Triplet Matching for Estimating Causal Effects With Three Treatment Arms: A Comparative Study of Mortality by Trauma Center Level

Comparing outcomes across different levels of trauma centers is vital in evaluating regionalized trauma care. With observational data, it is critical to adjust for patient characteristics to render valid causal comparisons. Propensity score matching is a popular method to infer causal relationships in observational studies with two treatment arms. Few studies, however, have used matching designs with more than two groups, due to the complexity of matching algorithms. We fill the gap by developing an iterative matching algorithm for the three-group setting. Our algorithm outperforms the nearest neighbor algorithm and is shown to produce matched samples with total distance no larger than twice the optimal distance. We implement the evidence factors method for binary outcomes, which includes a randomization-based testing strategy and a sensitivity analysis for hidden bias in three-group matched designs. We apply our method to the Nationwide Emergency Department Sample data to compare emergency department mortality among non-trauma, level I, and level II trauma centers. Our tests suggest that the admission to a trauma center has a beneficial effect on mortality, assuming no unmeasured confounding. A sensitivity analysis for hidden bias shows that unmeasured confounders, moderately associated with the type of care received, may change the result qualitatively. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.