Survival Analysis for Cardiac Risk Stratification

To the Editor:—In the January issue, Shaw and colleagues use the techniques of survival analysis to investigate the ability of exercise myocardial perfusion tomographic imaging to incrementally risk-stratify patients following risk assessment by history and exercise treadmill testing.1 We are concerned that choices made in the analysis of their data bring their results and conclusions into question. Shaw and colleagues used proportional hazards regression to assess the associations between clinical, exercise testing, and imaging variables and time to death. As noted in the editorial accompanying their article, they appropriately chose to use cardiac death, not coronary revascularization, as their outcome because the use of revascularization as an outcome would have introduced bias given that physicians use test results to choose therapy.2 Their decision to censor patients at the time of coronary revascularization, however, violates one of the basic assumptions of survival analysis and most likely invalidates the analysis. Survival analysis assumes that censoring is noninformative: that is, censoring occurs independent of the risk of outcome.3 If this assumption does not hold, a form of selection bias is introduced. In the study by Shaw and colleagues, the analysis assumes that had the censored subjects not been revascularized, they would have had the same risk of cardiac death as the other subjects. We believe that one cannot reasonably assume censoring in this case to be independent of the risk of cardiac death. For patients with intermediate Duke treadmill scores, Shaw and colleagues present Kaplan-Meier survival curves by the number of infarcted or ischemic territories on nuclear scanning. The decision to censor those subjects who underwent revascularization may have resulted in an exaggerated separation between the survival curves for the strata defined by imaging results. For those patients found to have no infarcted or ischemic territories on imaging, censoring due to revascularization implies either a false-negative scan or the presence of very aggressive disease. In either case, these subjects would most likely have a higher cardiac death rate than that of other patients with negative scans who remained under observation. Censoring these subjects would make the prognosis for the group with negative scans look better than it is. Conversely, consider subjects with three or more infarcted or ischemic territories on the scan. Under most circumstances, these subjects would be candidates for revascularization, and we would expect them to be censored. Patients remaining under observation would be those who had a false-positive scan or were felt to be poor surgical candidates. If the majority from this high-risk group who remained under observation were, in fact, subjects with false-positive scans, the identified high-risk cohort would be artificially “healthier” and bias results toward the null. On the other hand, if the majority were poor surgical candidates, censoring those revascularized would leave a “sicker” group in the study and thus incorrectly magnify the differences in mortality based on scan result. We cannot know the net effect of the bias, but given that there is at least a reasonable possibility that it is causing a bias away from the null, we have to question the significance of the finding that the number of ischemic or infarcted territories predicts survival. If extended follow-up data are available for those who underwent revascularization in this study, the authors might reanalyze their data without censoring at the time of revascularization. Instead, they could include revascularization as a time-dependent covariate in an extended Cox regression. In this way, they would preserve cardiac mortality as their main outcome while adjusting for the effects of revascularization within each group. We hope that this approach proves possible and look forward to learning of their revised results.