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Abstract:
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Conditional randomization tests are often used in matched observational studies to provide inference without strong distributional assumptions on the response. Instead, these tests typically assume homogeneity of propensity scores within matched sets (matched adjustability), and independence between the matched design chosen and the treatment values actually observed. In fact, because matching in practice is inexact, both of these assumptions can fail in ways that produce randomization tests with badly miscalibrated type I error rates. We offer design-based partial solutions to both problems. We present a new form of weighted randomization inference that incorporates estimates of the propensity score in order to address violations of matched adjustability. We also explore partially-randomized matched designs that guarantee independence between the matched design selected and the observed treatment. We assess the value of these solutions in comparison to and in combination with more standard tools such as propensity score calipers and regression adjustment.
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