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Yue Wu, Cecilia S Lee, Aaron Y Lee, Russell N Van Gelder; Algorithmic optimization of residency matching for a win-win outcome. Invest. Ophthalmol. Vis. Sci. 2021;62(8):2648.
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© ARVO (1962-2015); The Authors (2016-present)
The current system for pairing medical students to residency programs has been relatively unchanged for half a century. The residency matching algorithms, including SF Match for ophthalmology, are based on Gale-Shapley, a ‘stable-marriage’ method that favors applicant outcomes. We sought to develop a new matching algorithm (ResOpt) and compared it to Gale-Shapley.
We obtained anonymized rank lists and match data for applicants and programs in ophthalmology from SF Match between 2011 to 2019. The matches of SF Match and ResOpt were compared in terms of the average rank of matches for both applicants and programs, the percentage of applicants matching to their top choices, and the change in match composition.
For 2011 to 2019, ResOpt always fully matches and avoids the Supplemental Offer and Acceptance Program. In addition, ResOpt consistently matches more applicants to their most preferred programs (Figure 1a). Under ResOpt, 78.7% (3308/4205) of applicants matched their top 3 choices compared to 71.5% (2991/4181) under SF Match. Furthermore, ResOpt achieves better average ranks for both applicants and programs (Figure 1b and 1c), without drastically changing the match composition (Figure 2a). Rank composition analysis (Figure 2b) shows the applicants whose outcomes improve often improve by multiple ranks, while applicants who worsen mostly drop 1 rank.
ResOpt is a credible alternative as a matching algorithm, as it consistently improves matches for most applicants and programs.
This is a 2021 ARVO Annual Meeting abstract.
Figure 1. a) Cumulative percentage of applicants matching into their top programs, b) the average applicant rank of their matched programs, and c) the average program rank of the programs' matched applicants under ResOpt and SF Match.
Figure 2. Rank composition comparison between ResOpt and SF Match. a) Percentage breakdown of applicant status change. Similar outcomes are defined as when applicants matched within one rank of their SF match under ResOpt from 2011-2019. b) Flow of applicant matched ranks between SF Match and ResOpt in 2019, where 1 represents applicants matching their top choice and U for applicants being unmatched. Flows of applicants with the i) exact same matches are yellow, ii) improved match outcomes green, iii) previously unmatched and became matched blue, iv) worse outcomes orange, and v) previously matched but became unmatched red.
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