Likelihood ratios, sensitivity, and specificity values can be back-calculated when the odds ratios are known
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Updated: May 18, 2026

Signal Acquisition, Score Interpretation, and Economics of a Non-Invasive Point-of-Care Test for Coronary Artery Disease
Published on: August 9, 2024
David L Simel1, Joshua Easter, George Tomlinson
1Department of Medicine, Durham Veterans Affairs Medical Center and Duke University, Durham, NC 27705, USA. david.simel@duke.edu
Objective:
To provide a solution for calculating the true-positive, false-positive, false-negative, and true-negative results from studies where only the odds ratios (ORs), number of patients with the finding, and number of patients with the target condition are given.
Results:
The quadratic formula shown here allows investigators conducting systematic reviews to back-calculate the sensitivity, specificity, and likelihood ratios (LRs) from the OR. A spreadsheet that requires only the OR, and the row and column total from the 2 × 2 table enables the back-calculation of the individual true positives, false positives, false negatives, and true negatives. Solutions are also available for the special situations when the OR = 1 or the OR is nonestimable because of zero false positives or false negatives.
Conclusions:
A simple spreadsheet enables those conducting systematic reviews of diagnostic tests to include studies that report only the OR. This approach should enrich the number of studies retained in meta-analyses of diagnostic tests where the desire is to create summary sensitivity, specificity, or LRs.
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