Robust inference for matching under rolling enrollment

Abstract Matching in observational studies faces complications when units enroll in treatment on a rolling basis. While each treated unit has a specific time of entry into the study, control units each have many possible comparison, or “pseudo-treatment,” times. Valid inference must account for correlations between repeated measures for a single unit, and researchers must decide how flexibly to match across time and units. We provide three important innovations. First, we introduce a new matched design, GroupMatch with instance replacement, allowing maximum flexibility in control selection. This new design searches over all possible comparison times for each treated-control pairing and is more amenable to analysis than past methods. Second, we propose a block bootstrap approach for inference in matched designs with rolling enrollment and demonstrate that it accounts properly for complex correlations across matched sets in our new design and several other contexts. Third, we develop a falsification test to detect violations of the timepoint agnosticism assumption, which is needed to permit flexible matching across time. We demonstrate the practical value of these tools via simulations and a case study of the impact of short-term injuries on batting performance in major league baseball.