The area of dynamic treatment regimes (DTR) aims to make inference about adaptive, multistage decision-making in clinical practice. A DTR is a set of decision rules, one per interval of treatment, where each decision is a function of treatment and covariate history that returns a recommended treatment. Q-learning is a popular method from the reinforcement learning literature that has recently been applied to estimate DTRs. While, in principle, Q-learning can be used for both randomized and observational data, the focus in the literature thus far has been exclusively on the randomized treatment setting. We extend the method to incorporate measured confounding covariates, using direct adjustment and a variety of propensity score approaches. The methods are examined under various settings including non-regular scenarios. We illustrate the methods in examining the effect of breastfeeding on vocabulary testing, based on data from the Promotion of Breastfeeding Intervention Trial.
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