Sensitivity and specificity are usefully combined in likelihood ratios. The likelihood ratio of a positive test result (LR^{+}) is the ratio of the probability of a positive test result if the outcome is positive (true positive) to the probability of a positive test result if the outcome is negative (false positive). It can be expressed as follows:

LR^{+} represents the increase in odds favouring the outcome given a positive test result. For the data in Table 1, LR^{+} is 0.64/(1 - 0.53) = 1.36. This indicates that a positive result is 1.36 times as likely for a patient who died as for one who survived.

The pre-test probability of a positive outcome is the prevalence of the outcome. The pre-test odds [1] can be used to calculate the post-test probability of outcome and are given by:

Applying Bayes' theorem [2], we have:

Post-test odds for the outcome given a positive test result = pre-test odds × LR^{+}

For the data given in Table 1, the prevalence of death = 126/1391 = 0.09 and the pre-test odds of death = 0.09/(1 - 0.09) = 0.099. Therefore:

Post-test odds of death given a positive test result = 0.099 × 1.36 = 0.135

For a simpler interpretation, these odds can be converted to a probability using the following:

For the data in Table 1 this gives a probability = 0.135/(1 + 0.135) = 0.12. This is the probability of death given a positive test result (i.e. the PPV).

Similarly, we can define LR^{-} as the ratio of the probability of a negative test result if the outcome is positive to the probability of a negative test result if the outcome is negative. It can be expressed as follows:

LR^{-} represents the increase in odds favouring the outcome given a negative test result. For the data given in Table 1, LR^{-} is (1 - 0.64)/0.53 = 0.68. This indicates that a negative result is 0.68 times as likely for a patient who died as for one who survived. Applying Bayes' theorem, we have the following:

Post-test odds for the outcome given a negative test result = pre-test odds × LR^{-}

For the data in Table 1:

Post-test odds of death given a negative test result = 0.099 × 0.68 = 0.067

Converting these odds to a probability gives 0.067/(1 + 0.067) = 0.06. This is the probability of death given a negative test result (i.e. 1 - NPV). Therefore, NPV = 1 - 0.06 = 0.94, as shown above.

A high likelihood ratio for a positive result or a low likelihood ratio for a negative result (close to zero) indicates that a test is useful. As previously stated, a greater prevalence will raise the probability of a positive outcome given either a positive or a negative test result.