Utilizing the results of DTA studies

Clinical questions regarding the diagnosis of disease is a challenge in the era of EBM because of the challenge to understand and apply the results of DTA studies.

Currently, The Likelihood Ratio (LR) is used to assess how good a diagnostic test is and to help in selecting an appropriate diagnostic test(s) or sequence of tests in order to rule in or rule out a disease.

LR for a positive test equals sensitivity / (1-specificity). The LR for a negative test equals (1-sensitivity) / specificity. A LR greater than 1 produces a post-test probability which is higher than the pre-test probability. An LR less than 1 produces a post-test probability which is lower than the pre-test probability.

LR has definite advantages over sensitivity and specificity because it is easy to understand and apply, is less likely to change with the prevalence of the disorder, and most importantly can be used to calculate post-test probability for a target disorder.

Working example: DTA of serum ferritin for iron deficiency anemia:

Sensitivity = 731/809 = 90 per cent
Specificity = 1500/1770 = 85 per cent
LR+ = sens / (1-spec) = 90/15 = 6
LR- = (1-sens) / (spec) = 10/85 = 0.12
Prevalence = 809/2579 = 31 per cent

Pre-test odds = pre-test probability / (1-pre-test probability)

i.e. Pre-test odds = prevalence / (1-prevalence) = 31/69 = 0.46

Post-test odds = pre-test odds * LR
Post-test Probability = post-test odds / (post-test odds + 1)

Post-test odds = pre-test odds * LR = 0.46*0.12 = 0.06
Post-test probability = post-test odds / (post-test odds + 1) = 0.06 / (0.06 + 1) = 5 per cent

After the serum ferritin test is done and your patient is found to have a normal level, the post-test probability of your patient having iron deficiency anemia is therefore reduced to 5 per cent.

Now you can calculate the Post-test probability if the test is positive.