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 \(\:{T}ᵢ=ω\:{S}ᵢOSCE+(1-ω\:){W}ᵢ\) , where \(\:{S}ᵢOSCE\:\) is an equally weighted mean of \(\:K\) OSCE stations with global ratings \(\:{G}ᵢₖ∈\:\{1,2,3,4\}\) . Station cut scores were estimated using (a) Borderline Regression Method (BRM) for comparison and (b) Bayesian regression \(\:{S}ᵢₖ~\:N({α\:}ₖ+{β\:}ₖg({G}ᵢₖ),{σ\:}ₖ²)\) , giving posterior \(\:{c}ₖ={α\:}ₖ+{β\:}ₖg(B)\) at borderline \(\:B=2\) . Borderline semantics were represented via a trapezoidal fuzzy set \(\:{μ}border(G)\) with centroid \(\:{B}F\) , producing fuzzy-adjusted cuts \(\:{c}ₖF={α\:}ₖ+{β\:}ₖg({B}F)\) . A hybrid OSCE standard \(\:{c}OSCE*=λ\:E[{c}OSCE]+(1-λ)E[{c}OSCEF]\) was mapped to the mixed-format cut \(\:{c}T*\) . A decision band \(\:{Δ\:}\) combined Bayesian credible uncertainty and fuzzy \(\:α\:\) -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.