Revisiting the Analysis of Matched-Pair and Stratified Experiments in the Presence of Attrition

TL;DR

This paper critically examines common practices in analyzing matched-pair and stratified experiments with attrition, clarifying when dropping pairs or stratifying improves estimation of treatment effects.

Contribution

It provides a theoretical analysis of the estimands resulting from different handling of attrition in matched-pair and stratified designs, challenging some conventional advice.

Findings

Dropping pairs with attrition does not generally recover the average treatment effect.

Dropping pairs may help estimate a convex weighted average of conditional effects.

Stratification and fixed effects have nuanced impacts on estimand interpretation.

Abstract

In this paper we revisit some common recommendations regarding the analysis of matched-pair and stratified experimental designs in the presence of attrition. Our main objective is to clarify a number of well-known claims about the practice of dropping pairs with an attrited unit when analyzing matched-pair designs. Contradictory advice appears in the literature about whether or not dropping pairs is beneficial or harmful, and stratifying into larger groups has been recommended as a resolution to the issue. To address these claims, we derive the estimands obtained from the difference-in-means estimator in a matched-pair design both when the observations from pairs with an attrited unit are retained and when they are dropped. We find limited evidence to support the claims that dropping pairs helps recover the average treatment effect, but we find that it may potentially help in recovering a convex weighted average of conditional average treatment effects. We report similar findings for stratified designs when studying the estimands obtained from a regression of outcomes on treatment with and without strata fixed effects.