Proportional Hazards Model with Covariate Measurement Error and Instrumental Variables

• Activity Number: 477
• Type: Topic Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Xiao Song*+ and Ching-Yun Wang
• Companies: University of Georgia and Fred Hutchinson Cancer Research Center
• Keywords: Generalized methods of moments ; Nonparametric correction ; Survival

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 paper, we develop a simple nonparametric correction approach for the proportional hazards model using measurements on instrumental variables observed in a subset of the sample. The instrumental variable is 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.