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Causal mediation analysis is an important statistical method in social andmedical studies, as it can provide insights about why an intervention works andinform the development of future interventions. Currently, most causalmediation methods focus on mediation effects defined on a mean scale. However,in health-risk studies, such as alcohol or risky sex, outcomes are typicallycount data and heavily skewed. Thus, mediation effects in these setting wouldbe natural on a rate ratio scale, such as in Poisson and negative binomialregression methods. Existing methods also mainly rely on the assumption of nounmeasured confounding between mediator and outcome. To allow for potentialconfounders between the mediator and outcome, we define the direct and mediatoreffects on a new scale and propose a multiplicative structural mean model formediation analysis with count outcomes. The estimator is compared with bothPoisson and negative binomial regression methods assuming sequentialignorability using a simulation study and a real world example about analcohol-related intervention study. Mediation analyses using the new methodsconfirm the study hypothesis that the intervention decreases drinking bydecreasing individual's normative perceptions of alcohol use.

On estimating causal controlled direct and mediator effects for count outcomes without assuming sequential ignorability