Likelihood ratios, sensitivity, and specificity values can be back-calculated when the odds ratios are known

Area of Science:

• Medical Informatics
• Biostatistics
• Diagnostic Test Evaluation

Background:

• Systematic reviews and meta-analyses are crucial for synthesizing evidence from diagnostic test studies.
• A common limitation is the heterogeneity of reported results, particularly the absence of 2x2 contingency table data.
• Odds Ratios (ORs) are frequently reported, but direct calculation of sensitivity, specificity, and likelihood ratios (LRs) from ORs alone is not straightforward.

Purpose of the Study:

• To develop a method for calculating true-positive, false-positive, false-negative, and true-negative results from studies reporting only Odds Ratios (ORs).
• To enable the derivation of sensitivity, specificity, and Likelihood Ratios (LRs) when only ORs and patient counts are available.

Main Methods:

• Utilized a quadratic formula to back-calculate diagnostic accuracy metrics from the OR.
• Developed a spreadsheet tool requiring only the OR and 2x2 table row/column totals for calculating individual contingency table values.
• Addressed special cases including OR=1 and non-estimable ORs due to zero counts.

Main Results:

• The quadratic formula successfully allows for the back-calculation of sensitivity, specificity, and LRs from the OR.
• The spreadsheet tool enables the derivation of true positives, false positives, false negatives, and true negatives.
• Solutions were provided for scenarios with OR=1 and when ORs were non-estimable.

Conclusions:

• A user-friendly spreadsheet tool facilitates the inclusion of studies reporting only ORs in systematic reviews of diagnostic tests.
• This method enhances the pool of studies available for meta-analyses aiming to summarize sensitivity, specificity, or LRs.
• The approach supports more comprehensive evidence synthesis in diagnostic test research.