title: Partially Linear Single Index Cox Regression Model in Nested Case-Control Studies.
abstract: The nested case-control (NCC) design is widely used in epidemiologic studies as a cost-effective subcohort sampling method to study the association between a disease and its potential risk factors. NCC data are commonly analyzed using Thomas' partial likelihood approach under the Cox proportional hazards model assumption. However, the linear modeling form in the Cox model may be insufficient for practical applications, especially when there are a large number of risk factors under investigation. In this paper, we consider a partially linear single index proportional hazard model, which includes a linear component for covariates of interest to yield easily interpretable results and a nonparametric single index component to adjust for multiple confounders effectively. We propose to approximate the nonparametric single index function by polynomial splines and estimate the parameters of interest using an iterative 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.
authors.affiliation: Departments of Population Health and Environmental Medicine, New York University, School of Medicine, New York, USA.
authors.forename: Shulian
authors.initials: S
authors.lastname: Shang
authors.affiliation: Departments of Population Health and Environmental Medicine, New York University, School of Medicine, New York, USA.
authors.forename: Mengling
authors.initials: M
authors.lastname: Liu
authors.affiliation: Departments of Population Health and Environmental Medicine, New York University, School of Medicine, New York, USA.
authors.forename: Anne
authors.initials: A
authors.lastname: Zeleniuch-Jacquotte
authors.affiliation: Departments of Population Health and Environmental Medicine, New York University, School of Medicine, New York, USA.
authors.forename: Tess V
authors.initials: TV
authors.lastname: Clendenen
authors.affiliation: Nutritional Epidemiology Unit, National Cancer Institute, Milan, Italy.
authors.forename: Vittorio
authors.initials: V
authors.lastname: Krogh
authors.affiliation: Public Health and Clinical Medicine/Nutritional Research, Umeå University, Umeå, Sweden.
authors.forename: Goran
authors.initials: G
authors.lastname: Hallmans
authors.affiliation: Department of Statistics, North Carolina State University, Raleigh, USA.
authors.forename: Wenbin
authors.initials: W
authors.lastname: Lu
keywords: nested case-control study; nonlinear effect; nonparametric regression; risk-set sampling; single index model