Post-test Probability

Post-test probability: is the probability of the presence of a disease after a confirmatory diagnostic test.

Method I:  Let us estimate post-test probability by hand calculation using the data from the study by Capra et al (1). To do this, we need to know the pre-test probability and the positive likelihood ratio values.

For this purpose, let us assume the pre-test probability as 0.55. And, we will use the likelihood ratio value from Capra et al (1) study.

The likelihood ratios are:
Likelihood ratios

Step I: Calculate pre-test odds from pre-test probability.

post-test probability - hand calculation step 1

Step II: Calculate post-test odds by multiplying pre-test odds and positive likelihood ratio.

post-test probability - hand calculation step 2

Step III: Calculate post-test probability from post-test odds.

post-test probability - hand calculation step 3

The post-test probability or the probability of having the disease after performing the diagnostic test is 62.65%.

Method II: Now, let us estimate post-test probability using Fagan’s nomogram for Bayes theorem (2). To do this, we need to know pre-test probability and positive likelihood ratio values. Let us use the same values as mentioned in the method above.

viz., pre-test probability = 0.55; positive likelihood ratio = 1.3752

The Fagan’s nomogram has three calibrated vertical lines (2). The vertical line on the right represents the pre-test probability. The line in the middle represents the positive likelihood ratio. The line on the left represents the post-test probability of having the disease.

Fagan's Nomogram

P(D) = the probability that the patient has the disease before the test,
P(D|T) = the probability that the patient has the disease after the test result.
P(T|D) = the probability of the test result if the patient has the disease,
P(T|D̄) = the probability of the test result if the patient does not have the disease.

Step I: Draw a straight line connecting the pre-test probability i.e., P(D) value, 0.55 or 55% and positive likelihood ratio i.e., [P(T|D) / P(T|D̄)] value, 1.3752.

Step II: Now, extend the line to intersect the calibrated vertical line on the left to determine the post-test probability, P(D|T).

We find that the straight line intersects the post-probability vertical line between 60% to 70%, approximately at 63% or 0.63. This value is very close to the actual value (0.6265) calculated by hand.


  1. Capra, F., Vanti, C., Donati, R., Tombetti, S., O’reilly, C. and Pillastrini, P., 2011. Validity of the straight-leg raise test for patients with sciatic pain with or without lumbar pain using magnetic resonance imaging results as a reference standard. Journal of manipulative and physiological therapeutics, 34(4), pp.231-238.
  2. Fagan TJ. Letter: nomogram for Bayes theorem. The New England journal of medicine. 1975;293(5):257.