Numeric Instability of Predictive Values

Abstract

In this month’s Annals, Hogg et al examine the performance of the Simplify D-dimer among patients presenting to the emergency department (ED) with pleuritic chest pain. The authors conclude that this test cannot be relied on to exclude pulmonary embolism in these patients, despite reporting a negative predictive value of 99% for the Simplify D-dimer . How can such a conclusion be compatible with a near-perfect negative predictive value? To answer this question, we must begin with the standard 2 2 matrix shown in the Figure. This 4-fold table clearly displays the dichotomous relationship between the presence or absence of a target disorder (disease) and a positive or negative test result. The 4 shaded central cells of the Figure, generated by superimposing 2 rows on 2 columns, contain the 4 mutually exclusive elements (true positive [TP], false positive [FP], true negative [TN], and false negative [FN]) from which the traditional triad of test performance characteristics is derived: (1) positive/negative predictive values, (2) sensitivity/specificity, and (3) positive/negative likelihood ratios. The definitions and attributes of these 3 pairs of test characteristics are summarized in Table 1. At first glance, positive and negative predictive values appear to be highly attractive test properties. Indeed, they seem to tell us exactly what we wish to know from a diagnostic test: if the test result is positive, then the positive predictive value (defined in Table 1 as [TP/(TPCFP)]) provides us with a numeric probabilitydexpressed as a simple percentage ranging from 0% to 100%dof ‘‘ruling in’’ the target disorder at which the test is aimed. Conversely, if the test is negative, the negative predictive value (defined in Table 1 as [TN/(TNCFN)]) provides a similarly straightforward probabilitydalso expressed as a simple percentagedof ‘‘ruling out’’ the target disorder we wish to exclude. Unfortunately, there is a hitch: predictive values are highly vulnerable to fluctuations in disease prevalence, causing numeric instability, which markedly constrains their clinical usefulness. When disease prevalence (defined as the proportion of patients in a population with the target disorder) increases, the positive predictive value of any given diagnostic test must increase, and, reciprocally, the negative predictive value of that same test must decrease. Similarly, as prevalence