SeriesRefining clinical diagnosis with likelihood ratios
Section snippets
Likelihood ratios for tests with two outcomes
The simple 2×2 table in the lower panel of figure 1 shows the calculation for the likelihood ratio. In this example, 15 people are sick and 12 (80%) have a true-positive test for the disease. By contrast, 85 are well but five (6%) have a false-positive test. Thus, the likelihood ratio for a positive test is simply the ratio of these two percentages (80%/6%), which is 13. Stated in another way, people with the disease are 13 times more likely to have a positive test than are those who are well.
Why bother?
Since most doctors are already familiar with terms like sensitivity and specificity,2 is learning to use likelihood ratios worth the additional effort? Likelihood ratios have several attractive features that the traditional indices of test validity do not share.4
First, not all tests have dichotomous results. Formulae for test validity do not work when results are anything other than just positive or negative. Many tests in clinical medicine have continuous results (eg, blood pressure) or
Putting likelihood ratios to work
Tests are not undertaken in a vacuum; a clinician always has an estimate (although usually not explicitly quantified) of the probability of a given disease before doing any test. According to Bayesian principles, the pretest odds of disease multiplied by the likelihood ratio gives the post-test odds of disease. For example, a pretest odds of 3/1 multiplied by a likelihood ratio of 2 would yield a post-test odds of 6/1. Unlike gamblers (or statisticians), most clinicians do not think in terms of
Size matters
Likelihood ratios of different sizes have different clinical implications. Clinicians intuitively understand that a likelihood ratio of 1·0 is unhelpful: the percentage of sick and well people with the test result is the same. The result does not discriminate between illness and health and the pretest probability is unchanged despite the inconvenience and cost (and perhaps risk) of the test.
As with all ratios, likelihood ratios start at unity and extend down to zero and up to infinity. Hence,
Likelihood ratios for tests with multiple outcomes
Calculation of likelihood ratios for tests with more than two outcomes is similar to the calculation for dichotomous outcomes; a separate likelihood ratio is simply calculated for every level of test result. In table 1, white-blood-cell counts are shown for 59 patients with appendicitis and 145 without the diagnosis. To calculate the likelihood ratio for a count of 7×109 cells per L, 2% is the numerator (those with appendicitis) and 21% the denominator (those without appendicitis); the
A useful mnemonic
Regrettably, nomograms and computers are usually not available at the bedside. Hence, a mnemonic suggested by McGee for simplifying the use of likelihood ratios has strong appeal.21 He notes that for pretest probabilities between 10% and 90% (the usual situation), the change in probability from a test or clinical finding is approximated by a constant. The clinician needs to remember only three benchmark likelihood ratios: 2, 5, and 10 (table 3). These correspond to the first three multiples of
The importance of accurate pretest probability
The medical history and physical examination remain fundamentally important. Indeed, a precise assessment of the chance of disease can be far more important than the likelihood ratios stemming from expensive, sometimes invasive tests.22 For some diseases, such as Alzheimer's dementia and sinusitis, clinical findings yield a highly accurate diagnosis. For other diseases, clinicians lack information about the predictive value of signs and symptoms; here they must rely on epidemiological data,
Diagnostic thresholds
Tests should only be used when they will affect management. If a clinician's pretest probability of disease securely rules in or out a diagnosis, further testing is unwarranted. More testing should be considered only in the murky middle zone of clinical uncertainty (figure 3). The location of these decision thresholds23 (A and B) along the continuum of diagnostic certainty needs to be determined before testing is done. Probabilities lower than point A effectively exclude the diagnosis in
Limitations of likelihood ratios
The effect of likelihood ratios on pretest probabilities is not linear. A likelihood ratio of 100 does not increase the pretest probability ten times more than does a ratio of 10, as figure 2, D shows.
For tests with several categories of results, extreme test values yield imprecise likelihood ratios. Few patients having values that are either very high or low result in little precision. Small changes in the numbers of patients in these cells can produce very different likelihood ratios. Stated
Uses for likelihood ratios
Likelihood ratios have a broad array of clinical applications, including symptoms, physical examinations, laboratory tests, imaging procedures, and scoring systems (table 4). Several resources have compiled reported likelihood ratios, including a handbook24 that contains more than 140. Another publication includes ratios for both diagnostic tests and clinical findings.22 Building on an accurate pretest probability of disease, likelihood ratios from ancillary tests can refine clinical
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Diagnostic tests
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