Proportional Hazards Model With Covariate Measurement Error and Instrumental Variables

Abstract

In biomedical studies, covariates with measurement error may occur in survival data. Existing approaches mostly require certain replications on the error-contaminated covariates, which may not be available in the data. In this article, we develop a simple nonparametric correction approach for estimation of the regression parameters in the proportional hazards model using a subset of the sample where instrumental variables are observed. The instrumental variables are related to the covariates through a general nonparametric model, and no distributional assumptions are placed on the error and the underlying true covariates. We further propose a novel generalized methods of moments nonparametric correction estimator to improve the efficiency over the simple correction approach. The efficiency gain can be substantial when the calibration subsample is small compared to the whole sample. The estimators are shown to be consistent and asymptotically normal. Performance of the estimators is evaluated via simulation studies and by an application to data from an HIV clinical trial. Estimation of the baseline hazard function is not addressed.

KEY WORDS:

• Generalized methods of moments
• Nonparametric correction
• Survival