  The natural indirect effect (NIE) and mediation proportion (MP) are two
measures of primary interest in mediation analysis. The standard approach for
estimating NIE and MP is through the product method, which involves a model for
the outcome conditional on the mediator and exposure and another model
describing the exposure-mediator relationship. The purpose of this article is
to comprehensively develop and investigate the finite-sample performance of NIE
and MP estimators via the product method. With four common data types, we
propose closed-form interval estimators via the theory of estimating equations
and multivariate delta method, and evaluate its empirical performance relative
to the bootstrap approach. In addition, we have observed that the rare outcome
assumption is frequently invoked to approximate the NIE and MP with a binary
outcome, although this approximation may lead to non-negligible bias when the
outcome is common. We therefore introduce the exact expressions for NIE and MP
with a binary outcome without the rare outcome assumption and compare its
performance with the approximate estimators. Based upon these theoretical
developments and empirical studies, we offer several practical recommendations
to inform practice. An R package mediateP is developed to implement the methods
for point and variance estimation discussed in this paper.
