Application of Conclusions - Diagnostic

The sensitivity and specificity pair is used to express the strength of a diagnostic study.

Corresponding confidence intervals around sensitivity and specificity give us an idea of how ‘close to the truth’ these estimates lie. However, given the result of a diagnostic test (positive or negative) neither the sensitivity nor specificity data can tell us how likely it is that the patient in question has or does not have the disease in question.

To make the transition from strength of a diagnostic test to likelihood of patient having disease we must introduce a new parameter: probability.

All clinicians work in terms of probability, some consciously, some unconsciously. Probability may be expressed numerically in the range 0-1. 0 means there is absolute certainty that the patient does not have the disease in question, whereas a probability of 1 indicates absolute certainty the patient does not. Absolute certainty is not always reached in clinical medicine. So clinicians work in terms of probability thresholds. An action threshold is a level of probability above which the clinician is happy to treat the patient for the disease in question, whereas an exclusion threshold is a level of probability below which that disease is disregarded by the clinician. In between these thresholds is a grey area.

It is our job as radiologists to use imaging to move the probability assessment above the action threshold or below the exclusion threshold.

In terms of radiology only two probability measures are important:

1/ Pre-test probability:
This is the clinician’s estimate of the patient probability of having disease given all available data. If this is above or below the clinician’s action or exclusion thresholds then no further diagnostic work is necessary. Conversely if it is between these thresholds we need to identify a diagnostic test the result of which will move the probability estimate above or below the thresholds.

2/ Post-test Probability:
Post-test probability is simply pre-test probability updated by additional information: the test result. This is the clinician’s bottom line – what does this test result mean to my patient?

So to apply the result of a diagnostic test to a patient we have to make the transition between sensitivity and specificity to disease probability.

This is achieved using ‘Bayes Theorem’. This mathematically combines patient data (pre test probability) and the strength of the test being used (sensitivity and specificity) to yield post-test probability:

While the equation looks difficult it is important to note that there are only 3 variables in the equation: sensitivity, specificity and pre-test probability. Therefore pre test probability (clinical information) is as important as strength of the diagnostic test in determining the test result.

From the analysis of strength section of this tutorial we have determined the sensitivity and specificity of the diagnostic test in question. We can now proceed to apply this test to a specific scenario – an individual patient. Rather than use this equation we can construct ‘graphs of conditional probability’ to determine post-test probability.

An example of a graph of conditional probability is presented below:
Pre-test probability is on the X-axis
Post-test probability is read from the Y-axis.
The two plots (blue and pink) represent positive and negative test results respectively.

In this scenario the test is weak.

Consider a situation where the clinician is very uncertain regarding the patients disease status: let’s say pretest probability is 50% or 0.5. From the above graph if the test result is negative post-test probability is 38% (0.38), whereas if the result is positive the post-test probability is 62% (or 0.62). In either situation we have not provided much of a service to the patient in our test selection. Regardless of the result we have not moved the probability of disease above a treatment or below an exclusion threshold. The weaker the test is, the more important the pre-test probability becomes during interpretation.

Consider the graph below, which represents a different diagnostic test. In this case a positive test result gives a post-test probability of 95% (0.95), whereas a negative test result gives a post-test probability of 5% (0.05). Both results have therefore changed a very uncertain clinical situation into one that is essentially definitive in determining the presence or absence of disease. This is a strong diagnostic test.

The stronger the test is, the less important the pre-test probability becomes during interpretation.

If you would like to link to a journal article illustrating the use of these concepts in practice, click here