The first positive: Computing positive predictive value at the extremes

Computing the positive predictive value (PPV) of a well-known test for a re latively common disease is a straightforward exercise. However, in the case of a new test for a rare disorder, the extreme numbers involved-the very l ow prevalence of the disorder and the lack of previous false-positive resul ts-make it difficult to compute the PPV. As new genetic tests become availa ble in the next decade, more and more clinicians will have to answer questi ons about PPVs in cases with extreme prevalence, sensitivity, and specifici ty. This paper presents some tools for thinking about these calculations. F irst, a standard PPV calculation with rough estimates of the prevalence, se nsitivity, and specificity is reviewed. The "zero numerator" problem posed by not having seen any false-positive results is then discussed, and a Baye sian approach to this problem is described. The Bayesian approach requires specification of a prior distribution that describes the initial uncertaint y about the false-positive rate. This prior distribution is updated as new evidence is obtained, and the updated expected false-positive rate is used to calculate PPVs. The Bayesian approach provides appropriate and defensibl e PPVs and can be used to estimate failure rates for other rare events as w ell.