Joint evaluation of placebo and treatment effects in cluster randomized trials by causal inference models

The term placebo effect refers to the psychobiological effect of a patient's knowledge or belief of being treated. A placebo effect is patient-driven, which makes it fundamentally different from the usual treatment effect resulting from external actions. In modern clinical research, the presence of a placebo effect is often treated as a nuisance issue, something to be "adjusted away" in estimating a treatment effect of primary interest. However, from a patient-centered perspective, we believe that a possible placebo produces substantial improvements in patient -centered outcomes. Understanding placebo effects is therefore an important part of patient-centered outcomes research. The available methods for estimating placebo effects are designed for individually randomized trials and are not directly applicable to cluster randomized trials (CRTs). There are several challenges in estimating placebo effects in CRTs. A major challenge is the possible presence of interference within clusters, in the sense that a subject's outcome may depend on the beliefs subjects in the same cluster about treatment assignment (mentality) and therefore possible correlation in outcome and mentality among subjects exists in the same cluster. In this article, we extend the previously developed causal inference framework to also encompass CRTs, using the G-Computation and inverse probability weighting (IPW) approaches. We also develop methodologies and further extend the G-Computation and IPW approaches to handle missingness for jointly evaluating placebo effect and treatment-specific effect, specifically in the context of CRTs. The proposed methods are demonstrated in simulation studies and a cluster randomized trial on effect of fermented dairy drink.