Marginal Models for Multivariate Failure Time Data with Generalized Dependence Structure

In epidemiologic studies, there is often more than one outcome measured on the same subject. Multiple failures from the same individual induce multivariate failure time data involving within-subject dependence. Furthermore, participants may not be independent within a cluster (e.g., as with members of the same family). Responses from subjects in the same cluster generate multivariate failure time data with between-subject dependence. In this research we consider a generalized dependence structure which consists of both between-subject and within-subject dependence instead of dealing only with one of the two types. We propose using a marginal approach to analyze multivariate failure time data with generalized dependence structure when the scientific interests are in the effects of covariates on the risk of failures and knowledge of the dependence structure is not available. Three types of marginal hazard models are proposed: distinct baseline hazard models, common baseline hazard models, and mixed baseline hazard models. All these hazard models are in the form of Cox regression models. The mixed baseline hazard model provides significantly greater modeling flexibility and applicability, and enables us to deal with some application problems the current existing methods can not handle. Inference on regression parameters for each type of model is based on a system of pseudo score equations obtained under the working assumption of independence, which is in the framework of generalized estimating equations. Relying on the theory of multivariate counting processes, stochastic integrals and local martingales, we have proven that the estimators for the proposed models are consistent and asymptotically