  Dynamic treatment regimes (DTRs) are sequences of functions that formalize
the process of precision medicine. DTRs take as input patient information and
output treatment recommendations. A major focus of the DTR literature has been
on the estimation of optimal DTRs, the sequences of decision rules that result
in the best outcome in expectation, across the complete population were they to
be applied. While there is a rich literature on optimal DTR estimation, to date
there has been minimal consideration of the impacts of nonadherence on these
estimation procedures. Nonadherence refers to any process through that an
individual's prescribed treatment does not match their true treatment. We
explore the impacts of nonadherence and demonstrate that generally, when
nonadherence is ignored, suboptimal regimes will be estimated. In light of
these findings we propose a method for estimating optimal DTRs in the presence
of nonadherence. The resulting estimators are consistent and asymptotically
normal, with a double robustness property. Using simulations we demonstrate the
reliability of these results, and illustrate comparable performance between the
proposed estimation procedure adjusting for the impacts of nonadherence and
estimators that are computed on data without nonadherence.
