# Likelihood ratios (2xk table)

## Description

Allows to calculate likelihood ratios for different test levels from a 2xk table.

When test results have a continuous or ordinal outcome then valuable information is lost when the data are dichotomized for the calculation of sensitivity, specificity and likelihood ratios as in ROC curve analysis.

**Interval likelihood ratios** may be more powerful because they use more information contained in the data.

The likelihood ratio can be used to calculate the post-test probability of disease from the pre-test probability of disease (see below).

## Required input

First, select the number of different test levels.

Next, enter the number of cases in the diseased group that test positive and negative at the different test levels.

## Results

For each test levels the program calculates corresponding Likelihood ratio with 95% Confidence interval.

Confidence intervals for the likelihood ratios are calculated using the "Log method" as given on page 109 of Altman et al. 2000.

The likelihood ratio can be used to calculate the post-test odds from the pre-test odds of disease:

The relation between odds and probability is:

Using these equations, you can calculate the post-test probability of disease from the pre-test probability of disease.

If, for example, the pre-test probability of disease is 0.6 then the pre-test odds is 0.6/(1-0.6) = 1.5. For a case with a test result corresponding with diagnostic level 2, the likelihood ratio is 12, and the post-test odds is 1.5 x 12 = 18. The post-test probability of disease is 18/(1+18) = 0.95.

## Literature

- Altman DG, Machin D, Bryant TN, Gardner MJ (Eds) (2000) Statistics with confidence, 2
^{nd}ed. BMJ Books. - Gardner IA, Greiner M (2006) Receiver-operating characteristic curves and likelihood ratios: improvements over traditional methods for the evaluation and application of veterinary clinical pathology tests. Veterinary Clinical Pathology, 35:8-17.