Dimension Reduction in Multivariate Baseline Proportional Hazards Model

Abstract

In this talk, we consider a nested family of multivariate baseline proportional hazards model for analyzing survival data. The family contains the Cox proportional hazards model and the continuously stratified proportional hazards model as special cases. It maintains the practically desirable hazard-ratio interpretation of target parameters, while allowing the control of multi-dimensional covariates in a nonparametric manner. The model also allows data-adaptive dimension reduction to reduce the effect of curse of dimensionality. Our goal is to strike a balance between flexibility and parsimony. Under the proposed model, we characterize the semiparametric efficiency bound for parameters of interest. Further, we propose a complete estimation procedure for the parameters coupled with partial sufficient dimension reduction. We also show that the proposed pseudo maximum likelihood estimator is semiparametric efficient.