Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series A, Pt. 3, 408-434

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

By

RALPH A. DeMASI, Glaxo wellcome Research Institute, Research Triangle Park

BAHJAT QAQISH

And

PRANAB KUMAR SEN, University of North Carolina at Chapel Hill, Chapel Hill

SUMMARY. This research develops methods which bring together models for multivariate 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 observed as one of the generalised 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 (conditional) partial likelihood for the first two failures. Maximum partial likelihood estimators ( MLPEs) are obtained and their large-sample properties are examined. Weak convergence results for martingle 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 realised random covariates.

AMS (1991) subject classification. 62N02, 62H12, 62F12

Key words and phrases. Proportional hazards, conditional model, partial likelihood, asymptotic distribution

Full paper (PDF)

This article in Mathematical Reviews