Likelihood ratios; Pre and post test probability
Diagnosis and Screening: Likelihood ratios; pre and post test probability
What is a likelihood ratio?
The likelihood ratio provides a direct estimate of how much a test result will change the odds of having a disease, and incorporates both the sensitivity and specificity of the test.
The likelihood ratio for a positive result (LR+) tells you how much the odds of the disease increase when a test is positive.
The likelihood ratio of a positive test result (LR+) is sensitivity divided by (1 specificity)

The likelihood ratio for a negative result (LR) tells you how much the odds of the disease decrease when a test is negative.

*Note that the calculation of likelihood ratios is currently not tested as a skill in the UK MFPH Part A examination.
Interpretation of Likelihood Ratios
The further away a likelihood ratio (LR) is from 1, the stronger the evidence for the presence or absence of disease.

LR >1 indicates that the test result is associated with the presence of the disease.

LR <0.1 indicates that the test result is associated with the absence of disease.
Pretest probability (~ prevalence)
This is the proportion of people in the population at risk who have the disease at a specific time or time interval, i.e. the point prevalence or the period prevalence of the disease. In other words, it is the probability −before the diagnostic test is performed − that a patient has the disease. Pretest probabilities may be estimated from routine data, practice data or clinical judgement.
Posttest probability
This is the proportion of patients testing positive who truly have the disease. It is similar to the positive predictive value but apart from the test performance also includes a patient based probability of having disease
Posttest probability =  Posttest odds  
(1 + Posttest odds) 
Using Pre and Posttest probability and LR
By comparing the pre and posttest probabilities, it is possible to determine whether probability of diagnosis has risen (i.e. the posttest probability has increased) or fallen (i.e. posttest probability has decreased). In this way, it is possible to provide comprehensive information about a screening test in order to enable informed choice. In practice assessing posttest probability is commonly done by using a Likelihood Ratio Nomogram (below)
Summary of calculations of key features of screening tests

© Dr Murad Ruf and Dr Oliver Morgan 2008