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 absence of it helps corroborate the causal conclusion. This paper 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.