An EM algorithm for the proportional hazards model with doubly censored data

In this paper, we consider a new procedure for estimating parameters in the proportional hazards model with doubly censored data. Computing the maximum likelihood estimator with doubly censored data is often nontrivial and requires a certain constraint optimization procedure, which is computationally unstable and sometimes fails to converge. We propose an approximated likelihood and study the maximum approximated likelihood estimator, which is obtained by maximizing the approximated likelihood. In comparison to the maximum likelihood estimator, this new estimator is stable and always converges with an efficient EM algorithm we develop. The stability of the new estimator even with moderate sample sizes is amply demonstrated through simulated and real data. For theoretical justification of the approximated likelihood, we show the consistency of the maximum approximated likelihood estimator.