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 patients 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).
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