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Yue Wu, Theodore Spaide, Yuka Kihara, Cecilia S Lee, Ryan T. Yanagihara, Julia Owen, Aaron Y Lee, Russell Van Gelder; Global maximal utility optimizer for resident matching. Invest. Ophthalmol. Vis. Sci. 2020;61(7):5120.
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© ARVO (1962-2015); The Authors (2016-present)
The resident matching algorithm, Gale-Shapley, currently used by SF Match and the National Residency Match Program, has been in use for over 40 years without fundamental alteration. The algorithm is a ‘stable-marriage’ method that favors applicant outcome. Other stable match algorithms, including those that favor program outcome, or those that maximize total utility of the system (favoring neither applicant nor program) are available. We sought to compare the outcomes of simulated matches with these algorithms using anonymized real-world match data for ophthalmology residency.
Nine years (2011-2019) of anonymized rank lists for ophthalmology residency applicants and programs as well as the matches were provided by SF Match. We developed a framework to maximize the global weighted preference for both students and programs (MaxOpt). This global utility is maximized when the combined total rank of applicants and programs is minimized. The resultant matches were compared to that of actual SF Match results.
MaxOpt matches similar applicants to SF Match (Fig 1a) across all years; more than 90% of applicants obtain the same match status. However under MaxOpt, the average program matched ranks improves by 3.81 rank positions versus a 0.67 rank position decrease for the average student (Fig 1b). We find that 54% of previously matched candidates match at the identical program with MaxOpt and SF Match. While another 18% match match within 2 ranks of their SF Match programs (Fig 2a). Next, 77% of programs over the years match at least as well under MaxOpt in terms of median matched applicant, with 55% doing better (Fig 2b).
The global maximal utility optimizer (MaxOpt) achieves greater overall utility for both applicants and programs. Moreover, MaxOpt can be applied to any utility function, potentially allowing for weighted preferences in match list submissions by both applicants and programs. Alteration of fundamental match algorithms may result in globally improved match performance.
This is a 2020 ARVO Annual Meeting abstract.
Figure 1. a) Change in applicant match under MaxOpt vs SF Match; b) Avg matched ranks under MaxOpt vs SF Match.
Figure 2. a) Change in 2019 matched program ranks for applicants under MaxOpt vs SF Match; b) Change in 2019 matched applicant ranks for programs under MaxOpt vs SF Match.
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