2020/07/25 by Jacques Balayla, Balayla, Jacques · 1 citation
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods in Clinical Trials
paper · pdf · doi:10.48550/arxiv.2007.13046
openalex publication_date 2020/07/25 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Using Bayes' Theorem, we derive generalized equations to determine the\npositive and negative predictive value of screening tests undertaken\nsequentially. Where a is the sensitivity, b is the specificity, \φ is the\npre-test probability, the combined positive predictive value, \ρ(\φ), of\nn serial positive tests, is described by:\n \ρ(\φ) =\n frac\φ ∏i=1nan\φ ∏i=1nan+(1-\φ) ∏i=1n(1-bn)\n If the positive serial iteration is interrupted at term position ni-k by a\nconflicting negative result, then the resulting negative predictive value is\ngiven by:\n \ψ(\φ) =\n frac[(1-\φ)bn-] ∏_i=b1+^b(n-1)+(1-bn+)[\φ(1-an-)] ∏_i=a1+^a(n-1)+an++[(1-\φ)bn-] ∏_i=b1+^b(n-1)+(1-bn+)\n Finally, if the negative serial iteration is interrupted at term position\nni-k by a conflicting positive result, then the resulting positive\npredictive value is given by: \λ(\φ)= frac\φ\nan+ ∏_i=a1-^a(n-1)-(1-an-)\φ\nan+ ∏_i=a1-^a(n-1)-(1-an-)+[(1-\φ)(1-bn+)] ∏_i=b1-^b(n-1)-bn-\n The aforementioned equations provide a measure of the predictive value in\ndifferent possible scenarios in which serial testing is undertaken. Their\nclinical utility is best observed in conditions with low pre-test probability\nwhere single tests are insufficient to achieve clinically significant\npredictive values and likewise, in clinical scenarios with a high pre-test\nprobability where confirmation of disease status is critical.\n