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Causal inference methods can be applied to estimate the effect of a pointexposure or treatment on an outcome of interest using data from observationalstudies. For example, in the Women's Interagency HIV Study, it is of interestto understand the effects of incarceration on the number of sexual partners andthe number of cigarettes smoked after incarceration. In settings like thiswhere the outcome is a count, the estimand is often the causal mean ratio,i.e., the ratio of the counterfactual mean count under exposure to thecounterfactual mean count under no exposure. This paper considers estimators ofthe causal mean ratio based on inverse probability of treatment weights, theparametric g-formula, and doubly robust estimation, each of which can accountfor overdispersion, zero-inflation, and heaping in the measured outcome.Methods are compared in simulations and are applied to data from the Women'sInteragency HIV Study.

Exposure Effects on Count Outcomes with Observational Data, with Application to Incarcerated Women