Keywords: Propensity score, Optimal Matching Algorithm, Potential Outcome Framework, Conditional Inference, Sensitivity Analysis
Comparing emergency department mortality across levels of trauma centers (non-trauma, level I and II centers) is vital in evaluating trauma care. Given the observational nature of the data source, it is critical to adjust for patient characteristics to render valid comparisons across trauma levels. Propensity score matching has been established as a robust method to infer causal relationships in observational studies with two treatment arms. Few studies, however, have used matching designs with more than two groups. This is due to the complexity of multiple-group matching algorithms and to the lack of optimal results. We propose an iterative three-way matching algorithm that outperforms the nearest neighbor algorithm. We apply the algorithm to the Nationwide Emergency Department Sample to generate well-balanced triplets and find a significant difference in mortality across the trauma care levels. To examine the robustness of the result to hidden bias, we generalize Rosenbaum's two-group sensitivity analysis to the three-group setting. Our sensitivity analysis shows that unmeasured confounders moderately associated with the treatment assignment may change the result qualitatively.