Hepatic Encephalopathy, PPV and NPV

Last week we talked about sensitivity and specificity, which we calculated using this table:

Table 1: Useful grid for calculating test characteristics.

There are several other useful test characteristics which can be calculated using these numbers, but today we just reviewed positive predictive value and negative predictive value (PPV and NPV).  The PPV and NPV are the proportion of positive or negative results which actually mean that the person does or doesn't have the target disorder.  This is calculated as PPV = A / (A+B) and NPV = D / (C+D).  To put it another way, the PPV/NPV are your post-test probability.

A crucial thing to remember about the PPV/NPV is that, unlike sensitivity and specificity, they are directly proportional to the prevalence of the target disorder.  This is handily illustrated by a recent study in the Postgraduate Medical Journal, illustrating the characteristics of clock-drawing as a diagnostic test and grading instrument for hepatic encephalopathy.  Their attempt to use this simple bedside test to follow the progression of the disorder made a lot of sense, but in one of their first tables they report that, for the simple diagnosis of hepatic encephalopathy, being unable to draw a pretty perfect clock has a sensitivity of 86%, a specificty of 80%, and a PPV of 96%.

Fig. 1 PPV is directly proportional to prevalence.

Recall that everyone in the study already had a clinical diagnosis of hepatic encephalopathy.  It turns out that clinical diagnsosi is fairly accurate, and when the investigators applied their diagnostic gold standard (a composite of two well-validated neuropsychiatric tests) the actual prevalence of the disorder in the test population was close to 100%.  Because the prevalence was so high, any diagnostic test would have a high PPV, regardless of its test characteristics, since the likelihood of a false positive was so low.  Imagine you have a breathalyzer that doesn't work very well, and you're looking for drunk people on the Las Vegas strip on New Year's Eve.  Even if it only picks up 1 case in 10, it will always be right because everybody's drunk.

So it's worth knowing PPVs and NPVs for individual diagnostic tests, but you also have to know where they came from.  If the prevalence in the study population was basically the same as the prevalence in your patient population, then you can probably rely on its accuracy in your patient's case; however, if it was much higher or lower you'll need to adjust it or use a different measure - more on both topics later.