## Introduction to Likelihood Ratios

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Before you read this section, you should understand the
concepts of sensitivity, specificity, pretest probability,
predicitive value of a positive test, and predictive value of a
negative test. You should be comfortable working the problems on
the 2 by 2 table practice page.

Likelihood ratios are an alternate method of assessing the
performance of a diagnostic test. As with sensitivity and
specificity, two measures are needed to describe a dichotomous
test (one with only two possible results). These two measures are
the *likelihood ratio of a positive test* and the *likelihood
ratio of a negative test*.

Before defining these terms, it might help to list a few
advantages of learning and using the likelihood ratio method.
After all, if you already know how to compute posttest
probability using sensitivity and specificity, why bother with
likelihood ratios?

### Advantages of the likelihood ratio
approach

- The likelihood ratio form of Bayes Theorem is easy to
remember:
**Posttest Odds = Pretest Odds x LR.**
- Likelihood ratios can deal with tests with more than two
possible results (not just normal/abnormal).
- The magnitude of the likelihood ratio give intuitive
meaning as to how strongly a given test result will raise
(rule-in) or lower (rule-out) the likelihood of disease.
- Computing posttest odds after a series of diagnostic
tests is much easier than using the
sensitivity/specificity method.
**Posttest Odds =
Pretest Odds x LR**_{1}** x LR**_{2}**
x LR**_{3}** ... x LR**_{n}**.**

The likelihood ratio is a ratio of two probabilities:

**LR = The probability of a given test result among people
with a disease divided by the probability of that test result
among people without the disease.**

In probability notation: **LR = P(T**_{i}**|D**^{+}**)
/ P(T**_{i}**|D**^{-}**)**.

Don't worry if this does not make much sense yet. The next two
sections will apply likelihood ratios using both simple and more
complex examples. Their meaning and utility should become more
apparent then.