Background Pass-fail decisions in clinical examinations must be defensible, yet traditional standard-setting approaches often report a single cut score without explicitly quantifying uncertainty-an issue amplified in small cohorts and mixed-format assessments (e.g., OSCE plus written). We propose a Bayesian fuzzy hybrid standard-setting framework that (i) treats station cut scores as posterior distributions and (ii) models the inherently linguistic “borderline” construct using fuzzy membership, yielding both a central standard and a principled borderline review band. Methods A mixed-format assessment model was specified with total score <InlineEquation ID="IEq1"><EquationSource Format="TEX">\(\:{T}_{i}=\omega\:{S}_{i}^{\text{OSCE}}+(1-\omega\:){W}_{i}\)</EquationSource></InlineEquation>, where <InlineEquation ID="IEq2"><EquationSource Format="TEX">\(\:{S}_{i}^{\text{OSCE\:}}\)</EquationSource></InlineEquation> is an equally weighted mean of <InlineEquation ID="IEq3"><EquationSource Format="TEX">\(\:K\)</EquationSource></InlineEquation> OSCE stations with global ratings <InlineEquation ID="IEq4"><EquationSource Format="TEX">\(\:{G}_{ik}\in\:\{\text{1,2},\text{3,4}\}\)</EquationSource></InlineEquation>. Station cut scores were estimated using (a) Borderline Regression Method (BRM) for comparison and (b) Bayesian regression <InlineEquation ID="IEq5"><EquationSource Format="TEX">\(\:{S}_{ik}\sim\:\text{}\text{N}\left({\alpha\:}_{k}+{\beta\:}_{k}g\left({G}_{ik}\right),{\sigma\:}_{k}^{2}\right)\)</EquationSource></InlineEquation>, giving posterior <InlineEquation ID="IEq6"><EquationSource Format="TEX">\(\:{c}_{k}={\alpha\:}_{k}+{\beta\:}_{k}g\left(B\right)\)</EquationSource></InlineEquation> at borderline <InlineEquation ID="IEq7"><EquationSource Format="TEX">\(\:B=2\)</EquationSource></InlineEquation>. Borderline semantics were represented via a trapezoidal fuzzy set <InlineEquation ID="IEq8"><EquationSource Format="TEX">\(\:{\mu}_{\text{border}}\left(G\right)\)</EquationSource></InlineEquation> with centroid <InlineEquation ID="IEq9"><EquationSource Format="TEX">\(\:{B}_{F}\)</EquationSource></InlineEquation>, producing fuzzy-adjusted cuts <InlineEquation ID="IEq10"><EquationSource Format="TEX">\(\:{c}_{k}^{F}={\alpha\:}_{k}+{\beta\:}_{k}g\left({B}_{F}\right)\)</EquationSource></InlineEquation>. A hybrid OSCE standard <InlineEquation ID="IEq11"><EquationSource Format="TEX">\(\:{c}_{\text{OSCE}}^{\text{}}=\lambda\:\text{E}\left[{c}_{\text{OSCE}}\right]+(1-\lambda)\text{E}\left[{c}_{\text{OSCE}}^{F}\right]\)</EquationSource></InlineEquation> was mapped to the mixed-format cut <InlineEquation ID="IEq12"><EquationSource Format="TEX">\(\:{c}_{T}^{\text{}}\)</EquationSource></InlineEquation>. A decision band <InlineEquation ID="IEq13"><EquationSource Format="TEX">\(\:{\Delta\:}\)</EquationSource></InlineEquation> combined Bayesian credible uncertainty and fuzzy <InlineEquation ID="IEq14"><EquationSource Format="TEX">\(\:\alpha\:\)</EquationSource></InlineEquation>-cut uncertainty to classify candidates as Pass, Fail, or Borderline review. The full workflow was demonstrated using a collected sample dataset (n=34, k=6) to illustrate reporting and reproducibility. Results Station-level BRM cut scores ranged from 59.5 to 62.4, while Bayesian station cut scores produced interpretable 95% credible intervals around similar means. The Bayesian OSCE cut score mean was approximately 61.2 with a narrow posterior interval, and the hybrid mixed format cut score was approximately 60.8 (0-100 scale). The uncertainty-aware decision band produced 22 Pass (64.7%), 10 Fail (29.4%), and 2 Borderline review (5.9%) classifications, explicitly isolating boundary cases rather than forcing deterministic decisions. Bootstrap resampling indicated that the hybrid central standard was stable and comparable to BRM, while adding transparency via a bounded review zone. Conclusions Here the Bayesian-fuzzy hybrid framework retained the interpretability of borderline regression but provided explicit uncertainty quantification and a structured bandfor borderline review. The results ought to be understood as methodological and illustrative but not confirmation of universal superiority; external validation in larger multi-centre clinical examination cohorts is necessary prior to routine operational implementation.

Bayesian and fuzzy hybrid standard setting for pass-fail decisions in clinical examinations

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2026年7月9日

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Yogeesh N.,
Mohammed Almakki,
Asokan Vasudevan,
Shiney John,
Mayibongwe Tafara Mudzengi

摘要

Background

Pass-fail decisions in clinical examinations must be defensible, yet traditional standard-setting approaches often report a single cut score without explicitly quantifying uncertainty-an issue amplified in small cohorts and mixed-format assessments (e.g., OSCE plus written). We propose a Bayesian fuzzy hybrid standard-setting framework that (i) treats station cut scores as posterior distributions and (ii) models the inherently linguistic “borderline” construct using fuzzy membership, yielding both a central standard and a principled borderline review band.

Methods

A mixed-format assessment model was specified with total score \(\:{T}_{i}=\omega\:{S}_{i}^{\text{OSCE}}+(1-\omega\:){W}_{i}\), where \(\:{S}_{i}^{\text{OSCE\:}}\) is an equally weighted mean of \(\:K\) OSCE stations with global ratings \(\:{G}_{ik}\in\:\{\text{1,2},\text{3,4}\}\). Station cut scores were estimated using (a) Borderline Regression Method (BRM) for comparison and (b) Bayesian regression \(\:{S}_{ik}\sim\:\text{}\text{N}\left({\alpha\:}_{k}+{\beta\:}_{k}g\left({G}_{ik}\right),{\sigma\:}_{k}^{2}\right)\), giving posterior \(\:{c}_{k}={\alpha\:}_{k}+{\beta\:}_{k}g\left(B\right)\) at borderline \(\:B=2\). Borderline semantics were represented via a trapezoidal fuzzy set \(\:{\mu}_{\text{border}}\left(G\right)\) with centroid \(\:{B}_{F}\), producing fuzzy-adjusted cuts \(\:{c}_{k}^{F}={\alpha\:}_{k}+{\beta\:}_{k}g\left({B}_{F}\right)\). A hybrid OSCE standard \(\:{c}_{\text{OSCE}}^{\text{*}}=\lambda\:\text{E}\left[{c}_{\text{OSCE}}\right]+(1-\lambda)\text{E}\left[{c}_{\text{OSCE}}^{F}\right]\) was mapped to the mixed-format cut \(\:{c}_{T}^{\text{*}}\). A decision band \(\:{\Delta\:}\) combined Bayesian credible uncertainty and fuzzy \(\:\alpha\:\)-cut uncertainty to classify candidates as Pass, Fail, or Borderline review. The full workflow was demonstrated using a collected sample dataset (n=34, k=6) to illustrate reporting and reproducibility.

Results

Station-level BRM cut scores ranged from 59.5 to 62.4, while Bayesian station cut scores produced interpretable 95% credible intervals around similar means. The Bayesian OSCE cut score mean was approximately 61.2 with a narrow posterior interval, and the hybrid mixed format cut score was approximately 60.8 (0-100 scale). The uncertainty-aware decision band produced 22 Pass (64.7%), 10 Fail (29.4%), and 2 Borderline review (5.9%) classifications, explicitly isolating boundary cases rather than forcing deterministic decisions. Bootstrap resampling indicated that the hybrid central standard was stable and comparable to BRM, while adding transparency via a bounded review zone.

Conclusions

Here the Bayesian-fuzzy hybrid framework retained the interpretability of borderline regression but provided explicit uncertainty quantification and a structured bandfor borderline review. The results ought to be understood as methodological and illustrative but not confirmation of universal superiority; external validation in larger multi-centre clinical examination cohorts is necessary prior to routine operational implementation.