Improving the Estimation of Prediction Increment Measures in Logistic and Survival Analysis.

Proper confidence interval estimation of the area under the receiver operating characteristic curve (AUC), the net reclassification index (NRI), and the integrated discrimination improvement (IDI) is an area of ongoing research. The most common confidence interval estimation methods employ asymptotic theory. However, developments demonstrate that degeneration of the normal distribution assumption under the null hypothesis exists for measures such as the change in AUC (ΔAUC) and IDI, and confidence intervals estimated under the normal distribution assumption may be invalid. We aim to study the performance of confidence intervals derived assuming asymptotic theory and those derived with non-parametric bootstrapping methods. We examine the performance of ΔAUC, NRI, and IDI in both the logistic and survival regression context. We explore empirical distributions and compare coverage probabilities of asymptotic confidence intervals with those produced from bootstrapping methods through simulation. The primary finding in both the logistic framework and the survival analysis framework is that the percentile CIs performed well regarding coverage, without compromise to their width; this finding was robust in most scenarios. Our results suggest that the asymptotic intervals are only appropriate when a strong effect size of the added parameter exists, and that the percentile bootstrap interval exhibits at least a reasonable coverage while maintaining the shortest width in nearly all simulated scenarios, making this interval the most reliable choice. The intent is that these recommendations improve the accuracy in the estimation and the overall assessment of discrimination improvement.