I have N number of patients each who could have 1 of 5 diseases (A, B, C, D, E). There is clinical information that may improve the accuracy of doctor diagnoses of these N patients. All diagnoses will be confirmed.
I want to test whether that information improves diagnostic accuracy. To do this, I am going to calculate the AUC for each diagnosis for a doctor before he has this clinical information and after. I will calculate the percent agreements for each set of diagnoses. I want to be able to show that the AUC for each disease increases 15%. Based on previous studies, lets say I know the doctors' concordance statistic, or $c$-statistic, before given the clinical information is 70 units and the SD is 2 units. I want a power of 0.9 at a significance level of 0.05.
I need to calculate the minimum sample size needed for this. In STATA, I have found that my N must be 46, randomized 1:1 to receive diagnoses without the new information and with the new information. My problem is exactly how to interpret this. This is really for the binary diagnosis of A versus not A. Therefore, for 5 different possibilities I will need 115 (5 x 23) of each diagnosis in each group.