FRIDAY, October 27, 2006
Time: 1:30 PM
Constant Hall 1043

Title: Multivariate Times to Events Analysis with Stable Family Frailty Models Tumor

Nalini Ravishanker
Department of Statistics
University of Connecticut

Multivariate times to events occur in several application areas ranging from biomedical studies to marketing analyses, and the use of frailty models for inference in this context is well known. It is assumed that given the unobserved frailty random variable, the hazard for each time to event follows a modified proportional hazards model with the frailty variable, covariate effect, and baseline hazard acting multiplicatively. Although the positive stable distribution is an attractive candidate as a frailty distribution, lack of a closed form expression for its density function makes likelihood based inference cumbersome. This is also true for the PVF frailty model (the PVF is a transformed positive stable), the additive positive stable frailty model, and the bivariate positive stable frailty model. Incorporation of auxiliary variables permits feasible computation of the likelihood, and fully Bayesian inference for such models for carrying out simultaneous inference on all the model parameters will be described. Feasible computation of useful dependence measures is also discussed. The methods will be illustrated on biomedical data and marketing data.