Interval Likelihood Ratios and the Diagnostic Process.

Abstract

In this issue of Pediatrics, Liang et al1 apply the concept of interval likelihood ratios (ILRs) to the diagnosis of urinary tract infections (UTIs) in children under the age of 2 years. The authors conducted a cross-sectional study of a cohort of children <2 years of age who had a urine culture and urine analysis (UA) simultaneously obtained from their emergency department. Their analysis, in contrast to most previous reports, derives ILRs for the scaled results of the UA relative to the diagnosis of UTIs.Most readers will be familiar with the terms sensitivity and specificity. ILRs are closely related to sensitivity and specificity but have at least 2 advantages. First, a separate ILR can be derived for each value of a test result when there can be more than just positive or negative results. For example, a urine dipslide can quantify the presence of leukocyte esterase (LE) as trace, 1+, 2+, or 3+. Liang et al1 showed 3+ LE increases the probability a child has a UTI compared with an LE of 1+ or 2+. This result may not be surprising, but by describing the relationship between LE and UTIs in ILR terms, the diagnostician can better refine her estimate of the probability of UTI, adjusting the probability more for 3+ LE than for 1+ LE.2A second advantage of ILR is that the diagnostician can use relatively simple arithmetic to estimate the probability of a diagnosis (eg, UTI) given a laboratory result (eg, 3+ LE). Starting with a previous probability of disease, she converts this to the odds of disease (probability/1 − probability) and multiplies it by the appropriate ILR (eg, 38 for 3+ LE) to generate the posterior odds. She can then convert the posterior odds back to a probability (probability = posterior odds/[1 + odds]). If the pretest probability of UTI is 5%,3 the odds are 0.05/(1 − 0.05) or (rounding) 0.05. Next, 0.05 × 38 is ∼2 (I rounded the ILR to 40). Finally, the posttest probability is 2/(2 + 1) or 0.67. With a little rounding (and practice), this calculation is easily done in your head.Of course, the probability estimate resulting from this calculation depends on the probability you start with. Liang et al1 found a pretest probability of UTI of 9.2%, which is somewhat higher than that in other large studies of UTI risk in febrile infants,3 probably as a result of some selection bias. That is why the posttest probability reported by Liang et al1 after a 3+ LE is 79%, not 67%. However, ILRs are relatively resistant to selection bias. For this reason, it behooves the diagnostician to know how to apply ILRs to her own estimates of pretest probability to calculate a posttest probability.It is tempting to take this posttest probability of UTI and apply another ILR because, after all, the UA gives us many results. For example, if microscopy showed there were many bacteria in the urine, we might take the posttest odds (2) after the LE and apply the ILR for many bacteria (14), generating a new posttest odds of 28. The corresponding probability would be 28 of 29 or over 96%! This approach of multiplying all of the applicable ILR together by the pretest odds is a technique called sequential Bayes’, and it has been used in computer-based diagnostic systems for decades.4 But the approach is fraught with risk because it assumes the ILRs are independent of one another, given the presence of UTI. We know this cannot always be true. Surely, the probability of seeing white cells on microscopy is not independent of the likelihood of seeing LE on a dipslide.Accommodating these interdependencies among ILRs requires more sophisticated statistical modeling, measuring the associations among different tests, and calculating the diagnostic value of different combinations of results.5 Liang et al1 have not conducted these analyses, but truthfully, these approaches generally require larger sample sizes than were available in this study (198 cases of UTI).Nonetheless, Liang et al1 have taken a step toward helping us be more quantitative in our diagnostic reasoning. This is one important strategy to reduce diagnostic errors, which represent “a major public health problem likely to affect every one of us at least once in our lifetime, sometimes with devastating consequences.”6 If we can learn to apply basic quantitative diagnostic tools like ILR to our medical practice, we are likely to reduce important causes of diagnostic errors (faulty data collection or interpretation, flawed reasoning, or incomplete knowledge) and their downstream impact on our patients.7