Signature
LR_pos = Se / (1 - Sp); LR_neg = (1 - Se) / Sp; DOR = LR_pos / LR_neg
| Inputs | Definition | Unit |
|---|---|---|
Se | Sensitivity of the index test at the threshold used | proportion |
Sp | Specificity of the index test at the same threshold | proportion |
LR_pos | Ratio of the probability of a positive result with the condition to that without it | ratio |
|---|---|---|
LR_neg | Ratio of the probability of a negative result with the condition to that without it | ratio |
DOR | Odds of a positive result with the condition divided by the odds without it | ratio |
Function
Diagnostic test accuracy measures and the expected value of test results
Maps the cross-classification of index test results against a reference standard to the measures of accuracy, conditional on disease status (sensitivity, specificity) or on the test result (predictive values), and combines accuracy with prevalence and the consequences of true and false results into the expected net monetary benefit of testing. The notation follows the Diagnostic Accuracy article and its two triage tests.
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Implementations
Excel
Likelihood ratios and diagnostic odds ratio from named sensitivity and specificity
With Sens and Spec named, the formulas return the positive and negative likelihood ratios and the diagnostic odds ratio, held in LRPos, LRNeg and DiagOR.
=Sens/(1-Spec); =(1-Sens)/Spec; =LRPos/LRNeg
Assumptions
Sensitivity and specificity from the same study and threshold for likelihood ratios
Both proportions come from one two-by-two table at one threshold, so the ratios describe one way of using the test.
No empty cells for finite likelihood ratios
LR_pos has no finite value when Sp is 1, LR_neg is undefined when Sp is 0, and DOR is 0 or has no finite value when any cell of the table is 0; the formulas need Se and Sp strictly above 0 and below 1.
Worked examples
Likelihood ratios of triage test A
With sensitivity 0.96 and specificity 0.76, LR_pos is 0.96 over 0.24, or 4.0, LR_neg is 0.04 over 0.76, about 0.0526, and the DOR is 76, as in the article. At 5 per cent prevalence the pre-test odds of about 0.0526 times 4 give post-test odds of about 0.2105, a post-test probability of 0.1739, the PPV of HE-FM-DXA-001.
Se = 0.96; Sp = 0.76; LR_pos = 4; LR_neg = 0.0526; DOR = 76
Likelihood ratios of triage test B
With sensitivity 0.80 and specificity 0.96, LR_pos is 20, LR_neg about 0.2083 and the DOR 96, as in the article.
Se = 0.8; Sp = 0.96; LR_pos = 20; LR_neg = 0.2083; DOR = 96
Common errors
Ranking tests by the diagnostic odds ratio
Test B's DOR of 96 beats test A's 76, yet test A gives more net monetary benefit at 5 per cent prevalence (HE-FM-DXA-005); the DOR reflects the product of false negatives and false positives, while a clinician is usually interested in their sum and a model in their separate consequences.
Pooling likelihood ratios separately across studies
Separate pooling ignores the correlation between the positive and negative ratios and can produce impossible estimates; likelihood ratios for a model are better derived from jointly pooled sensitivity and specificity.
Sources
Likelihood ratios and diagnostic odds ratio in the Cochrane DTA Handbook chapter 10
Macaskill P, Gatsonis C, Deeks JJ, Harbord RM, Takwoingi Y. Chapter 10: Analysing and presenting results. In: Deeks JJ, Bossuyt PM, Gatsonis C, editors. Cochrane Handbook for Systematic Reviews of Diagnostic Test Accuracy. Version 1.0. The Cochrane Collaboration; 2010. Section 10.2.3.3: likelihood ratios update the pre-test probability using Bayes' theorem; LR+ = sens/(1 minus spec), greater than 1 if the test is informative, and LR- = (1 minus sens)/spec, less than 1 if informative; section 10.2.3.4: DOR = LR+/LR-, estimated as (ad)/(bc), of little direct clinical relevance because the clinician is usually interested in the sum of false negatives and false positives whereas the DOR reflects their product; section 10.4.2: separate pooling of likelihood ratios can produce impossible estimates.
Canonical Identity
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