Partially Linear Single Index Cox's Regression Model in Nested Case-Control Studies

• Activity Number: 411
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Shulian Shang*+ and Mengling Liu and Anne Zeleniuch-Jacquotte and Tess Clendenen and Alan A Arslan and Vittorio Krogh and Goran Hallmans and Yongzhao Shao and Wenbin Lu
• Companies: New York University and New York University and New York University and New York University and New York University and National Cancer Institute and Umeå University and New York University and North Carolina State University
• Keywords: Nested case-control study ; Risk-set sampling ; Nonparametric regression ; Non-linear effect ; Single index model

Abstract

The nested case-control (NCC) design is widely used in epidemiological studies as a cost effective subcohort sampling method to study the association between a disease and potential risk factors. NCC data are commonly analyzed using Thomas' partial likelihood approach under Cox's proportional hazards model, however, the proportional hazards assumption may not always be satisfied for the assumed linear modeling form. In order to adequately adjust for potential non-linear effects of covariates and to provide an effective way of handling multiple nuisance confounders, we consider a partially linear single index proportional hazard model, which includes a linear component and a nonparametric single index component. We propose to approximate the nonlinear component by polynomial splines and estimate the parameters of interest using an iterative computation algorithm based on the partial likelihood. Asymptotic properties of the resulting estimators are established. The proposed methods are evaluated using simulations and applied to an NCC study of ovarian cancer.