Effect Aliasing in Observational Studies

TL;DR

This paper develops a theory of aliasing in observational studies, showing how certain covariate-treatment combinations can confound effect estimates, and introduces a new matching method to create balanced designs from observational data.

Contribution

It introduces a formal theory of aliasing in observational studies and proposes a novel matching approach to mitigate confounding effects.

Findings

The theory explains how aliasing affects treatment effect estimation in observational data.

A new matching method improves balance in confounded factorial designs.

The approach outperforms traditional difference-in-differences in robustness.

Abstract

In experimental design, aliasing of effects occurs in fractional factorial experiments, where certain low order factorial effects are indistinguishable from certain high order interactions: low order contrasts may be orthogonal to one another, while their higher order interactions are aliased and not identified. In observational studies, aliasing occurs when certain combinations of covariates -- e.g., time period and various eligibility criteria for treatment -- perfectly predict the treatment that an individual will receive, so a covariate combination is aliased with a particular treatment. In this situation, when a contrast among several groups is used to estimate a treatment effect, collections of individuals defined by contrast weights may be balanced with respect to summaries of low-order interactions between covariates and treatments, but necessarily not balanced with respect to summaries of high-order interactions between covariates and treatments. We develop a theory of aliasing in observational studies, illustrate that theory in an observational study whose aliasing is more robust than conventional difference-in-differences, and develop a new form of matching to construct balanced confounded factorial designs from observational data.