
Contents
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What Is Bayes’ Theorem? What Is Bayes’ Theorem?
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Calculating Pre-Test Probability Calculating Pre-Test Probability
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Updating Pre-Test Probability Updating Pre-Test Probability
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The Trouble With Pre-Test Probabilities and Likelihood Ratios The Trouble With Pre-Test Probabilities and Likelihood Ratios
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What Is a ‘Good’ Likelihood Ratio? What Is a ‘Good’ Likelihood Ratio?
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The Example of Prostate Cancer Screening The Example of Prostate Cancer Screening
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Non-Binary Conditions Non-Binary Conditions
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Summary Summary
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Notes Notes
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5 C5Test Accuracy As Likelihood Ratios
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Published:December 2022
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Abstract
This chapter introduces readers to the use of Bayes’ theorem as a potential way to address the drawbacks of sensitivity, specificity, and predictive values. It describes the process of updating the probability of a condition based on test results and that the principal statistics (Bayes’ factors) are the likelihood ratios which are calculated from all four squares of a 2×2 table. It explains how the application of Bayes’ theorem to medical testing begins with a calculation of the pre-test probability of a condition using intuition and experience or, where available, a data-driven approach. It continues with the method of combining pre-test probabilities with likelihood ratios to give post-test probabilities, which can be illustrated with a Fagan nomogram but is best performed with a smartphone app. It concludes with a discussion of screening tests which are typically performed at very low pre-test probability when tests with very high diagnostic accuracy are needed.
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