S-score: a new score for binary qualitative proficiency testing schemes interpretable as the z-score

Abstract

The S-score is a new performance score applicable to proficiency testing (PT) for binary data. It allows the proficiency test provider to choose how the assigned value (AV) is defined, e.g., positive versus negative, either by the PT provider or by laboratory consensus based on participating laboratories. It is a flexible tool that can be used to select as a maximum four types of proficiency test items (PTIs) depending on the required correct results and expected correct results predefined by the PT provider. Regarding the required correct results, for an easy tasks, e.g., easy analyte detection, correct results matching with the assigned value are required for all PTI1s. For difficult tasks, e.g. close to the limit of detection (LOD) with replicated samples and for mixed tasks with unreplicated, an acceptable range of correct results is required using the binomial probability density from at least six PTI2s. Regarding correct results expected but not required for difficult tasks, results matching with the assigned value are requested by the PT provider for all PTI3s and by a participating laboratory consensus (LC) for all PTI4s. The S-score was designed as a numerical indicator taking into account all the combinations of the different types of PTIs. The decimal part summarizes the laboratory results indicating the rate of incorrect results in relation to the different PTIs assigned values. The integer part provides a similar interpretation to the one of the z-score for quantitative PT, with ‘satisfactory’ (1 ≤ S-score < 2), ‘questionable’ (2 ≤ S-score < 3), and ‘unsatisfactory’ (S-score ≥ 3) performance, respectively.

Appendices

Appendix

Computational annex (pseudo-code)

Algorithm 1

Computation of $m_{\min }$ (Table 2, α = 0.05)

Algorithm 2

Computation of $y_{\min }$ (Table 4, α = 0.01) or (Table 3, α = 0.05)

Algorithm 3

Computation of $y_{\max }$ (Table 4, α = 0.01) or (Table 3, α = 0.05)