Mediation analysis is widely used on data arising from social and biomedical sciences. Some fundamental issues include measure of effect size, sensitivity analysis with respect to the violation of the sequential ignorability assumption, and statistical test of mediation effect. This presentation centers on my recent work on these fronts. Using the concept of likelihood, total effect and mediated effect are redefined and new effects are introduced. Decomposition of the total effect is easy to interpret and contains a new component, the unmediated effect. Most importantly, all effects are positive and the mediated effect size relative to the total effect or the mediator effect is bounded in interval (0, 0.5). This general framework applies to any likelihood-generating models used for the mediator and the outcome. The sensitivity analysis part focuses on linear structural equation models in the presence of treatment-mediator interaction. Explicit expressions of the maximum likelihood estimate of model parameters are provided. They provide new insight into how violation of sequential ignorability confounds parameter estimates. The re-defined mediated effect is no longer unbounded with respect to the sensitivity parameter. Finally, a test that is approximately uniformly more powerful than the current best (i.e., the joint significance test) is introduced. While this presentation may sound technical it is actually not. Much of it will be devoted to a demonstration of the R package iMediate that implements these newly developed methods.

Kai Wang, PhD