Nonparametric Survival Analysis in Time-Varying Coefficient Models

The Cox model has been widely used for the analysis of survival data under the proportional hazards assumption. The subject of examining the hazard proportionality assumption in survival data analysis has been studied extensively. One of methods for modeling nonproportional hazards is to use time-varying coefficient functions associated with covariates. In this paper, we propose a simple nonparametric method for estimating timevarying coefficient functions in hazard regression model via penalized likelihood by using a lower-dimensional approximation. Also, Bayesian confidence intervals are computed derived from Bayes model for the lower-dimensional approximations. The proposed method is illustrated by using a real data on patients diagnosed with AIDS in Australia.