Bayesian analysis for partly linear Cox model with measurement error and time‐varying covariate effect

The Cox proportional hazards model is commonly used to estimate the association between time‐to‐event and covariates. Under the proportional hazards assumption, covariate effects are assumed to be constant in the follow‐up period of study. When measurement error presents, common estimation methods that adjust for an error‐contaminated covariate in the Cox proportional hazards model assume that the true function on the covariate is parametric and specified. We consider a semiparametric partly linear Cox model that allows the hazard to depend on an unspecified function of an error‐contaminated covariate and an error‐free covariate with time‐varying effect, which simultaneously relaxes the assumption on the functional form of the error‐contaminated covariate and allows for nonconstant effect of the error‐free covariate. We take a Bayesian approach and approximate the unspecified function by a B‐spline. Simulation studies are conducted to assess the finite sample performance of the proposed approach. The results demonstrate that our proposed method has favorable statistical performance. The proposed method is also illustrated by an application to data from the AIDS Clinical Trials Group Protocol 175.