Partial-Linear Single-Index Cox Regression with Multiple Time-Dependent Covariates

• Activity Number: 349 - Lifetime Data Science Student Awards
• Type: Topic-Contributed
• Date/Time: Thursday, August 12, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Lifetime Data Science Section
• Author(s): Myeonggyun Lee* and Andrea B. Troxel and Sophia Kwon and Anna Nolan and Mengling Liu
• Companies: New York University Grossman School of Medicine and New York University Grossman School of Medicine and New York University Grossman School of Medicine and New York University Grossman School of Medicine and New York University Grossman School of Medicine
• Keywords: B-spline smoothing; metabolic syndrome; partial-linear single-index model; semiparametric model; time-dependent Cox regression

Abstract

In longitudinal studies with time-to-event outcomes, covariates of interest may have values that change over time. The classical Cox regression model can handle time-dependent covariates but assumes linear effects on the log hazard function. When multiple and correlated time-dependent covariates are under study, it is of great interest to model their joint effects by allowing a flexible functional form and to delineate their relative contributions to survival risk. Motivated by a large cohort study investigating the effects of repeatedly measured metabolic syndrome on the risk of developing lung disease, we propose a partial-linear single-index Cox regression model. The proposed method reduces the dimensionality of multiple covariates and provides interpretable estimates of the covariate effects. We develop an iterative algorithm, using a spline technique to model the nonparametric single index component for possibly nonlinear joint effects, followed by maximum partial likelihood estimation of parameters. We establish the asymptotic properties of the estimator. Our proposed method is illustrated using Monte Carlo simulation studies and applied to the cohort study.