  A parametric expression for causal natural direct and indirect effects is
derived for the setting of a binary outcome with a binary mediator. The
proposed effect decomposition does not require the outcome to be rare and
generalizes the existing ones, allowing for interactions between both the
exposure and the mediator and confounding covariates. Further, it outlines the
relationship between the causal effects and the correspondent pathway-specific
logistic regression parameters, in parallel with results derived under the rare
outcome assumption. Formulae for standard errors, obtained via the delta
method, are also given. A simulation study is implemented which compares these
estimators to a number of competing ones. An empirical application to data
coming from a microfinance experiment performed in Bosnia and Herzegovina is
illustrated as an example.
