Bayesian Causal Inference in Sequentially Randomized Experiments with Noncompliance

Scientific researchers utilize randomized experiments to draw casual statements. Most early studies as well as current work on experiments with sequential intervention decisions has been focusing on estimating the causal effects among sequential treatments, ignoring the non-compliance issues that experimental units might not be compliant with the treatment assignments that they were originally allocated. A series of methodologies have been developed to address the non-compliance issues in randomized experiments with time-fixed treatment. However, to our best knowledge, there is little literature studies on the non-compliance issues in sequential experiments settings. In this paper, we go beyond the traditional methods using per-protocol, as-treated, or intention-to-treat analysis and propose a latent mixture Bayesian framework to estimate the sample-average treatment effect in sequential experiment having non-compliance concerns.