  Causal inference methods can be applied to estimate the effect of a point
exposure or treatment on an outcome of interest using data from observational
studies. For example, in the Women's Interagency HIV Study, it is of interest
to understand the effects of incarceration on the number of sexual partners and
the number of cigarettes smoked after incarceration. In settings like this
where 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 the
counterfactual mean count under no exposure. This paper considers estimators of
the causal mean ratio based on inverse probability of treatment weights, the
parametric g-formula, and doubly robust estimation, each of which can account
for overdispersion, zero-inflation, and heaping in the measured outcome.
Methods are compared in simulations and are applied to data from the Women's
Interagency HIV Study.
