Role of placebo samples in observational studies

In an observational study, it is common to leverage known null effects 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 concerns about unmeasured confounding bias while the absence of it helps corroborate the causal conclusion. This article describes a framework for using a placebo sample to detect and remove bias. We state the identification assumptions and develop estimation and inference methods based on outcome regression, inverse probability weighting, and doubly robust approaches. Simulation studies investigate the finite-sample performance of the proposed methods. We illustrate the methods using an empirical study of the effect of the earned income tax credit on infant health.