Controls, belief updating, and bias in medical RCTs

Abstract

We develop a formal model of placebo e§ects. If subjects in seemingly-ideal single-stage RCTsupdate beliefs about breakthroughs based upon personal physiological responses, mental e§ectsdi§er across medications received, treatment versus control. Consequently, the average cross-arm health di§erence becomes a biased estimator. Constructively, we show: bias can be alteredthrough choice of control; higher-e¢ cacy controls mitigate upward bias; and e¢ cacy states canbe revealed through controls of intermediate e¢ cacy or controls that mimic a subset of e¢ cacystates. Consistent with experimental evidence, our theory implies outcomes within-arm andcross-arm di§erences can be non-monotone in treatment probability. Finally, we develop noveldi§erences-in-di§erences and triangle equality tests to detect RCT bias.