Semiparametric transformation Model with measurement error in Covariates: An Instrumental variable approach

TL;DR

This paper introduces a new instrumental variable approach for estimating regression coefficients in semiparametric transformation models with measurement error in covariates, applicable to censored survival data.

Contribution

It develops counting process based estimating equations and establishes their large sample properties, addressing measurement error using instrumental variables in survival analysis.

Findings

Estimators have desirable large sample properties.

Finite sample performance is validated through simulations.

Method successfully applied to AIDS clinical trial data.

Abstract

Linear transformation model provides a general framework for analyzing censored survival data with covariates. The proportional hazards and proportional odds models are special cases of the linear transformation model. In biomedical studies, covariates with measurement error may occur in survival data. In this work, we propose a method to obtain estimators of the regression coefficients in the linear transformation model when the covariates are subject to measurement error. In the proposed method, we assume that instrumental variables are available. We develop counting process based estimating equations for finding the estimators of regression coefficients. We prove the large sample properties of the estimators using the martingale representation of the regression estimators. The finite sample performance of the estimators are evaluated through an extensive Monte Carlo simulation study. Finally, we illustrate the proposed method using an AIDS clinical trial (ACTG 175) data.