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An *NRMP* Match Made in Heaven
— MEDICAL SCHOOL —
McGovern Medical School at the University of Texas
Health Science Center at Houston
— GRADUATING CLASS —
With thousands of other students, I spent most of February and March eagerly anticipating the results of the Match, second guessing my final rank list, fearfully wondering about the SOAP process and repeating this cycle in an unhealthy manner. I was moderately successful at breaking this sequence, if only for a few days, by focusing on my last few clinical rotations while rekindling old hobbies and watching movies. At the end of February, I watched a new release starring Jennifer Lopez and Owen Wilson entitled Marry Me, a textbook romantic comedy with outrageous story lines and feel-good moments. Although I should have been content in my cheesy cinematic experience, I noticed that I was falling back into my cycle as I mirrored Lopez's concern about finding her perfect match—only mine was a residency program. Instead of searching for another distraction, I thought it would be better to consider the idea of a “perfect” match and learn more about the history and mathematics behind this process that stresses out so many medical students across the world even though, ultimately, it might all be worth it on Match day.
To begin, we must backtrack to the early 20th century when the number of hospitals needing interns far outnumbered the number of incoming residents. At this time, hospitals pressured students into filling positions with time-sensitive signing offers while students were forced to decide between job security and the uncertainty of waiting for a better offer. Hospitals went so far as to begin offering students binding positions as early as the second year of medical school (1, 2). In response to this chaos, in 1945, the Association of American Medical Colleges adopted the “Cooperative Plan” in which medical schools would not release medical student information to hospitals until the summer between years 3 and 4 of school (1). Although this may have prevented hospitals from sending students offers along with their medical school acceptance letters, this plan was far from perfect.
With less time to fill positions, the time period students had in which to answer offers from hospitals grew shorter and shorter: hospitals wanted a prompt answer so that they could reach out to their next preferred applicant if their first choice declined. F.J. Mullin, former Dean of Students at the University of Chicago, recalled, “Students sometimes [would] get panicky and accept poor internships way down on their lists because they ha[d] not heard from a higher position on their order of preference” (1).
Mullin suggested an idea to help facilitate match outcomes, which he termed a clearinghouse, with the use of rank lists to produce a match. This idea was based off of similar, successful, small-scale regional programs. Following a trial run, in 1952 it was agreed that a centralized match should be used for the internship process (1). Mullin, along with Stanford academic John M. Stalnaker, originally outlined an algorithm for the match; however, they received backlash from medical students that the proposal was flawed. The algorithm was replaced with another called the Boston Pool Plan, which—using the model of deferred acceptance—better accommodated for student preferences (1–3). In 1998, the algorithm was overhauled by Alvin Roth and Elliott Peranson to optimize the results for medical students based on the 1962 Gale–Shapley stable marriage algorithm and the 1984 Roth and Vates accommodation for couples' match preferences (2). This stable matching theory has been used across multiple subspecialities and industries, earning Roth and Shapley the 2012 Nobel Prize in Economics. More recently, the Match was expanded in 2020 to include doctor of osteopathic medicine (DO) applicants, a change termed the Single Match (1).
To adequately describe the current Match algorithm, I must first define an unstable match. An unstable match exists when BOTH hospital A prefers an outside intern to one of its admitted interns AND the same outside intern prefers hospital A to their current hospital. A stable match is defined as the absence of unstable matches (4).
The current simple Match algorithm is known as the Gale–Shapley deferred acceptance algorithm. The proof that backs this algorithm includes two observations. First, hospitals propose to students in decreasing order of preference. Second, once students are matched, they can only “upgrade” their match or accept a proposal from a hospital higher on their list. Hospitals continue to propose in decreasing order of preference only if there are unmatched spots (4). Students keep only the best hospital that has proposed to them. In this scenario, all of the matches created are stable. The algorithm becomes more complex with the couples' match; however, the applicant optimization remains the same.
A few concepts not accounted for in this algorithm include the limitation of interview invites, subspecialty residency positions, and preinterview and postinterview communications. Although the first two factors are a reflection of limited residency positions and limited resources for those residents, the last topic has become especially controversial. Unfortunately, the integrity of the match process relies heavily on both hospitals and medical students being completely honest with themselves about their preferences for programs. Even so, students and institutions have never been prohibited from declaring a program's ranking. Although prior studies have shown that postinterview communication has little impact on an applicant's rank position (5), a survey-based study showed that 70% of surveyed applicants informed their top program that they had ranked it highly; 70% of this subset reported a sense of distress in making such a proclamation (6). Importantly, “20% of applicants ... reported changing their rank list based on their engagement in postinterview communication” (6). These findings demonstrate a potential flaw in the submission of true preference lists.
Prior recommendations urge institutions to consider setting clear expectations for applicants on interview day and further urge the NRMP to prohibit communication about rank preference altogether (7). Unfortunately, both historically and in the present day, these recommendations vary from institution to institution and even in discussions with my own mentors. From the perspective of a medical student who recently underwent the process, I imagine that a clear guideline from the NRMP about postinterview communication—implemented in a uniform manner—would help mitigate some of the mixed messaging currently in place. If students are changing rank lists based on these communications, even if well intended, then this will give rise to an atmosphere of disingenuity and distress. I believe that both Jennifer Lopez and most of the romantic comedy movie industry would be disappointed in my conclusion that a stable match is better than a “perfect” match, and, furthermore, dramatic declarations of love from one party to another may ultimately do more harm than good.
- Roth AE. The origins, history, and design of the resident match. JAMA. 2003;289:909-12. [PMID: 12588278] doi:10.1001/jama.289.7.909
- Roth AE. Deferred acceptance algorithms: history, theory, practice, and open questions. Int J Game Theory. 2008;36:537-569. doi:10.1007/s00182-008-0117-6
- Mullin FJ, Stalnaker JM. The matching plan for internship placement. J Med Educ. 1952;27:193-200. [PMID: 14938854] doi:10.1097/00001888-195205000-00008
- Wayne K. Stable matching [PowerPoint slides]. Pearson–Addison Wesley; 2005. Accessed at www.cs.princeton.edu/~wayne/kleinberg-tardos/pdf/01StableMatching.pdf on 26 February 2022.
- Swan EC, Baudendistel TE. Relationship between postinterview correspondence from residency program applicants and subsequent applicant match outcomes. J Grad Med Educ. 2014;6:478-83. [PMID: 26279772] doi:10.4300/JGME-D-13-00329.1
- Berriochoa C, Reddy CA, Dorsey S, et al. The residency match: interview experiences, postinterview communication, and associated distress. J Grad Med Educ. 2018;10:403-408. [PMID: 30154970] doi:10.4300/JGME-D-17-01020.1
- Grimm LJ, Avery CS, Maxfield CM. Residency postinterview communications: more harm than good? [Editorial]. J Grad Med Educ. 2016;8:7-9. [PMID: 26913094] doi:10.4300/JGME-D-15-00062.1