Regression analysis of bivariate current status data under the Gamma-frailty proportional hazards model using the EM algorithm

The Gamma-frailty proportional hazards (PH) model is commonly used to analyze correlated survival data. Despite this model’s popularity, the analysis of correlated current status data under the Gamma-frailty PH model can prove to be challenging using traditional techniques. Consequently, in this paper we develop a novel expectation–maximization (EM) algorithm under the Gamma-frailty PH model to study bivariate current status data. Our method uses a monotone spline representation to approximate the unknown conditional cumulative baseline hazard functions. Proceeding in this fashion leads to the estimation of a finite number of parameters while simultaneously allowing for modeling flexibility. The derivation of the proposed EM algorithm relies on a three-stage data augmentation involving Poisson latent variables. The resulting algorithm is easy to implement, robust to initialization, and enjoys quick convergence. Simulation results suggest that the proposed method works well and is robust to the misspecification of the frailty distribution. Our methodology is used to analyze chlamydia and gonorrhea data collected by the Nebraska Public Health Laboratory as a part of the Infertility Prevention Project.