John W. Robinson, M.D., Ph.D., LLC

Statistics ▪ Analytics ▪ Data Science

Design Suggestion: Consider Competing Risks in Studies with Time-to-Event Outcomes

A competing risk, or competing event, is an event that alters the probability of the event of interest, in the context of a study in which the primary outcome is the time to the event of interest (survival time). For example, if the event of interest is death due to cardiac causes, death due to non-cardiac causes is a competing event. A flawed study design might regard death due to non-cardiac causes as independent censoring rather than a competing event, implicitly assuming that an individual dying from a non-cardiac cause had, just prior to death, the same risk of death due to cardiac causes as an individual followed for the same duration who had not yet died. Of course, this is not a reasonable assumption, since non-cardiac causes of death include, for example, stroke due to atherosclerotic carotid artery disease, a condition that is clearly associated with risk of cardiac death.

Investigators frequently ignore the effects of competing risks when comparing time-to-event outcomes between treatment groups and use methods that assume independent censoring, such as the Kaplan-Meier estimator, log-rank test, and Cox proportional hazards regression. Each of these methods assumes that any factor that interupts observation of the time from study entry to the event of interest is unrelated to an individual’s risk for the event of interest. If this assumption does not hold, these methods are biased.

A better approach is to acknowledge the potential for competing risks when it exists and to plan to use methods that properly account for them. A general approach for comparing time-to-event outcomes between treatment groups in the presence of competing risks is based on estimation of cumulative incidence functions for the event of interest and each of the competing events. Cumulative incidence functions, if properly estimated, are unbiased in the presence of competing risks and can be compared between treatment groups using specialized non-parametric tests and regression techniques.

Bill-Axelson A, Holmberg L, Garmo H, et al. Radical prostatectomy or watchful waiting in early prostate cancer. N Engl J Med 2014;370(10):932-42.

Jones CU, Hunt D, McGowan DG, et al. Radiotherapy and short-term androgen deprivation for localized prostate cancer. N Engl J Med 2011;365(2):107-18.

Gray RJ. A class of k-sample tests for comparing the cumulative incidence of a competing risk. Ann Stat 1988;16(3):1141-54.

Fine JP, Gray RJ. A proportional hazards model for the subdistribution of a competing risk. J Am Stat Assoc 1999;94(446):496-509.

Pintilie M. Competing Risks: A Practical Perspective. West Sussex, England: John Wiley and Sons, 2006.