Does a Developed Comorbidity Index Really Add Value? A Selection-Aware Bootstrap for Post-Selection Concordance

Abstract

Disease-specific comorbidity indices are routinely developed by building several candidate constructions and reporting the best-scoring one, then claiming it adds discriminative value over a fixed off-the-shelf comparator such as the Charlson or Elixhauser score. We show that the optimism correction in standard use does not make that claim valid. Because it corrects the selected model as if it were the only one ever fit, it omits the winner's-curse term from choosing the best of several candidates; so its confidence interval for the incremental concordance is not merely optimistic in small samples but structurally miscalibrated, and does not shrink as the sample grows. At a true null it inflates false claims of added value above the nominal level, increasingly so as more candidates are screened. We introduce a drop-in selection-aware bootstrap that re-runs the best-of-several selection inside each resample with the comparator held fixed, removing the structural bias. In a fully-known-truth simulation, 95% coverage under the standard correction falls from 0.94 with one candidate to 0.70 with a hundred, while the selection-aware interval holds near nominal; its coverage matches a calibrated cross-validation interval, and at a matched error rate it is at least as powerful. The results hold under Uno's concordance, and a semi-synthetic experiment on real survey data confirms when the correction matters. In practice, if several constructions were tried, report a selection-aware interval, most needed with many similar-quality candidates and few events per candidate. The scope is discrimination only; software and results reproduce every finding.