## Using likelihood ratios to analyze a series of tests

Patients often undergo a series of diagnostic tests during the course of an evaluation. Computing the probability of disease depending on the results of 5 diagnostic tests can be a tedious task using the sensitivity and specificity method. You must take the posttest probability calculated from test 1 and plug it into the pretest probability for test 2 and so on until all five test results have been included in the analysis.

### Example 4 - Exercise thallium scintigraphy

Consider a simple example with only two tests done in series. A patient with a low to moderate (20%) suspicion for coronary artery disease is exercised on the Bruce protocol and then undergoes thallium scintigraphy. First, consider the possible treadmill results in terms of the number of millimeters of ST segment depression:

 ST Depression Likelihood Ratio 2.5 or more 39 2-2.49 11 1-1.99 4.2 0.05-0.99 0.93 <0.05 0.23

Notice that as with the thyroxine example, there is a big difference between slightly positive (1mm=LR 4.2) and strongly positive (2.5mm=LR 39). It is not a good idea to lump all the positive results together when computing posttest probability.

If our patient with a 0.2 prior probability of coronary artery disease has 1.5mm ST segment depression, what is the posttest probability of disease? Use the calculator below to check your work.

Now, if the thallium scintigram shows a reversible perfusion defect (LR=11.8), what is the probability of coronary artery disease taking both parts of the test into acount? Insert the posttest probability after the treadmill part above into the pretest probability below.

An even easier approach is just to multiply all the likelihood ratios for the variuos test results together and just treat them as the likelihood ratio for the series of tests. In our case, LRtotal = 4.2 x 11.8 = 49.56. Check that this calculation below gives the same result as the two-stage calculation above.

Thus, evaluating a series of tests takes hardly more effort than evaluating a single test.

In summary, likelihood ratios can be used to compute posttest probability of disease. They are more useful than sensitivity and specificity in that they can be used for diagnostic tests with more than two results, they can more easily be applied to a series of diagnostic tests, their values convey intuitive meaning and the likelihood ratio form of Bayes theorem is easier to remember.