PhD Thesis Defence Public Lecture (DSAS) - Dan Liu
The statistical study of dynamic treatment regimes (DTR) is concerned with estimating sequential treatment decision rules tailored to patient-level information across multiple stages of intervention. Regression-based methods in DTR have been proposed 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 several problems in the context of DTR with measurement error or misclassification in the observed data.
The first problem deals with covariate measurement error in Q-learning with continuous outcomes. The true covariate is not observable but replicate measurements for the covariate are available in each stage of the Q-learning. We propose a modified Q-learning algorithm with regression calibration to handle the measurement error. The proposed method makes use of the replicates measurements to create the estimates of the unobserved true covariate as substitute values in each stage of Q-learning.
The second problem explores covariate measurement error in dynamic weighted survival modeling (DWSurv), a regression-based method dealing with survival outcomes. Internal validation data is 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 problem examines Q-learning with binary outcomes with the outcome subject to misclassification. We investigate the outcome misclassification effect for internal validation data and develop a correction method to adjust for the misclassification 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.
For all the proposed methods, extensive simulation studies are conducted to assess the performance of the methods, and real data are analyzed for illustration. The results showcase the importance of incorporating the errors and the competency of the proposed methods in obtaining the optimal DTR.
