I have done two prediction model in R as an example as below:
model 1: glm(y~x1+x2+x3+x4+x5+x6+x7, data = dat, family = binomial(link = "logit"))
model 2: glm(y~x1+x2+x3+x4+x5+x6+x7+g1+g2+g3+g4+g5+g6, data = dat, family = binomial(link = "logit"))
then plotted the ROC curves and calculated AUC for each after 10-fold cross-validation. However, I would like to know whether `Delong's test's is appropriate for comparing the significant difference of these two AUCs? AUC1 = 0.94 and AUC2 = 0.91
Comparing AUROC curves is equivalent to comparing two Wilcoxon test statistics, as the AUROC with binary Y is the $c$-index, i.e., concordance probability that is a unitless version of the Wilcoxon test. The Wilcoxon test here is comparing predicted risks of those who had an event with the predicted risk of those who didn't. No one takes the difference between two Wilcoxon statistics, and doing so would be an indirect test, i.e., comparing the comparisons of A and B with A and C to compare B with C. The bottom line is that differences in concordance probabilities lack statistical power and have a degenerate distribution making it very hard for p-values to be accurate. See this for powerful approaches that also provide more insights.
