On the dependence of the critical success index (CSI) on prevalence

Recently the critical success index (CSI) has been increasingly discussed and advocated as a unitary outcome measure in various clinical situations where large numbers of true negatives may influence the interpretation of other more traditional outcome measures such as sensitivity and specificity, or when unified interpretation of positive predictive value (PPV) and sensitivity (Sens) is needed. The derivation of CSI from measures including PPV has prompted questions as to whether and how CSI values may vary with disease prevalence (P), just as PPV estimates are dependent on P, and hence whether CSI values are generalizable between studies with differing prevalences. As no detailed study of the relation of CSI to prevalence has been undertaken hitherto, the dataset of a previously published test accuracy study of a cognitive screening instrument was reinterrogated to address this question. Three different methods were used to examine the change in CSI across a range of prevalences, using both Bayes formula and equations directly relating CSI to Sens, PPV, P, and to test threshold (Q). These approaches showed that, as expected, CSI does vary with prevalence, but the dependence differs according to the method of calculation adopted. Bayesian rescaling both Sens and PPV generates a concave curve, suggesting that CSI will be maximal at a particular prevalence which may vary according to the particular dataset.