## Using likelihood ratios
to analyze a series of tests

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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, LR_{total}
= 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.

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