Variability in Causal Effects on a Binary Outcome and Noncompliance in a Multisite Randomized Trial

Noncompliance to treatment assignment is widespread in randomized trials and presents challenges in causal inference. In the presence of noncompliance, the most commonly estimated effect of treatment assignment, also known as the intent-to-treat (ITT) effect, is biased. Of interest in this setting is the complier average causal effect (CACE), the ITT effect among compliers. A further complication arises when the outcome variable is partially observed. My research focuses on estimating the distribution of a site-specific CACE in a multisite randomized controlled trial (MRCT) by maximum likelihood (ML). Assuming compliance missing at random (MAR). We express the likelihood as an integral with respect to random effects that cannot be evaluated analytically. We derive ML estimators by a combination of the EM algorithm and Newton Raphson method conditional on random effects and, then, integrate each estimator and the likelihood with respect to the random effects by adaptive Gauss Hermite quadrature (AGHQ). Next, we extend this approach to both outcome and imperfect compliance MAR. A distinctive feature of the approach is to estimate a site-specific CACE and its variance over sites efficiently. We applied our method to data sets from two MRCTs with imperfect compliance: the e-assist intervention trial to assess the effectiveness of the e-assist intervention in promoting colorectal cancer screening outcome fully observed; and the National Study of Learning Mindsets trial to evaluate the effectiveness of a growth mindset program in improving academic achievement outcomes MAR among ninth-graders.