Bayesian Mediation Analysis for Individualized Treatment Rules

The value of an individualized treatment rule (ITR), defined as the expected outcome under treatment assignment according to the rule, is useful for assessing average clinical benefit but does not explain how the benefit of a rule is generated. We propose a causal mediation framework for decomposing the value contrast between a prespecified candidate ITR and a clinically meaningful reference rule into direct and indirect components. Using rule-specific nested potential outcomes, we define natural direct and indirect rule effects that quantify the extent to which the improvement in value arises through pathways operating directly on the outcome versus through a specified mediator. We give identification conditions under which these components are identified by a rule-level mediation g-formula. For estimation, we adapt Bayesian causal mediation forests to obtain posterior inference for the value contrast and its path-specific components. Our simulations demonstrate that the proposed estimator achieved near-nominal credible interval coverage with decreasing bias and root mean squared error as sample size increased in settings with varying direct and mediated contributions. We further illustrate the method using data from the TRIUMPH trial, decomposing the cognitive benefit of a lifestyle intervention rule through candidate neurovascular, cardiorespiratory, and behavioral mediators. The proposed framework complements optimal ITR learning with explanation using mediation, providing a natural approach for mechanistic evaluation of ITRs.