Diagnostic odds ratio

The rationale for the diagnostic odds ratio is that it is a single indicator of test performance (like accuracy and Youden's J statistic) but which is independent of prevalence (unlike accuracy) and is presented as an odds ratio, which is familiar to medical practitioners.

[clarification needed] The standard error of the log diagnostic odds ratio is approximately: From this an approximate 95% confidence interval can be calculated for the log diagnostic odds ratio: Exponentiation of the approximate confidence interval for the log diagnostic odds ratio gives the approximate confidence interval for the diagnostic odds ratio.

[citation needed] The diagnostic odds ratio may be expressed in terms of the sensitivity and specificity of the test:[1] It may also be expressed in terms of the Positive predictive value (PPV) and Negative predictive value (NPV):[1] It is also related to the likelihood ratios,

[4] Traditional meta-analytic techniques such as inverse-variance weighting can be used to combine log diagnostic odds ratios computed from a number of data sources to produce an overall diagnostic odds ratio for the test in question.

[citation needed] The log diagnostic odds ratio can also be used to study the trade-off between sensitivity and specificity[5][6] by expressing the log diagnostic odds ratio in terms of the logit of the true positive rate (sensitivity) and false positive rate (1 − specificity), and by additionally constructing a measure,

If b ≠ 0 then there is a trend in diagnostic performance with threshold beyond the simple trade-off of sensitivity and specificity.

The typical response to such a scenario is to add 0.5 to all cells in the contingency table,[1][7] although this should not be seen as a correction as it introduces a bias to results.