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Sensitivity, Specificity, Predictive Values: a review
Here is a quick review of the concepts, then their mathematical derivations, from which the discussion of MDQ predictive values derives.
General Relationships
Here are the general relationships between the concepts. If this is not familiar, you'll want a review, by example.
Gold standard positive |
Gold standard negative | Using the test result: | |||
Test result positive | True Positives | False Positives | Positive Predictive Value: true positive as % of all positive results | Post-test probability given a positive test is the PPV (versus the probability before the test) | |
Test result negative | False Negatives | True Negatives | Negative Predictive Value: true negative as % of all negative results | Post-test probability given a negative test is 100% minus the NPV | |
Sensitivity: test positives as % of all "real" positives |
Specificity: test negatives as % of all "real" negatives |
As mathematical ratios
Gold standard positive |
Gold standard negative | |||
Test positive | a | b | Positive Predictive Value: a/a+b | |
Test negative | c | d | Negative Predictive Value: d/c+d | |
Sensitivity: a/a+c | Specificity: d/b+d |
Examples at difference prevalences
Scenario
A: 100 true positives in 1000 patients |
sensitivity: 0.73 |
||
gold standard positive | gold standard negative | predictive value | |
test positive | 73 | 90 | 0.45 |
test negative | 27 | 810 | 0.97 |
sum | 100 | 900 | |
Scenario
B: 400 true positives in 1000 patients |
sensitivity: 0.73 |
||
gold standard positive | gold standard negative | predictive value | |
test positive | 292 | 60 | 0.83 |
test negative | 108 | 540 | 0.83 |
sum | 400 | 600 |
Predictive values obviously change as the prevalence changes. Repeating the above analyses at varying prevalences yields the following graph: