Collective versus Individual Effects in Survival Analysis of Multiple Failures

In survival analysis, we sometimes encounter data with multiple censored outcomes. Under certain scenarios, partial or even all covariates have ‘similar’ relative risks on the multiple outcomes in the Cox regression analysis. The similarity in covariate effects can be quantified using the proportionality of regression coefficients. Identifying the proportionality structure, or equivalently whether covariates have individual or collective effects, may have important scientific implications. In addition, it can lead to a smaller set of unknown parameters, which in turn results in more accurate estimation. In this article, we develop a novel approach for identifying the proportionality structure. Simulation shows the satisfactory performance of the proposed approach and its advantage over estimation under no assumed structure. We analyse three datasets to demonstrate the practical application of the proposed approach.