Why Match in Individually and Cluster Randomized Trials

The decision to match individuals or clusters in randomized trials is motivated by both practical and statistical concerns. Matching protects against chance imbalances in baseline covariate distributions and is thought to improve study credibility. Matching is also implemented to increase study power. This article compares the asymptotic efficiency of the pair-matched design, where units are matched on baseline covariates and the treatment randomized within pairs, to the independent design, where units are randomly paired and the treatment randomized within pairs. We focus on estimating the average treatment effect and use the efficient influence curve to understand the information provided by each design for estimation of this causal parameter. Our theoretical results indicate that the pairmatched design is asymptotically less efficient than its non-matched counterpart. Our simulations confirm these results asymptotically and in finite samples. Our approach is estimator-independent, avoids all parametric modeling assumptions, and applies equally to individually randomized and cluster randomized trials.

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