A Semiparametric Mixture Model for Analyzing Clustered Competing Risks Data

A very general class of multivariate life distributions is considered for analyzing failure time clustered data that are subject to censoring and multiple modes of failure. Conditional on cluster-specific quantities, the joint distribution of the failure time and event indicator can be expressed as a mixture of the distribution of time to failure due to a certain type (or specific cause), and the failure type distribution. We assume here the marginal probabilities of various failure types are logistic functions of some covariates. The cluster-specific quantities are subject to some unknown distribution that causes frailty. The unknown frailty distribution is modeled nonparametrically using a Dirichlet process. In such a semiparametric setup, a hybrid method of estimation is proposed based on the i.i.d. Weighted Chinese Restaurant algorithm that helps us generate observations from the predictive distribution of the frailty. The Monte Carlo ECM algorithm plays a vital role for obtaining the estimates of the parameters that assess the extent of the effects of the causal factors for failures of a certain type. A simulation study is conducted to study the consistency of our methodology. The proposed methodology is used to analyze a real data set on HIV infection of a cohort of female prostitutes in Senegal.