First-event or marginal estimation of cause-specific hazards for analysing correlated multivariate failure-time data?

In the analysis of multivariate failure-time data, the effect of a treatment or an exposure on the hazard of each failure type is sometimes evaluated using only the information on the first event that occurs in every individual, ignoring all events that follow. A Cox proportional hazards model may be fitted to such data, yielding a cause-specific hazard ratio (HR) estimate of the exposure for each failure type conditional on surviving all other failure types. However, such an estimate would not fully utilize all the available information on event times. Alternatively, a marginal approach may be implemented to model the time distribution of each failure type beyond the subject's first failure to (any) second and later failures. We investigate the performance of these two approaches by simulating positive and negative correlated event times from exponential distributions. Surprisingly, our results suggest that the first-event-only method (when multiple failures are possible) performs as well as the marginal method in most practical situations. Generally, for a modest sample size of 400, it is possible to achieve at least 85 per cent coverage of the true marginal HR with the first-event method. Although the coverage is poor for a correlation of 0.7 and beyond, such a high correlation between competing event times may be biologically rather implausible.