Statistical Inference of a Bivariate Proportional Hazard Model with Grouped Data

Abstract

This paper studies the estimation of a semiparametric bivariate proportional hazard model from grouped event time data. As a direct generalization of the bivariate exponential distribution of Marshall and Olkin, the model, on the one hand, controls for the effects of observed covariates, and on the other, achieves great exibility through nonparametrically specified baseline hazards. The model is most relevant in analyzing the joint distribution of two event times arising from systems of two components. Examples include the two infection times of the left and the right kidneys of patients and the two retirement times of married couples. To estimate this semiparametric model from grouped data, we propose a maximum likelihood estimator and a minimum chi-square estimator. Both estimation methods exploit the fact that the most flexible model structure that can be identified with grouped data is finite-dimensional. Compared with the maximum likelihood estimation, the minimum chi-square procedure is computationally more attractive but applies only to many observations per cell cases where the covariates are either categorical or amendable to sensible grouping. Specification tests for different model assumptions are also discussed.