#### PE likelihood

Once a clinical suspicion of PE has been raised, the Wells score is a pre-test probability stratifying tool intended to help judge when and what clinical tests are needed to further clarify the patient's condition (note its not validated in pregnancy, cancer, after >2 doses of anticoagulation - in these cases the best clinical probability estimate is from clinical gestalt). After having a test, a post-test probability is quantifies the likelihood of having the condition given the new information that the result of test tells us.

We regard the CTPA as the gold standard test for confirming PE, but it should be noted it is not always correct in the information it gives. According to a study conducted on 7,248 patients with suspected PE, the CTPA showed a sensitivity and specificity of 83% and 96% respectively(1). Equally, in low risk patients (ie those with a low pre-test probability), we regard a negative D-dimer as a reliable rule-out tool, but how true is this? D-dimer assays used at RCHT laboratory have a manufacturer's published sensitivity of 100% and specificity of 48.3%(2).

A likelihood ratio is a way of applying these sensitivity/specificity measures to the patient in front of us. Through the likelihood ratio (LR) of a test, we can have an insight into what a positive or negative result means to our patient. Having in mind the sensitivity and specificity of CTPA, the likelihood ratio of a positive result (LR+) will be 20.75 (LR+ = 0.83/1-0.96) and LR- 0.17 (LR- = 1-0.83/0.96). Equally, the D-dimer LR+ will be 1.92 and the LR- will be 0.02.

These relatively abstract concepts can be represented in a nomogram, which we can use to rapidly calculate a post-test probability. A blank version for your own use with D-dimer and CTPA are available if you click the test in this sentence.

An example using the nomogram is:

A 64-year-old female attends complaining about chest pain, problems with breathing and coughing blood. After a history and examination, the clinician suspects an acute PE. Therefore, to determine the diagnostic approach the Wells’ Score is calculated. The results of the score are 6.5 because the patient had a heart rate of 112bpm, had haemoptysis, signs of a DVT and she mentions that she has been undergoing therapy for colorectal cancer for the past 2 months.

This score correlates with a risk of this patient having PE of around 40%. According to the score this is a high risk patient, so the recommended diagnostic test is oriented to confirm the suspected PE (ie a CTPA) rather than a rule out approach (D-dimer).

After the result of the CTPA is available, we can read off the post-test probability, which for the example is around 93% if the CTPA is positive and between 5 and 10% if it is negative.

What does this mean in the real world?

In reality, the above example is a little false - there's published discrepancy of the sensitivity and specificity of CTPAs, and these parameters are also likely to be dynamic concepts as they rely on image technicalities and the reporting radiologist. Therefore the definite point on the likelihood ratio axis is more accurately represented as a range (for instance the LR+ being 8.6-20 (2)). Due to the logarithmic scale, this can have huge effect on our post-test probability.

Still, the nomogram approach to PE interpretation can help with ascertaining just how certain (or uncertain!) we are that someone either has a PE or not. This can be an important step when discussing indication to treat and prognosis.