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Title: Efficient estimation of a hazard-based partial sufficient dimension reduction model for right-censored data Authors:  Ming-Yueh Huang - Academia Sinica (Taiwan) [presenting]
Abstract: In many applications, it is important to summarize the hazard ratio of certain primary exposure variables, while controlling for many other covariates flexibly. When the number of controlled covariates is large, existing methods usually lead to stringent parametric assumptions or unstable nonparametric estimation. To address this issue, we introduce partial sufficient dimension reduction for survival data by introducing a nested family of multivariate baseline proportional hazards models. The family contains the Cox proportional hazards model and the continuously stratified proportional hazards model as special cases. The model maintains the practically desirable hazard-ratio interpretation of target parameters, while allowing data-adaptive dimension reduction of multi-dimensional covariates to reduce the effect of curse of dimensionality. The goal is to strike a balance between flexibility and parsimony, similar to the existing partial sufficient dimension reduction methods for uncensored data. Under the proposed model, we characterize the semiparametric efficiency bound and propose an efficient estimator. The efficiency gain compared to the continuously stratified proportional hazards model is also proved.