Frailty modeling of multivariate times to events based on positive stable family

Date of Completion

January 2004






Random effect models are extremely useful for multivariate times to events analysis (Hougaard, 2000); examples abound in the survival analysis literature. Dependent multivariate times to events are available in many cases where subjects in the same group are related to each other or when there are multiple recurrence times of events for the same subject. The variability in times to events data arises due to the variation within subjects and between subjects. The variation among subjects within the same groups may be explained by a random effect known as frailty in the survival analysis literature. The positive stable distribution is an attractive candidate as a frailty distribution because it has certain unique features, and also allows for more heterogeneity, permitting flexible modeling. I pursue different functions of positive stable frailty models, which enable us to capture more heterogeneity and describe the rich dependence structure. Lack of a closed form expression for the density function of the positive stable distribution makes likelihood based inference cumbersome for the PVF frailty model (the PVF is a transformed form of the positive stable), the additive positive stable frailty model, and the bivariate positive stable frailty model, which is discussed here. Incorporating an auxiliary variable, I describe fully Bayesian inference for such models, which permits simultaneous inference of all the model parameters. I also describe the dependence measures for the shared PVF frailty, and the multivariate positive stable frailty models. ^