  In precision medicine, Dynamic Treatment Regimes (DTRs) are treatment
protocols that adapt over time in response to a patient's observed
characteristics. A DTR is a set of decision functions that takes an individual
patient's information as arguments and outputs an action to be taken. Building
on observed data, the aim is to identify the DTR that optimizes expected
patient outcomes. Multiple methods have been proposed for optimal DTR
estimation with continuous outcomes. However, optimal DTR estimation with
binary outcomes is more complicated and has received comparatively little
attention. Solving a system of weighted generalized estimating equations, we
propose a new balancing weight criterion to overcome the misspecification of
generalized linear models' nuisance components. We construct binary
pseudo-outcomes, and develop a doubly-robust and easy-to-use method to estimate
an optimal DTR with binary outcomes. We also outline the underlying theory,
which relies on the balancing property of the weights; provide simulation
studies that verify the double-robustness of our method; and illustrate the
method in studying the effects of e-cigarette usage on smoking cessation, using
observational data from the Population Assessment of Tobacco and Health (PATH)
study.
