Efficient estimation of optimal regimes under a no direct effect assumption*

We derive new estimators of an optimal joint testing and treatment regime under the no direct effect 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 with an optimal 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 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).