Controls, Belief Updating, and Bias in Medical RCTs

We develop a formal model of placebo effects. If subjects in seemingly-ideal single-stage RCTs update beliefs about breakthroughs based upon personal physiological responses, mental effects differ across medications received, treatment versus control. Consequently, the average cross-arm health difference becomes a biased estimator. Constructively, we show: bias can be altered through choice of control; higher-efficacy controls mitigate upward bias; and efficacy states can be revealed through controls of intermediate efficacy or controls that mimic a subset of efficacy states. Consistent with experimental evidence, our theory implies outcomes within-arm and cross-arm differences can be non-monotone in treatment probability. Finally, we develop novel differences-in-differences and triangle equality tests to detect RCT bias