Sensitivity, Specificity and Likelihood Ratios

 

Sensitivity:

The probability that a test will produce a True Positive result when used on a population with the disease.  Tests with high sensitivity are good screening tests; a negative test result can help RULE OUT disease.

Sensitivity = TP / TP + FN  or  True Positives / total # with disease

 

Specificity:

The probability that a test result will produce a True Negative result when used on a population without the disease.  Tests with high specificity are good confirmatory tests; a positive test result can help RULE IN disease.

Specificity = TN / TN + FP  or  True Negatives /  total # without disease

 

Positive Predicted Value:

The probability that someone has a disease given a positive test result

PPV = TP/ TP+FP   or   True Positives / All who tested positive

 

Negative Predicted Value:

The probability that someone does NOT have a disease given a negative test result

NPV = TN / TN + FN or   True Negatives / All who tested negative

 

Prevalence:

Varies directly with PPV and inversely with NPV.  In other words, as the prevalence increases, the PPV increases.  As the prevalence increases the NPV decreases.

 

2 X 2 Table:

Short Cuts:

Sensitivity = use left column: TP / TP + FN

Specificity = use right column: TN/ TN + FP

PPV = use top row: TP / TP + FP

NPV = use bottom row: TN / TN + FN

 

Negative Likelihood Ratio (LR-):

How much the odds of the disease decrease when a test is negative.

LR- = (1-Sensitivity) / Specificity 

 

Positive Llikelihood Ratio (LR+):

How much the odds of the disease increase when a test is positive.

LR+= Sensitivity / (1-Specificity) 

 

How to apply LR using the Fagan nomogram:

The Fagan nomogram is a graphical tool for estimating how much the result on a diagnostic test changes the probability that a patient has a disease. 

To use this tool, you need to provide your best estimate of the probability of the disease prior to testing. This is usually related to the prevalence of the disease, though this may be modified up or down on the basis of certain risk factors that are present in your patient pool or possibly in this particular patient. You also need to know the likelihood ratio for the diagnostic test.

With this information, draw a line connecting the pre-test probability and the likelihood ratio. Extend this line until it intersects with the post-test probability. The point of intersection is the new estimate of the probability that your patient has this disease.