The Role of Placebo Samples in Observational Studies

In an observational study, it is common to leverage known null effect to detect bias. One such strategy is to set aside a placebo sample -- a subset of data immune from the hypothesized cause-and-effect relationship. Existence of an effect in the placebo sample raises concern of unmeasured confounding bias while absence of it corroborates the causal conclusion. This paper establishes a formal framework for using a placebo sample to detect and remove bias. We state identification assumption, and develop estimation and inference methods based on outcome regression, inverse probability weighting, and doubly-robust approaches. Simulation studies and an empirical application illustrate the finite-sample performance of the proposed methods.