  We derive new estimators of an optimal joint testing and treatment regime
under the no direct effect (NDE) assumption that a given laboratory,
diagnostic, or screening test has no effect on a patient's clinical outcomes
except through the effect of the test results on the choice of treatment. We
model the optimal joint strategy using an optimal regime structural nested mean
model (opt-SNMM). The proposed estimators are more efficient than previous
estimators of the parameters of an opt-SNMM because they efficiently leverage
the `no direct effect (NDE) of testing' assumption. Our methods will be of
importance to decision scientists who either perform cost-benefit analyses or
are tasked with the estimation of the `value of information' supplied by an
expensive diagnostic test (such as an MRI to screen for lung cancer).
