High-dimensional $A$-learning for optimal dynamic treatment regimes

Abstract

Precision medicine is a medical paradigm that focuses on finding the most effective treatment decision based on individual patient information. For many complex diseases, such as cancer, treatment decisions need to be tailored over time according to patients' responses to previous treatments. Such an adaptive strategy is referred as a dynamic treatment regime. A major challenge in deriving an optimal dynamic treatment regime arises when an extraordinary large number of prognostic factors, such as patient's genetic information, demographic characteristics, medical history and clinical measurements over time are available, but not all of them are necessary for making treatment decision. This makes variable selection an emerging need in precision medicine. In this paper, we propose a penalized multi-stage A-learning for deriving the optimal dynamic treatment regime when the number of covariates is of the non-polynomial (NP) order of the sample size. To preserve the double robustness property of the A-learning method, we adopt the Dantzig selector which directly penalizes the A-leaning estimating equations. Oracle inequalities of the proposed estimators for the parameters in the optimal dynamic treatment regime and error bounds on the difference between the value functions of the estimated optimal dynamic treatment regime and the true optimal dynamic treatment regime are established. Empirical performance of the proposed approach is evaluated by simulations and illustrated with an application to data from the STAR*D study.

Data‐adaptive longitudinal model selection in causal inference with collaborative targeted minimum loss‐based estimation

“…This selection is decided by a penalized loss function for the updated nested conditional expectations of the outcome. Related work for dynamic treatment regimes by Shi et al (2018) involves a high-dimensional covariate selection method constrained by a doubly robust estimating equation that involves the product of the errors of the estimated time-specific probability of treatment and nested outcome expectation. Rather than using cross-validation to select the tuning parameter as we do, their method uses a doubly robust Bayesian information criterion.…”

“…Recently, Shi et al . () proposed using the Dantzig selector based on the A‐learning estimating function for high‐dimensional covariate selection in dynamic treatment regimes.…”

“…Machine learning methods have been used for the estimation of the treatment model (s) in both longitudinal and non-longitudinal settings (eg, Neugebauer et al, 2007;Petersen et al, 2007;Benkeser et al, 2017;Ertefaie et al, 2017;Shortreed and Ertefaie, 2017;Schnitzer and Cefalu, 2018). Recently, Shi et al (2018) proposed using the Dantzig selector based on the A-learning estimating function for high-dimensional covariate selection in dynamic treatment regimes.…”

High-dimensional inference for personalized treatment decision

“…The outcome of interest is the Quick Inventory of Depressive SymptomatologySelf-report QIDS-SR 16 . Similar to existing studies on STAR*D [15], we transform the outcome to be the negative of the original outcome. We are interested in making optimal treatment decision between SER and BUR to maximize the mean outcome.…”

“…Existing methods can be broadly partitioned into regression-based or classification-based approaches. Popular regression-based approaches include Q-learning [21, 11, 3, 6, 7, 17] and A-learning [13, 10, 8, 16, 15]. Q-learning models the conditional mean of the outcome given covariates and treatment while A-learning directly models the interaction between treatment and covariates that is sufficient for treatment decisions.…”