptoms return. In this study, we have quantified only the influence of attrition by death on reintervention. We have not ascertained the contribution of patient-physician decision making. It is possible that this, rather than pathophysiology, may have contributed to the finding of a reduced incidence of reintervention in older patients. 3,11
Is there a more insightful way to present event-free survival that is less counterintuitive
Yes.
In the setting of coronary artery disease, event-free survival gives rise to intellectually unappealing estimates of the same magnitude for a young patient, whose outcome is dominated by reintervention, and an older patient, whose outcome is dominated by death. The separate analysis of reoperation, PTCA, and death, followed by synthesizing them as competing risks, achieves the same overall result as event-free survival but, in addition, permits detailed examination and interpretation of each component’s contribution to the overall outcome.
Competing risks
The answers to the specific questions posed for this study have required the use of a method of analysis and presentation that is uncommon in coronary bypass surgery, although occasionally employed in other cardiac surgical settings. 9,10,13-15 On occasion, single and multiple event analyses seemingly have been pitted against one another when, as in this study, they are complementary and based on the same underlying hazard functions. 9,10
Competing risks analysis was described by Daniel Bernoulli 16 in 1760 to answer the question, "If in a given population smallpox could be eradicated, what would be the effect on the population mortality structure at different ages?" The analysis of time-related events was thereby generalized to consider not just isolated events, but the simultaneous consequences of multiple events. Bodnar, Haberman, and Wain 17 introduced competing risks into the analysis of morbid events after heart valve replacement in 1979, calling it the name used in population demography, multiple decrement analysis . Grunkemeier and colleagues 9,10 then introduced the designation "actual vs. actuarial," although we find this distinction troublesome.
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Limitations |
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TopAbstractIntroductionPatients and methods Results Discussion Limitations Appendix: Discussion References |
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18-20
We have limited our competing risks analysis to mutually exclusive end states. In fact, the technique has been generalized to an entire chain of events. 15
Finally, calculations of actual benefits are related to length of follow-up. We have used 12 years as the time point for benefit assessment because the number of patients beyond that point was small. As patients age and follow-up increases, we anticipate more long-range benefits to accrue to those operated on at younger ages, and for whom death is not the major issue at the 12-year follow-up interval.
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Appendix: Discussion |
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TopAbstractIntroductionPatients and methods Results Discussion Limitations Appendix: Discussion References |
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I predict that this concept applied to medicine will add as much benefit, if not more, than has our attention to the instantaneous hazard function that Dr Blackstone has showed us to be so valuable in his former work.
Life has been said to be a sexually transmitted, uniformly fatal condition. The implication of that to biostatisticians is that all survival curves converge on zero. The implication of that for cardiac surgeons is that we cannot be held completely responsible for preventing death. In fact, an ideal surgical operation would be one that deferred death from a cardiac reason until death could occur from another reason, particularly if no further cardiac interventions were required after the initial operation.
Unless we were very sophisticated biostatisticians, last year we went home from this meeting and, on the basis of these same data, said to our patients with coronary disease that they had dramatic survival benefit and lower reintervention benefit from coronary bypass in which two ITAs were used compared with one. To have been completely accurate, we would have said, "If you live for 12 years, your reintervention procedure rate will be 8% with bypass surgery and 7% with PTCA." The patient might have asked us, "But, doctor, what are my chances of dying over this 12-year period that you are talking about?" And you would have said, "27%, but one third of those deaths are not things I can prevent because they are noncardiac." This would have been a very confusing but accurate conveyance of this same information. This year you can go home and tell your patients, "If I do two ITA grafts instead of one, over the next 12 years of your life you have 2% less chance of death, 2% less chance of reintervention with bypass surgery, and 2% less chance of revascularization again with PTCA. That’s six big things out of a hundred that you would rather not have happen to you over the next 12 years that summarizes the total benefit to you if I do a second ITA graft."
I do not know what this says to you, but it says to me that my standard operation has changed from this day forward: from a single ITA graft, because of lack of real valid evidence as to the magnitude of benefit, to a standard of two ITA grafts, because I can quantitate the benefit in a way patients understand that is accurate and applicable. This is a dramatic contribution to our profession. I congratulate the authors.
Dr Blackstone. Thank you very much, Dr Jones, for those kind remarks. Coming from a person like you that I respect very much, this means more than you can imagine.
Allow me one further refinement of your comments. Not all patients will receive 2 + 2 + 2 benefits from the use of both ITAs. Some will receive less and others more. Unfortunately, identifying who will benefit more and who will benefit less is not simple to generalize, even though we have emphasized age as one of those considerations in this presentation. However, the equations presented are actually perfectly capable of being used for quantifying the benefit for an individual patient.
Appendix I: Confounding by changing mode of reintervention
During the time frame of this study, the modes of reintervention evolved from reoperation only to either reoperation or percutaneous interventions (Appendix
Fig 1). The correlates of PTCA being the mode of reintervention included more recent date of operation, bilateral versus single ITA grafting, left anterior descending coronary artery disease for which ITAs were placed to this artery, and younger age at operation (Appendix
Table I). In contrast, a reoperation was more likely to be the reintervention earlier in the experience, in older patients, in those with only a single ITA and vein grafts, and in left main disease.
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Thus, for the category (compartment) death CD(t), reoperation CR(t), and PTCA CP(t), the change (increase) in number of patients with time t will be related to the respective transition rates (hazard functions) 
D(t), R(t), and P(t) as they draw patients from the category alive without reintervention CA(t):
Conservation of patients means that if the equations above are normalized to 100 patients, at any time t:
Independence also implies that the hazard function for event-free survival will be:
Finally, CA(t) can be thought of as surviving [SD(t)], being free of reoperation [SR(t)], and being free of PTCA [SP(t)]:
where:
The survivorship functions were obtained analytically by the parametric survival analysis system.
With the use of all this information, integration to obtain CD(t), CR(t), and CP(t) was performed numerically.
Appendix III: Investigation of possible informative censoring
An assumption of this competing risks analysis was that each of the events, and therefore their corresponding hazard functions, was independent one from the other. This has sometimes been called noninformative censoring, because migration from the category alive without reintervention into any event category behaves as a censoring mechanism for all other event categories. One test of the reasonableness of this assumption of independence is the comparison of survival without reintervention to overall survival, the latter including all deaths at all times, including those subsequent to reinterventions (Appendix Fig 2 ).
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Acknowledgments |
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6 |
Footnotes |
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*Available by anonymous ftp://uabcvsr.cvsr.uab.edu for the SAS system.
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References |
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TopAbstractIntroductionPatients and methods Results Discussion Limitations Appendix: Discussion References |
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