title: Likelihood ratios, sensitivity, and specificity values can be back-calculated when the odds ratios are known.
abstract: 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.
authors.affiliation: Department of Medicine, Durham Veterans Affairs Medical Center and Duke University, Durham, NC 27705, USA. david.simel@duke.edu
authors.forename: David L
authors.initials: DL
authors.lastname: Simel
authors.forename: Joshua
authors.initials: J
authors.lastname: Easter
authors.forename: George
authors.initials: G
authors.lastname: Tomlinson
mesh_terms: D003627:Data Interpretation, Statistical; D005188:False Negative Reactions; D005189:False Positive Reactions; D006801:Humans; D016013:Likelihood Functions; D015201:Meta-Analysis as Topic; D016017:Odds Ratio; D012680:Sensitivity and Specificity; D012984:Software