Efficient estimation of a varying-coefficient partially linear proportional hazards model with current status data

We consider a varying-coefficient partially linear proportional hazards model with current status data. The proposed model enables one to examine the extent to which some covariates interact nonlinearly with an exposure variable, while other covariates present linear effects. B-splines are applied to model both the unknown cumulative baseline hazard function and the varying-coefficient functions with and without monotone constraints, depending on the nature of the nonparametric functions. The sieve maximum likelihood estimation method is used to get an integrated estimate for the linear coefficients, the varying-coefficient functions and the cumulative baseline hazard function. The proposed parameter estimators are proved to be semiparametrically efficient and asymptotically normal, and the estimators for the nonparametric functions achieve the optimal rate of convergence. Simulation studies and a real data analysis are used for assessment and illustration.