The goal of mediation analysis is to assess direct and indirect effects of a treatment
or exposure on an outcome. More generally, we may be interested in the context of
a causal model as characterized by a directed acyclic graph (DAG), where mediation
via a specific path from exposure to outcome may involve an arbitrary number of links
(or "stages"). Methods for estimating mediation (or pathway) effects are available
for a continuous outcome and a continuous mediator related via a linear model, while
for a categorical outcome or categorical mediator, methods are usually limited to
two-stage mediation. We present a method applicable to multiple stages of mediation
and mixed variable types using generalized linear models. We define pathway effects
using a potential outcomes framework and present a general formula that provides the
effect of exposure through any specified pathway. Some pathway effects are nonidentifiable
and their estimation requires an assumption regarding the correlation between counterfactuals.
We provide a sensitivity analysis to assess the impact of this assumption. Confidence
intervals for pathway effect estimates are obtained via a bootstrap method. The method
is applied to a cohort study of dental caries in very low birth weight adolescents.
A simulation study demonstrates low bias of pathway effect estimators and close-to-nominal
coverage rates of confidence intervals. We also find low sensitivity to the counterfactual
correlation in most scenarios.