Regression-based Methods for Dynamic Treatment Regimes with Mismeasured Covariates or Misclassified Response
Abstract
The statistical study of dynamic treatment regimes (DTRs) focuses on estimating sequential treatment decision rules tailored to patient-level information across multiple stages of intervention. Regression-based methods in DTR have been studied in the literature with a critical assumption that all the observed variables are precisely measured. However, this assumption is often violated in many applications. One example is the STAR*D study, in which the patient's depressive score is subject to measurement error. In this thesis, we explore problems in the context of DTR with measurement error or misclassification considered in the observed data.
The first project deals with covariate measurement error in Q-learning with continuous outcomes. The true covariate is not observable, but its replicate measurements are available in each stage. We propose a modified Q-learning algorithm with regression calibration to handle the measurement error. Given the replicate measurements, the proposed method obtains and uses the estimates of the unobserved true covariate in each stage of Q-learning.
The second project explores covariate measurement error in dynamic weighted survival modeling (DWSurv), a regression-based method dealing with survival outcomes in DTR. Internal validation data are assumed to be available with true covariates only observed in a subset of the data. Two correction methods are proposed to eliminate the effect of mismeasured covariate by obtaining the estimates of the missing true covariate in each stage of DWSurv. The consistency of the proposed estimator is established.
The third project examines Q-learning with binary outcomes being subject to misclassification. We investigate the outcome misclassification effect for internal validation data and develop a correction method to adjust for the effect in Q-learning. A probability relationship is established between the true outcome and the misclassified outcome. The estimation procedure in Q-learning is modified by including the derived probability relationship in the proposed method.
Extensive simulation studies are conducted to assess the performance of the proposed methods and to compare them with the naive method. Real data are analyzed for illustration of the proposed methods. The results showcase the importance of incorporating the errors in DTR and the competency of the proposed methods in obtaining the optimal DTR.