Matching is a common method of adjusting for confounding in observational studies. Studies in rare diseases usually include small numbers of exposed subjects, but the performance of matching methods in such cases has not been evaluated thoroughly. In this study, we compare the performance of several matching methods when number of exposed subjects is small. We used Monte Carlo simulations to compare the following methods: Propensity score matching (PSM) with greedy or optimal algorithm, Mahalanobis distance matching, and mixture of PSM and exact matching. We performed the comparisons in datasets with six continuous and six binary variables, with varying effect size on group assignment and outcome. In each case, there were 1,500 unexposed subjects and a varying number of exposed: N = 25, 50, 100, 150, 200, 250, or 300. The probability of outcome in unexposed subjects was set to 5% (rare), 20% (common), or 50% (frequent). We compared the methods based on the bias of estimate of risk difference, coverage of 95% confidence intervals for risk difference, and balance of covariates. We observed a difference in performance of matching methods in very small samples (N = 25-50) and in moderately small samples (N = 100-300). Our study showed that PSM performs better than other matching methods when number of exposed subjects is small, but the matching algorithm and the matching ratio should be considered carefully. We recommend using PSM with optimal algorithm and one-to-five matching ratio in very small samples, and PSM matching with any algorithm and one-to-one matching in moderately small samples.
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