The mean residual life model for the right‐censored data in the presence of covariate measurement errors

In this article, we consider the mean residual life regression model in the presence of covariate measurement errors. In the whole cohort, the surrogate variable of the error-prone covariate is available for each subject, while the instrumental variable (IV), which is related to the underlying true covariates, is measured only for some subjects, the calibration sample. Without specifying distributions of measurement errors but assuming that the IV is missing at random, we develop two estimation methods, the IV calibration and cohort estimators, for the regression parameters by solving estimation equations (EEs) based on the calibration sample and cohort sample, respectively. To improve estimation efficiency, a synthetic estimator is derived by applying the generalized method of moment for all EEs. The large sample properties of the proposed estimators are established and their finite sample performance are evaluated via simulation studies. Simulation results show that the cohort and synthetic estimators outperform the IV calibration estimator and the relative efficiency of the cohort and synthetic estimators mainly depends on the missing rate of IV. In the case of low missing rate, the synthetic estimator is more efficient than the cohort estimator, while the result can be reversed when the missing rate is high. We illustrate the proposed method by application to data from the patients with stage 5 chronic kidney disease in Taiwan.