A FRAILTY MODEL APPROACH FOR REGRESSION ANALYSIS OF BIVARIATE INTERVAL-CENSORED SURVIVAL DATA

Abstract

Owing to the fact that general semiparametric inference procedures are still underdeveloped for multivariate interval-censored event time data, we pro- pose semiparametric maximum likelihood estimation for the gamma-frailty Cox model under mixed-case interval censoring. We establish the consistency of the semiparametric maximum likelihood estimator (SPMLE) for the model parame- ters, including the regression coefficients and the cumulative hazard functions in the Cox model, and the variance of the gamma frailty. The SPMLEs of the cumu- lative hazard functions are shown to have a n 1=3 -rate of convergence, while those of the regression coefficients and the frailty variance have a n 1=2 -rate of convergence; here n denotes the number of study units. The asymptotic normality of the regres- sion coefficients and the frailty variance is also established, with the asymptotic variance given by the inverse of the efficient Fisher information matrix. A profile- likelihood approach is proposed for estimating the asymptotic variance. Based on the self-consistency equations and the contraction principle, we propose a stable and efficient computation algorithm. Simulation results reveal that the large sam- ple theories work quite well in finite samples. We analyze a dataset from an AIDS clinical trial by the proposed methods to assess the effects of the baseline CD4 cell counts on the times to CMV shedding in blood and urine.