Correction to Greenland, S., ‘The need for reorientation toward cost-effective prediction: Comments on ‘Evaluating the added predictive ability of a new marker: From area under the ROC curve to reclassification and beyond’ by M. J. Pencina, R. B. D'Agostino Sr, R. B. D'Agostino Jr, and R. S. Vasan (Statistics in Medicine 2007; DOI: 10.1002/sim.2995)’.
In the section on ‘Cost’ in my comment on Pencina et al. , the cost equations are incorrect. The correct formulas are as follows: Let B = true prevalence = Pr(Y = 1), B* = apparent prevalence = Pr(Y* = 1), Se = sensitivity = Pr(Y* = 1|Y = 1), Sp = sensitivity = Pr(Y* = 0|Y = 0), PPV = positive predictive value = Pr(Y = 1|Y* = 1), NPV = negative predictive value = Pr(Y = 0|Y* = 0), CX = cost of measuring X, Ctp = cost of true positive, Cfp = cost of false positive, Cfn = cost of false negative, and Ctn = cost of true negative. Then, the expected loss from using the existing set of variables without X is
Similarly, the expected loss upon adding X to the available variables is
The expected cost of adding X can thus be expressed as