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

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.

A mixed-format assessment model was specified with total score [Formula: see text], where [Formula: see text] is an equally weighted mean of [Formula: see text] OSCE stations with global ratings [Formula: see text]. Station cut scores were estimated using (a) Borderline Regression Method (BRM) for comparison and (b) Bayesian regression [Formula: see text], giving posterior [Formula: see text] at borderline [Formula: see text]. Borderline semantics were represented via a trapezoidal fuzzy set [Formula: see text] with centroid [Formula: see text], producing fuzzy-adjusted cuts [Formula: see text]. A hybrid OSCE standard [Formula: see text] was mapped to the mixed-format cut [Formula: see text]. A decision band [Formula: see text] combined Bayesian credible uncertainty and fuzzy [Formula: see text]-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.

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.

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.