  Mediation analysis is critical to understanding the mechanisms underlying
exposure-outcome relationships. In this paper, we identify the instrumental
variable (IV)-direct effect of the exposure on the outcome not through the
mediator, using randomization of the instrument. To our knowledge, such an
estimand has not previously been considered or estimated. We propose and
evaluate several estimators for this estimand: a ratio of inverse-probability
of treatment-weighted estimators (IPTW), a ratio of estimating equation
estimators (EE), a ratio of targeted minimum loss-based estimators (TMLE), and
a TMLE that targets the CSDE directly. These estimators are applicable for a
variety of study designs, including randomized encouragement trials, like the
MTO housing voucher experiment we consider as an illustrative example,
treatment discontinuities, and Mendelian randomization. We found the IPTW
estimator to be the most sensitive to finite sample bias, resulting in bias of
over 40% even when all models were correctly specified in a sample size of
N=100. In contrast, the EE estimator and compatible TMLE estimator were far
less sensitive to finite samples. The EE and TMLE estimators also have
advantages over the IPTW estimator in terms of efficiency and reduced reliance
on correct parametric model specification.
