In randomized trials, researchers are often interested in mediation analysis
to understand how a treatment works, in particular how much of a treatment's
effect is mediated by an intermediated variable and how much the treatment
directly affects the outcome not through the mediator. The standard regression
approach to mediation analysis assumes sequential ignorability of the mediator,
that is that the mediator is effectively randomly assigned given baseline
covariates and the randomized treatment. Since the experiment does not
randomize the mediator, sequential ignorability is often not plausible. Ten
Have et al. (2007, Biometrics), Dunn and Bentall (2007, Statistics in Medicine)
and Albert (2008, Statistics in Medicine) presented methods that use baseline
covariates interacted with random assignment as instrumental variables, and do
not require sequential ignorability. We make two contributions to this
approach. First, in previous work on the instrumental variable approach, it has
been assumed that the direct effect of treatment and the effect of the mediator
are constant across subjects; we allow for variation in effects across subjects
and show what assumptions are needed to obtain consistent estimates for this
setting. Second, we develop a method of sensitivity analysis for violations of
the key assumption that the direct effect of the treatment and the effect of
the mediator do not depend on the baseline covariates