Causal Progress with Imperfect Placebo Treatments and Outcomes

• In Event: Methodological Advances in Causal Inference

Abstract

In the quest to make defensible causal claims from observational data, it is sometimes possible to leverage information from “placebo outcomes” (aka “negative outcome controls”) or “placebo treatments.” Traditional approaches employing such information typically focus on point identification and assume (i) that these are “perfect placebos” (treatment has precisely zero effect on a placebo outcome, or placebo treatments have precisely zero effects on the outcome of interest); and (ii) that the placebo outcome/treatment suffers the same amount of confounding as does the real treatment- outcome relationship on some scale (“equi-confounding”). We show how the analysis of “omitted variable bias” in regression provides a flexible and powerful way to leverage information from placebo treatments and outcomes while relaxing these assumptions. Specifically, we provide a sensitivity analysis or partial identification framework in which users can see the implications of any claim they choose to make about the relative strengths of confounding suffered by a placebo treatment/outcome compared to the true treatment-outcome relationship, while allowing for “imperfect placebos” (e.g. placebo treatments with some non-zero effect on the outcome, placebo outcomes somewhat affected by the treatment). These tools can be used with any choice of placebo treatment or outcome, observed in the same dataset or in a separate one as the main treatment-outcome relationship. We also frame the conventional difference-in-difference approach as a special case of this, with a strict equi-confounding assumption regarding the pre-treatment outcome’s relationship to the treatment group indicator, to which our approach allows several useful relaxations.

Authors

• Adam Rohde, UCLA

• Chad Hazlett