  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. The recent GroupMatch framework (Pimentel et al.,
2020) solves this problem 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 provide three important innovations to address these
problems. First, we introduce a new design, GroupMatch with instance
replacement, that allows additional flexibility in control selection and proves
more amenable to analysis. Second, we propose a block bootstrap approach for
inference in GroupMatch with instance replacement and demonstrate that it
accounts properly for complex correlations across matched sets. Third, we
develop a permutation-based falsification test to detect possible violations of
the important timepoint agnosticism assumption underpinning GroupMatch, which
requires homogeneity of potential outcome means across time. 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.

Methodology