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Abstract:
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How many controls should be matched to a treated subject? Entire matching determines the optimal number by using propensity scores in a new way. The number is optimal because by it, all the bias can be removed on observed covariates while permitting a control sample of maximum size. As such, entire matching produces an estimator of the treatment effect that is unbiased when treatment assignment is strongly ignorable and, subject to this, has minimum standard error. A formal framework is established which allows proper comparison of matched designs, in which entire matching is shown to be the optimal design. In an application to a SEER-based observational study of the sentinel lymph node biopsy for melanoma, entire matching is shown to reduce more bias than pair matching, while maximizing the size of the control sample.
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