Penalized Likelihood-Based Estimation of Stratified Semiparametric Cox Models Under Partly Interval Censoring

In survival data analysis, the stratified Cox model becomes a popular option when the proportional hazards assumption of the conventional Cox model does not hold for certain covariates. For a stratified Cox model, when the observed survival times contain only right censoring, the method of maximum partial likelihood can still be implemented. However, if survival times include interval-censored observations, the method of maximum partial likelihood is not viable, and the partial likelihood approach cannot be applied. Furthermore, partial likelihood analysis does not supply a smooth estimate of the baseline hazard. In this paper, we consider the stratified Cox model under partly interval-censored survival times. We present a penalized likelihood method for estimating the model parameters, including the baseline hazards. Penalty functions are used to produce smoothed baseline hazards estimates, and also to relax the requirement on optimal number and location of the knots used in the baseline hazards estimates. We also derive a large sample normality result for the estimates, which can be used to make inferences on quantities of interest, such as survival probabilities, without relying on computing-intensive resampling methods.