2020/06/20 by Jacques Balayla, Balayla, Jacques · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods in Clinical Trials
paper · pdf · doi:10.48550/arxiv.2006.11641
openalex publication_date 2020/06/20 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Bayes' Theorem confers inherent limitations on the accuracy of screening tests as a function of disease prevalence. We have shown in previous work that a testing system can tolerate significant drops in prevalence, up until a certain well-defined point known as the prevalence threshold, below which the reliability of a positive screening test drops precipitously. Herein, we establish a mathematical model to determine whether sequential testing overcomes the aforementioned Bayesian limitations and thus improves the reliability of screening tests. We show that for a desired positive predictive value of ρ that approaches k, the number of positive test iterations ni needed is: ni =limρ→ k\lceil(ln[(ρ(ϕ-1))/(ϕ(ρ-1))])/(ln[(a)/(1-b)])\rceil where ni = number of testing iterations necessary to achieve ρ, the desired positive predictive value, a = sensitivity, b = specificity, ϕ = disease prevalence and k = constant. Based on the aforementioned derivation, we provide reference tables for the number of test iterations needed to obtain a ρ(ϕ) of 50, 75, 95 and 99% as a function of various levels of sensitivity, specificity and disease prevalence.