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

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.