A Markov chain Monte Carlo EM algorithm for analyzing interval censored data under the Cox proportional hazards model

This paper proposes a Monte Carlo EM (MCEM) algorithm for fitting the proportional hazards model for interval-censored failure-time data. The algorithm generates orderings of the failures from their probability distribution under the model. We maximize the average of the log-likelihoods from these completed data sets to obtain updated parameter estimates. As with the standard Cox model, this algorithm does not require the estimation of the baseline hazard function. The performance of the algorithm is evaluated using simulations, and the method is applied to data from AIDS and cancer studies. Our results indicate that our method produced more precise and unbiased estimates than methods of right and midpoint imputation. (December 1998)