Variable Selection in Regression-Based Estimation of Dynamic Treatment Regimes

Abstract

Dynamic treatment regimes (DTRs) consist of a sequence of decision rules, one per stage of intervention, that aim to recommend effective treatments for individual patients according to patient information history. DTRs can be estimated from models which include interactions between treatment and a (typically small) number of covariates which are often chosen a priori. However, with increasingly large and complex data being collected, it can be difficult to know which prognostic factors might be relevant in the treatment rule. Therefore, a more data-driven approach to select these covariates might improve the estimated decision rules and simplify models to make them easier to interpret. We propose a variable selection method for DTR estimation using penalized dynamic weighted least squares. Our method has the strong heredity property, that is, an interaction term can be included in the model only if the corresponding main terms have also been selected. We show our method has both the double robustness property and the oracle property theoretically; and the newly proposed method compares favorably with other variable selection approaches in numerical studies. We further illustrate the proposed method on data from the Sequenced Treatment Alternatives to Relieve Depression study.

Variable Selection for Individualized Treatment Rules with Discrete Outcomes

“…However, these methods all fail to achieve the strong heredity property, thus, further work is required to implement them in this setting. Bian et al (2021), borrowing on the work in Choi et al (2010) and Bhatnagar et al (2020) used the reparametrization to ensure strong heredity when using penalization in the context of ITR. Here, we modify the adaptive LASSO penalty, and show that by using these modified adaptive weights, not only can the blip parameters be unbiasedly estimated (asymptotically), but also the strong heredity constraint can be met.…”

“…The aims of our analysis are to determine the tailoring variables related to the decision rule and to obtain the estimated individualized treatment rule for CVD patients. We restrict our analysis to eight variables: mental component score (MCS), age, DASS-stress subscale score at baseline, sex, marital status, stomach condition, physical component score (PCS), and vision, as they were previously found to be useful for tailoring treatment using Bian et al (2021).…”

“…For example, a married woman who does not have either a vision problem nor a stomach ailment, and who has a DASS greater than 13, would be recommended for website plus weekly telephone coaching (A = 1). We compared our estimated treatment rule with the results using the approach in Bian et al (2021), wherein the DASS was treated as a continuous measure, and we found that 74% of the subjects' recommended treatments were the same under the two strategies. Moreover, all five non-zero estimated blip parameters had the same signs as the estimated blip parameters using Bian et al (2021).…”

“…It is therefore important to develop variable selection methods with the objective of optimizing patients' outcomes by identifying useful tailoring variables. Variable selection for ITRs has been studied in Bian et al (2021); Jeng et al (2018); Lu et al (2013); Shi et al (2018); all of these works focus on penalized regression-based estimation methods. Jeng et al (2018) and Lu et al (2013) only considered a singly robust method in which the propensity score must be correctly specified.…”

“…Jeng et al (2018) and Lu et al (2013) only considered a singly robust method in which the propensity score must be correctly specified. Shi et al (2018) used the Dantzig selector directly to penalize the A-learning (Murphy, 2003;Robins, 2004) estimating equation; Bian et al (2021) used penalized dynamic weighted ordinary least squares regression to perform variable selection. Both methods considered in Bian et al (2021) and Shi et al (2018) are doubly robust, i.e., they can yield consistent estimators while only requiring one of two nuisance models to be correct.…”