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Likelihood Ratio Versus Predictive Value :

June 5, 2018

One of the quandaries in interpreting medical research is how to use predictive values and likelihood ratios. This retrospective study of electrocardiogram findings in a group of children is highly illustrative.

One of the quandaries in interpreting medical research is how to use predictive values and likelihood ratios. This retrospective study of electrocardiogram findings in a group of children is highly illustrative.

Source: Schneider AE, Cannon BC, Johnson JN, et al. Left axis deviation in children without previously known heart disease. Pediatrics. 2018;141(3):e20171970; doi:10.1542/peds.2017-1970. See AAP Grand Rounds commentary by Dr. David Spar (subscription required).

Researchers at a single institution (Mayo Clinic) reviewed medical records of all children without known heart disease from 1 to 18 years of age who had ECG evidence of left axis deviation (LAD) over a 13 year period. They found that LAD findings on ECG were more likely to be clinically significant in children who had either a high degree of LAD (defined as less than negative 42 degrees axis on ECG), ECG evidence of chamber enlargement or hypertrophy, or abnormal cardiac physical exam. In general, the greater the number of the 3 features that were present, the greater the likelihood that the LAD was clinically important. They acknowledged some study limitations that are expected with retrospective studies, most prominently here the fact that only about half of the children had echocardiograms performed. Given that clinicians decided on ordering an echocardiogram, this could result in significant bias since it is likely the children with echocardiogram performed had a greater likelihood of significant disease. If this Mayo Clinic population consisted primarily of children referred by another provider, they could represent a more severe end of the disease spectrum, i.e. spectrum basis. Also, the researchers did not investigate the indication for the ECG in all cases, but the subset where this was illuminated had a variety of indications including clinical illness such as dyspnea or stroke.

However, I'm most interested in their use of predictive values to support their conclusion that children with LAD and at least 1 of the 3 factors above should be considered for an echocardiogram. Here's why.

The authors supplied us with sensitivities, specificities, and predictive values for heart disease based on the number of variables present: for no variables present, the positive predictive value (PPV) was 32% and the negative predictive value was 98%. For 1 variable, PPV was 18% and NPV 86%, while the values were 64% and 88% for 2 variables and 86% and 88% for all 3 present. What's wrong with that?

The problem with predictive values is that they will vary with the frequency of the disease in the patient population being studied. In this study, that means we're talking about children referred to Mayo Clinic for evaluation. That can be a very different population from children presenting to a primary care provider, or even from children presenting to a pediatric cardiology practice at a tertiary medical center. On the other hand, likelihood ratios (LR) do not depend on the frequency of the disease in the population, although they can be affected by spectrum bias to some extent.

It's quite easy to calculate LRs from the data the authors provided. For zero variables present, the LR for a positive test (LR+) is 2.63 and for a negative test (LR-) is 0.12. The corresponding values for 1, 2, and 3 variables present are 1.23 and 0.9, 9.67 and 0.73, and 25 and 0.76.

The path of least resistance is to look at predictive values because the numbers are in percentages that make inherent sense. LRs, on the other hand, provide us with no intuitive meaning for the numbers, except for individuals accustomed to using LRs. For example, an LR+ of 9.67 doesn't mean 9 times as likely, or 9%, or anything directly linked to the number 9 at all. Instead, LRs allow us to determine the post-test probability of the disease being present, assuming we know the pre-test probability. In this study, the overall rate of heart disease in the population was about 15%. An LR equal to 1 represents a test that has no role in diagnosing a particular condition. (Note that this is what the study found in children with just 1 risk variable present, more on that later.) The higher an LR+, the greater the post-test probability, so that the 9.67 number when calculated out results in moving the pre-test probability from 15% to a post-test probability of 63%. Whether or not that is important is a matter of individual debate. If you feel that the 15% rate is already high enough to order an echocardiogram on your patient, then it doesn't matter that the post-test probability is 63% or 18% (which happens to be the post-test probability if just 1 variable is present). I'd argue that 15% is pretty high, and I wouldn't want to miss serious heart disease, so I'd order an echocardiogram regardless.

To get at the other side of this, how low would be post-test probability need to be such that I wouldn't order an echocardiogram? Here's where the LR- becomes useful, and the only LR- in this study that results in any appreciable change is that associated with no variables present, where the post-test probability becomes 2%. Are you willing to accept missing 2% of the children and not order echocardiograms on all the children, regardless of the number of variables present? I'm not sure, but complicating the decision is that, in this study, only about half the children had echocardiograms performed, based on the judgment of their clinician. Presumably, all who had concerning symptoms received an echocardiogram, leaving the more asymptomatic of the group not represented in the study data.

One final point. The abstract concludes that "Clinicians should consider obtaining an echocardiogram in patients with LAD and ..." any of the 3 variables present. However, their data for just 1 variable present do not change post-test probability significantly, raising it from 15% to 18%. This is easily seen since the LR+ for 1 variable present is 1.23, pretty close to 1. I think their conclusion should have suggested echocardiogram for children with at least 2 variables present if they wanted to draw any conclusions from their data.

The information in the study is of interest but is of little utility without knowing echocardiogram information about the other half of the population. Mostly, though, I wish the investigators would make it a little easier on the reader by reporting and explaining LRs because predictive values can be seductively misleading.

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