One central goal of design of observational studies is to embed non-experimental data into an approximate randomized controlled trial using statistical matching. Researchers then make the randomization assumption in their downstream, outcome analysis. For matched pair design, the randomization assumption states that the treatment assignment across all matched pairs are independent, and that the probability of the first subject in each pair receiving treatment and the other control is the same as the first receiving control and the other treatment. In this article, we develop a novel framework for testing the randomization assumption based on solving a clustering problem with side-information using modern statistical learning tools. Our testing framework is nonparametric, finite-sample exact, and distinct from previous proposals in that it can be used to test a relaxed version of the randomization assumption called the biased randomization assumption. One important by-product of our testing framework is a quantity called residual sensitivity value (RSV), which quantifies the level of minimal residual confounding due to observed covariates not being well matched. We advocate taking into account RSV in the downstream primary analysis. The proposed methodology is illustrated by re-examining a famous observational study concerning the effect of right heart catheterization (RHC) in the initial care of critically ill patients.
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