  The current body of research on developing optimal treatment strategies often
places emphasis on intention-to-treat analyses, which fail to take into account
the compliance behavior of individuals. Methods based on instrumental variables
have been developed to determine optimal treatment strategies in the presence
of endogeneity. However, these existing methods are not applicable when there
are two active treatment options and the average causal effects of the
treatments cannot be identified using a binary instrument. In order to address
this limitation, we present a procedure that can identify an optimal treatment
strategy and the corresponding value function as a function of a vector of
sensitivity parameters. Additionally, we derive the canonical gradient of the
target parameter and propose a multiply robust classification-based estimator
for the optimal treatment strategy. Through simulations, we demonstrate the
practical need for and usefulness of our proposed method. We apply our method
to a randomized trial on Adaptive Treatment for Alcohol and Cocaine Dependence.
