A Simple Model Allowing Modification of the Effect of a Randomized Intervention by Post-Randomization Variables

We address several questions relating to the use of standard regression and Structural Nested Mean Model (SNMM) approach (e. g., Ten Have et al. 2007) to analyze post-randomization effect modifiers of the intent-to-treat effect of a randomized intervention on a subsequent outcome, which has not been well examined. We show through simulations that the SNMM performs better with respect to bias of estimates of the intervention and interaction effects than does the corresponding standard interaction approach when the baseline intervention is randomized and the post-randomization factors are subject to confounding, and even when there is no association between the intervention and effect modifier. However, causal inference under the SNMM makes untestable assumptions that the causal contrasts do not vary across observed levels of the intervention and post-randomization factor. In addition, the precision of the SNMM-based estimators depends on the effect of the randomized intervention on the post-randomization factor varying across baseline covariate combinations. These issues and methods are illustrated with the application of the standard and causal methods to a randomized cognitive therapy (CT) trial, for which there is a conceptual model of negative cognitive styles or distortions impacted by CT but then in turn modifying the effect of CT on subsequent suicide ideation and social problem solving outcomes.