A recent study published in JAMA, “Medicine’s Uncomfortable Relationship With Math: Calculating Positive Predictive Value,” highlighted a massive hole in our education. Out of 24 attendings, 26 residents, and a handful of medical students, < 25% of participants was able to correctly calculate the positive predictive value (PPV) of a test. Thus I thought it was time to give a brief review of this topic…. Stats 101 here we go….
Test Result Disease + Disease –
Positive True + (a) False + (b)
Negative False – (c) True – (d)
Sensitivity = a / a+c (true + / true pos + false neg)
Sensitivity is the probability that a test result will be positive when the disease is actually present. Essentially the rate of true positives
Specificity = d/b+d (true – / false pos + true neg)
Specificity is the probability that a test result will be negative when the disease is not there, the rate of true negatives
Positive Likelihood Ration = Sensitivity / 100 – Specificity
PLR is the ratio between the probability of a positive test result given presence of disease and the probability of a positive test result given the absence of the disease – essentially true positive rate / false positive rate
Disease Prevalence = a + c / (a + b + c + d) = true pos + false neg / total number subjects
Positive predictive Value = a/ (a+b) = true pos / true pos + false pos
PPV is the probability that the disease is present when the test is positive
Negative predictive value = d / (c+d) = true neg / false neg + true neg
NPV = probability disease not present when test is negative
The tricky part…. if the disease prevalence is known then it affects the PPV and NPV.
For starters the basic formula for PPV is
The basic formula for NPV is
