The flu and likelihood ratios

An interesting study was just published in the Annals of Internal Medicine. It was a meta-analysis of rapid influenza diagnostic tests (RIDT) and their characteristics. Since we have been spending so much time talking about test characteristics, this study provides a nice opportunity to discuss another way of looking at the values of positive and negative tests. This is going to be a fairly short post, since I simply want to discuss these additional tools.

In the current study the investigators evaluated how well these RIDTs predicted the disease. As we have discussed in multiple places on this blog (here, here and here, to name a few), it matters whether the test is used for screening or diagnosis. In this case, the testing was done in symptomatic populations, so for diagnostic reasons. The authors report that there was quite a bit of heterogeneity in their findings, but the ultimate result is reported as a positive (34.5) and negative (0.38) likelihood ratios. What are they and how do we interpret them?

A positive likelihood ratio, or LR+ is the ratio between sensitivity and 1-specificity (LR+=[sensitivity]/[1-specificity]). Sensitivity is the proportion of patients with the disease who are identified as having the disease, or true positives (TP), and specificity is the proportion of persons without the disease who are identified as not having the disease, or true negatives (TN). The opposite of TN, 1-TN, is the false positives (FP). So, the LR+ equates to the TP/FP, or the odds that a positive indicates true disease. In the current study it is 34, meaning that the odds are 34 to 1 that a positive test indicates the presence of the disease. Another way of putting it is that of the 35 total positive test results, 34 (97.1%) represent true disease. This is essentially equivalent to the positive predictive value (PPV).

Now, let's examine the negative likelihood ratio, or LR-. This is defined as the ratio between the opposite of sensitivity (1-sensitivity) and specificity (LR-=[1-sensitivity]/specificity]). 1-sensitivity is the proportion that are false negative (FN), while the specificity is the proportion of persons without the disease who are identified as such. In the study this LR- was 0.38, meaning that the odds that a negative result truly indicates the absence of disease are about 1 to 2 (0.36:1), or not so great. In other words, out of the total of 3 negative tests, 2 are truly negative, while 1 is a false negative, giving us the negative predictive value (NPV) of about 65% (actually it is 1-0.36=0.64, or 64%).

So, there you have it. The clinical take-away, as the authors noted, is that these RIDTs are good at ruling in the flu, but not at ruling it out. In other words, the problem here is the opposite of what we discussed in all those previous test, or the rate of false negatives. And this makes sense, given that the pre-test probability is reasonably enriched in populations with symptoms, in addition to the relatively poor sensitivities of these technologies.