Detection of and Correction for Violation of the Common Trend Assumption in Gain Score Analysis

Abstract

Gain score analysis or difference-in-differences allows researchers to identify valid causal effects even in the presence of unmeasured confounding. This identification hinges on its own unique assumption referred to as the common trend assumption. The assumption requires that the impacts of the confounding variables on the pre- and posttest scores are identical. Despite the importance, however, researchers have no way to empirically evaluate the assumption and, thus, have not well discussed or justified its plausibility in their research. This paper makes two contributions. First, the paper introduces a novel strategy that uses an additional variable that helps one to test the plausibility of the common trend assumption. Second, the papers develops a formal gain score analysis that corrects the violation of the common trend assumption and returns unbiased causal effects even though the common trend assumption is violated. The proposed approaches are illustrated by real data analysis.