With increasing frequency, likelihood ratios are replacing sensitivity and specificity for measuring the accuracy of diagnostic tests. The ratios can help clinicians interpret published data, and provide better and improved diagnoses in their own practice.
Most often, the dilemma facing a clinician is whether to rule in or rule out further testing based on a diagnosis. The dilemma occurs when the probability of disease is not low enough to exclude testing, yet not high enough to suggest treatment.
Ideally, the probability of the disease should be below the testing threshold or above the treatment threshold. In the first instance, the probability is too low to warrant potentially dangerous testing. And in the second instance, the probability is sufficiently high to justify treatment, so testing does not add any value.
Good and bad tests
It follows that a good test is one that results in a probability that is either above the treatment threshold or below the test threshold. And a bad test is one in which the probability continues to be between the two thresholds, noted Dr. Madhukar Pai, doctoral candidate from the division of epidemiology at University of California, Berkeley, in a presentation at the Clinical UltraSonography in Practice (CUSP) conference in Chennai.
A good test is one in which the post-test probability is high even when the pretest probability is low -- or vice-versa, when the post-test probability is low even when the pretest probability is high. The pretest probability is the index of suspicion, or the likelihood of the disease before the test is done; the post-test probability is the likelihood of the disease after the test is done.
This is where likelihood ratios help, according to Pai. A test with a high likelihood ratio can put the probability above the treatment threshold, and a test with a low likelihood ratio can drive it below the test threshold.
Arriving at the likelihood ratio
"The sensitivity and specificity are what most of us are familiar with. We could stop here and not proceed further, but the problem is, in real life you don’t have the luxury of having the gold-standard results," Pai said of the importance of likelihood ratios in interpreting diagnostic data.
The likelihood ratio is the ratio of two likelihoods or probabilities. To arrive at the likelihood ratio of a positive test (LR+), the true positive rate is divided by the false-positive rate. In other words, LR+ is the ratio of the probability of a positive test when the disease is actually present to the probability of a positive test when the disease is absent.
To arrive at the likelihood ratio of a negative test (LR-), the false-negative rate is divided by the true-negative rate. In other words, LR- is the ratio of the probability of a negative test when the disease is actually present to the probability of a negative test when the disease absent.
So if the LR+ is 10, it implies that people with the disease are 10 times more likely to test positive than people without the disease. The gold standard is what is used to determine the actual presence or absence of the disease.
Application of likelihood ratio
Consider a study published in the New England Journal of Medicine on the accuracy of nuchal fold thickness in detecting Down syndrome in the second trimester. Down syndrome was confirmed in 28 fetuses by karyotyping, the gold standard (NEJM, November 1987, Vol. 317:22, pp. 1371-1376).
Twenty-one fetuses showed abnormal nuchal fold thickness. So the sensitivity of the test is 75% (21/28). Of the 192 normal fetuses, 188 were negative or had normal nuchal fold thickness. So the specificity of the test is 98% (188/192).
In this case, the true-positive rate is 75% (21/28) and the false-positive rate is 2.08% (4/192). The LR+ is therefore 36. Similarly, LR- can be calculated from the false-negative rate and true-negative rate as 0.26.
These likelihood ratios from the published data can be applied in clinical practice. In his talk, Pai used the example of a 37-year-old woman with a history of a Down syndrome baby to illustrate the utility of likelihood ratios.
The pretest probability of the patient is calculated taking the history, maternal age, biochemistry, and all evidence that is available up to the point of doing the test. The post-test probability is either mathematically calculated or computed using a nomogram from the pretest probability and the LR.
Nomogram
The nomogram simplifies the calculation of the post-test probability. Otherwise, the calculation requires finding the post-test odds by multiplying the pretest odds with the LR, then converting the odds back into the probability scale.
The nomogram consists of three vertical axes parallel to each other. The first is the pretest probability axis, followed by the axis for the LR and the post-test probability axis.
If the patient has a 10% pretest probability for Down syndrome and the test for nuchal fold test thickness is positive, the pencil or the ruler is fixed at 10% on the pretest probability axis and intersected at 36 on the likelihood ratio axis of the nomogram. The post-test probability is then read off at the point the pencil intersects the third axis or the post-test probability axis.
In this example, the resulting post-test probability is 80%, which rules in Down syndrome. So the patient can opt for invasive testing and intervention.
However, if the nuchal fold thickness test is negative, the post-test probability drops to 3%. The post-test probability is read off from the nomogram as before. In this case, the pencil is placed at 10% on the pretest probability axis, intersected at 0.26 on the LR axis, and the post-test probability read off at the point it meets the third axis or the post-test probability axis.
In this instance, there is a 97% probability of the baby being healthy.
Estimates from published literature offer good examples for use in routine clinical practice, Pai concluded. And likelihood ratios are useful tools for estimating accuracy.
By N. Shivapriya
AuntMinnieIndia.com staff writer
October 13, 2004
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