“Based on these currently available standards, in our sample size calculations, we considered the null hypothesis H0: AUC = 0.8 versus either the one-sided (H1: AUC > 0.8) or two-sided (H1: AUC ≠ 0) alternative. For both alternatives, the necessary sample size was calculated to achieve at least 85% statistical power to detect AUC of 0.9. We assumed that the ratio of cases (those with diagnosed CaP) to controls (those without cancer) was between 2/3 and 1. The calculations were based on the estimate of AUC proposed by Hanley and McNeil that is a function of the ROC area and the sample size only. This method is based on an exponential distribution approximation to the standard error of the ROC area which has been shown to provide a very good approximation for a variety of underlying distributions for continuous diagnostic characteristics. The calculations show that the necessary sample size for the one-sided alternative is 120 samples while for the two-sided alternative it is 150 samples. ROC analysis was based on the nonparametric Mann-Whitney procedure. The resultant analysis indicates that a post hoc H0: AUC=0.9 is rejected at the 5% level using a two-sided statistical test.”

Note: A range is given for sample size ratio so we conduct a sensitivity analysis over the extremes of that range. They also give figures for the 1-sided and 2-sided test and these are both tested below.