MEDIATION ANALYSISWITHOUT SEQUENTIAL IGNORABILITY: USING BASELINE COVARIATES INTERACTEDWITH RANDOM ASSIGNMENT AS INSTRUMENTAL VARIABLES

Abstract

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 intermediate variable. 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.