Comment: LIKELIHOOD RATIOS AND PREDICTIVE VALUES: likelihood ratios do not change with disease prevalence, but predictive values do. In this study, the patient population was 69, with 8 having skull fractures. The prevalence is 12% (8/69) and simply doing nothing would mean a specificity of 88%. Ultrasonography detected 7 out of 8 fractures (sensitivity of 88%) and correctly categorized 59/61 patients without fractures (specificity of 97%). The authors conclude that point of care ultrasonography has a high specificity, but what does this mean to practicing clinicians? What is more important, is the likelihood ratios and the prevalence corrected predictive values. LIKELIHOOD RATIO: the positive likelihood ratio = (sensitivity)/(1-specificity). In this case the positive likelihood ratio = 27 (you are 27 times more likely to have a fracture if the test is positive vs negative). The negative likelihood ratio = (1-sensitivity)/specificity = (1-87.5%)/96.7% = 0.13 (you are 87% less likely to have a fracture if the test is negative vs positive). This is interesting, but in likelihood ratios, the number doesn't tell you the overall likelihood of disease! It only compares you against those with an opposite test result. That is why PREDICTIVE VALUES CORRECTED FOR 50% DISEASE PREVALENCE are so useful. To do this, we set disease prevalence at 50% and apply the test sensitivity and specificity to these values (since sensitivity and specificity are not influenced by disease prevalence). So, for example, let 500 kids have a fracture, and 500 do not have a skull fracture (prevalence of 50%). Point of care ultrasonography would detect 87.5% (437.5) and be false-positive in 16.4 giving a POSITIVE PREDICTIVE VALUE (50% prevalence) = 96%. So, if I'm really not sure what is going on (pre-test probability = 50%, a coin flip), and the test is positive, then I'm pretty confident the child has a fracture. But if the test is negative, I'm not so confident because the negative predictive value of the test (50% prevalence) is only 88%. What have we learned? In this case, a high specificity doesn't equal a high negative predictive value unless disease prevalence is low. If disease prevalence (our clinically estimated pre-test probability of disease) is mid to high, a negative skull ultrasound doesn't mean much. Pediatrics. 2013 Jun;131(6):e1757-64 (retrieved Feb, 2014).
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