Measures from Studies of Diagnostic Tests
When we order a diagnostic study, we are trying to gain information about the patient’s underlying probability of a disorder. That is, the diagnostic test moves us from a pre-test probability to a post-test probability. Historically, terms such as sensitivity and specificity have been used to describe the properties of a diagnostic test. But these terms have significant limitations, one of which is that they do not consider the pre-test probability at all.
Likelihood ratios overcome this limitation. Basically, a likelihood ratio (LR) converts pre-test odds to post-test odds. Because we think in terms of probabilities rather than odds, we can either use a nomogram to make the conversion for us or recall that for a probability p, odds = p/(1 – p) and p = odds/(1 + odds).
For example, suppose we suspect that a patient may have iron-deficiency anemia and quantify this suspicion with a pre-test probability of 25%. If the ferritin is 8 mcg/L, we can apply the likelihood ratio of 55 found from a literature search locating Guyatt, et al. (1992). The pre-test odds is one-third, which when multiplied by the LR of 55 yields a post-test odds of 18.3. This then can be converted back to a post-test probability of 95%. Alternatively, the widely available nomograms give the same result.
Clearly, this diagnostic test has drastically affected our sense of whether the patient has iron-deficiency anemia. Likelihood ratios for many common problems may be found in the recommended readings.
Perhaps the greatest stumbling block to the use of likelihood ratios is how to determine pre-test probabilities. This really should not be a major worry because it is our business to estimate probabilities of disease every time we see a patient. However, this estimation can be strengthened by using evidence-based principles to find literature to support your chosen pre-test probabilities. This further emphasizes that EBM affects all aspects of clinical decision-making.
Measures of Precision
Each of the measures discussed thus far is a point estimate of the true effect based on the study data. Because the true effect for all humans can never be known, we need some way of describing how precise our point estimates are. Statistically, confidence intervals (CIs) provide this information. An accurate definition of this measure of precision is not intuitive, but in practice the CI can provide answers to two key questions. First, does the CI cross the point of no effect (e.g., a relative risk of 1 or an absolute risk reduction of 0)? Second, how wide is the CI?
If the answer to the first question is yes, we cannot state with any certainty that there really is an effect of the treatment: a finding of “no effect” is considered plausible, because it is contained within the CI. If the CI is very wide, the true effect could be any value across a wide range of possibilities. This makes decision making problematic, unless the entire range of the CI represents a clinically important effect.