Regression analysis of multivariate grouped survival data

Multivariate failure time data arise when each study subject may experience several types of event or when there are clusterings of observational units such that failure times within the same cluster are correlated. The failure times are often subject to interval grouping or have truly discrete measurements. In this paper, the marginal distribution for each discrete failure time variable is formulated by a grouped-data version of the proportional hazards model while the dependence structure is unspecified. Generalized estimating equations in the spirit of Liang and Zeger (1986, Biometrika 73, 13-22) are proposed to estimate the regression parameters and survival probabilities. The resulting estimators are consistent and asymptotically normal. Robust estimators for the limiting covariance matrices are constructed. Simulation studies demonstrate that the asymptotic approximations are adequate for practical use and that ignoring the intracluster dependence in the variance-covariance estimation would lead to invalid statistical inference. A psychological experiment is provided for illustration.