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Likelihood Ratio Calculator

Formula

The formula to calculate Likelihood Ratio is:

Positive Likelihood Ratio (LR+):

$LR+ = \frac{SE}{100 - SP}$

Negative Likelihood Ratio (LR-):

$LR- = \frac{100 - SE}{SP}$

Where:

$LR$ is the Likelihood Ratio
$SE$ is the Sensitivity
$SP$ is the Specificity

Likelihood Ratio Definition

A likelihood ratio is defined as the probability that a patient has a disease given the result of a test. The positive likelihood ratio (LR+) tells you how much to increase the probability of having a disease given a positive test result, while the negative likelihood ratio (LR-) tells you how much to decrease the probability given a negative test result.

Example Calculation

Let's consider an example:

Sensitivity (SE): 90%
Specificity (SP): 80%

Using the formula to calculate Likelihood Ratios:

Positive Likelihood Ratio (LR+):

$LR+ = \frac{90}{100 - 80} = 4.5$

Negative Likelihood Ratio (LR-):

$LR- = \frac{100 - 90}{80} = 0.125$

This demonstrates that with a sensitivity of 90% and a specificity of 80%, the positive likelihood ratio would be 4.5 and the negative likelihood ratio would be 0.125.