STATISTICAL MODELS AND ASYMPTOTIC RESULTS FOR MULTIVARIATE FAILURE TIME DATA WITH GENERALIZED COMPETING RISKS∗

SUMMARY. This research develops methods which bring together models for multivari-ate failure time data and competing risks under a unified framework. We refer to the situation where observation continues past the first failure so that the remaining failures can be ob-served as one of generalized competing risks. Under this more general setup, event-specific proportional hazards models for the first failure are formulated, and given the time and type of the first failure, conditional proportional hazards models for the remaining failures are similarly formulated. Estimation involves cross-classifying subjects into disjoint sets and the (conditional) stratum-specific partial likelihoods are pooled across strata to yield a total (con-ditional) partial likelihood for the first two failures. Maximum partial likelihood estimators (MPLEs) are obtained and their large-sample properties are examined. Weak convergence results for martingale stochastic processes are used to establish the weak consistency and asymptotic normality of the MPLEs and statistical tests are derived to assess the significance of the dependence of failure times on previous failures and on realized random covariates. 1