A smoothed corrected score approach for proportional hazards model with misclassified discretized covariates induced by error‐contaminated continuous time‐dependent exposure

We consider the proportional hazards model in which the covariates include the discretized categories of a continuous time‐dependent exposure variable measured with error. Naively ignoring the measurement error in the analysis may cause biased estimation and erroneous inference. Although various approaches have been proposed to deal with measurement error when the hazard depends linearly on the time‐dependent variable, it has not yet been investigated how to correct when the hazard depends on the discretized categories of the time‐dependent variable. To fill this gap in the literature, we propose a smoothed corrected score approach based on approximation of the discretized categories after smoothing the indicator function. The consistency and asymptotic normality of the proposed estimator are established. The observation times of the time‐dependent variable are allowed to be informative. For comparison, we also extend to this setting two approximate approaches, the regression calibration and the risk‐set regression calibration. The methods are assessed by simulation studies and by application to data from an HIV clinical trial.