Standard measures of effect, including the risk ratio, the odds ratio, and the risk difference, are associated with a number of well-described shortcomings, and no consensus exists about the conditions under which investigators should choose one effect measure over another. In this paper, we introduce a new framework for reasoning about choice of effect measure by linking two separate versions of the risk ratio to a counterfactual causal model. In our approach, effects are defined in terms of "counterfactual outcome state transition parameters", that is, the proportion of those individuals who would not have been a case by the end of follow-up if untreated, who would have responded to treatment by becoming a case; and the proportion of those individuals who would have become a case by the end of follow-up if untreated who would have responded to treatment by not becoming a case. Although counterfactual outcome state transition parameters are generally not identified from the data without strong monotonicity assumptions, we show that when they stay constant between populations, there are important implications for model specification, meta-analysis, and research generalization.
Background: Causal mediation analysis can improve understanding of the mechanism s underlying epidemiologic associations. However, the utility of natural direct and indirect effect estimation has been limited by the assumption of no confounder of the mediator-outcome relationship that is affected by prior exposure (which we call an intermediate confounder)--an assumption frequently violated in practice.
Methods: We build on recent work that identified alternative estimands that do not require this assumption and propose a flexible and double robust targeted minimum loss-based estimator for stochastic direct and indirect effects. The proposed method intervenes stochastically on the mediator using a distribution which conditions on baseline covariates and marginalizes over the intermediate confounder.
Results: We demonstrate the estimator's finite sample and robustness properties in a simple simulation study. We apply the method to an example from the Moving to Opportunity experiment. In this application, randomization to receive a housing voucher is the treatment/instrument that influenced moving with the voucher out of public housing, which is the intermediate confounder. We estimate the stochastic direct effect of randomization to the voucher group on adolescent marijuana use not mediated by change in school district and the stochastic indirect effect mediated by change in school district. We find no evidence of mediation.
Conclusions: Our estimator is easy to implement in standard statistical software, and we provide annotated R code to further lower implementation barriers.
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