A Partially Linear Dynamic Single-Index Cox Regression Model

Oregon Convention Center 

In examining multiple time-dependent exposures in relation to time-to-event outcomes, the classical Cox regression model is limited in use due to its strong linearity assumption. While several Cox regression models have been developed to bypass this assumption, they overlook the temporal variations in the exposure mixture's impact on log hazard. To bridge this gap, we propose a novel Partial Linear Dynamic Single-Index Cox regression model. This model combines the time varying impact of exposure on the survival risk through an unknown nonparametric single-index function with the linear effects of additional covariates. We employed regression spline tensor basis to approximate the single-index function and propose a profile optimization algorithm to estimate the model. We also present LRT to compare our proposed model with the simple time-dependent cox model. After establishing the large sample properties for the proposed estimator, we evaluate its finite-sample performance under extensive simulation scenarios. We exemplify our model's application with the NYU CHES cohort.

environmental exposure

time-dependent exposure

exposure mixture

cox regression 

Section on Statistics in Epidemiology