Efficient Estimation of the Cox Model with Time-Varying Effects Under Two-Phase Designs

Music City Center 

Two-phase designs are often used in large epidemiological or clinical studies with potentially censored time-to-event outcomes when certain covariates are too expensive to be collected on all participants. Important examples include the case-cohort design, which selects all cases and a random subcohort for the measurement of the expensive covariate, and the nested case-control design, which selects a small number of controls at each observed event time. Existing research on two-phase studies with time-to-event outcomes largely focuses on estimating time-fixed covariate effects. In this talk, we propose a semiparametric approach to estimate time-varying expensive covariate effects under two-phase sampling using B-splines. We devise a computationally efficient and numerically stable EM-algorithm to maximize the semiparametric likelihood. In addition, we establish the consistency, asymptotic normality, and asymptotic efficiency of the estimators. Furthermore, we demonstrate the superiority of the proposed methods over existing ones through extensive simulation studies. Finally, we demonstrate our method on data from a large cohort study, looking at the association between oxidative stress and colorectal cancer incidence.

Missing data

Biased sampling design

Case-cohort design

Nested case-control design

EM algorithm

Semiparametric efficiency