Bayesian Updating and Sequential Testing: Overcoming Inferential Limitations of Screening Tests
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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 n_i needed is: n_i =lim_ρ→ k⌈ln[ρ(ϕ-1)/ϕ(ρ-1)]/ln[a/1-b]⌉ where n_i = 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.
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