Partially Linear Hazard Regression with Varying-coefficients for Multivariate Survival Data

This paper studies estimation of partially linear hazard regression models with varying coefficients for multivariate survival data. A profile pseudo-partial likelihood estimation method is proposed. The estimation of the parameters of the linear part is accomplished via maximization of the profile pseudo-partial likelihood, while the varying-coefficient functions are considered as nuisance parameters profiled out of the likelihood. It is shown that the estimators of the parameters are √ n-consistent and the estimators of the nonparametric coefficient functions achieve optimal convergence rates. Asymptotic normality is obtained for the estimators of the finite parameters and varying-coefficient functions. Consistent estimators of the asymptotic variances are derived and empirically tested, which facilitate inference for the model. We prove that the varying-coefficient functions can be estimated as well as if the parametric components were known and the failure times within each subject were independent. Simulations are conducted to demonstrate the performance of the proposed estimators. A real dataset is analysed to illustrate the proposed methodology.