Abstract:
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Matching in observational studies faces complications when units enroll in treatment on a rolling basis. While treated units have a specific time of entry into the study, control units each have many possible comparison times. The recent GroupMatch framework proceeds by searching over all possible pseudo-treatment times for each control and selecting those permitting the closest matches based on covariate histories. However, valid methods of inference have been described only for special cases of the general GroupMatch design, and these rely on strong assumptions. We introduce a new design that allows additional flexibility in control selection and proves more amenable to analysis. For inference, we propose a block bootstrap approach and demonstrate that it accounts for complex correlations across matched sets. Additionally, we develop a permutation-based falsification test to detect possible violations of an important homogeneity-across-time assumption underpinning GroupMatch. Via simulation and a case study of the impact of short-term injuries on batting performance in major league baseball, we demonstrate the effectiveness of our methods for data analysis in practice.
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