
Bayesian Updating and Sequential Testing: Overcoming Inferential Limitations of Screening Tests
Bayes' Theorem confers inherent limitations on the accuracy of screening...
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The Stochastic Score Classification Problem
Consider the following Stochastic Score Classification Problem. A doctor...
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Prevalence Threshold and the Geometry of Screening Curves
The relationship between a screening tests' positive predictive value, ρ...
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More testing or more disease? A counterfactual approach to explaining observed increases in positive tests over time
Observed gonorrhea case rates (number of positive tests per 100,000 indi...
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Is Group Testing Ready for Primetime in Disease Identification?
Large scale disease screening is a complicated process in which high cos...
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Optimization of Ensemble Supervised Learning Algorithms for Increased Sensitivity, Specificity, and AUC of PopulationBased Colorectal Cancer Screenings
Over 150,000 new people in the United States are diagnosed with colorect...
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Reliable AttributeBased Object Recognition Using High Predictive Value Classifiers
We consider the problem of object recognition in 3D using an ensemble of...
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Derivation of Generalized Equations for the Predictive Value of Sequential Screening Tests
Using Bayes' Theorem, we derive generalized equations to determine the positive and negative predictive value of screening tests undertaken sequentially. Where a is the sensitivity, b is the specificity, ϕ is the pretest probability, the combined positive predictive value, ρ(ϕ), of n serial positive tests, is described by: ρ(ϕ) = ϕ∏_i=1^na_n/ϕ∏_i=1^na_n+(1ϕ)∏_i=1^n(1b_n) If the positive serial iteration is interrupted at term position n_ik by a conflicting negative result, then the resulting negative predictive value is given by: ψ(ϕ) = [(1ϕ)b_n]∏_i=b_1+^b_(n1)+(1b_n+)/[ϕ(1a_n)]∏_i=a_1+^a_(n1)+a_n++[(1ϕ)b_n]∏_i=b_1+^b_(n1)+(1b_n+) Finally, if the negative serial iteration is interrupted at term position n_ik by a conflicting positive result, then the resulting positive predictive value is given by: λ(ϕ)= ϕ a_n+∏_i=a_1^a_(n1)(1a_n)/ϕ a_n+∏_i=a_1^a_(n1)(1a_n)+[(1ϕ)(1b_n+)]∏_i=b_1^b_(n1)b_n The aforementioned equations provide a measure of the predictive value in different possible scenarios in which serial testing is undertaken. Their clinical utility is best observed in conditions with low pretest probability where single tests are insufficient to achieve clinically significant predictive values and likewise, in clinical scenarios with a high pretest probability where confirmation of disease status is critical.
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