cstatistikkAUC

cstatistikkAUC refers to the concordance statistic (c-statistic) and its common interpretation as the area under the receiver operating characteristic curve (AUC). It is a measure of a predictive model’s discrimination: the ability to distinguish between subjects with and without an outcome. For binary outcomes, the c-statistic is numerically equivalent to the ROC AUC.

Definition and calculation: conceptually, the c-statistic is the probability that a randomly chosen case (positive outcome) receives a higher predicted risk than a randomly chosen control (negative outcome). The ROC AUC is the integral of sensitivity plotted against 1 − specificity across all decision thresholds. In practice, AUC is estimated from model predictions and observed outcomes; methods for variance and confidence intervals include DeLong’s test and bootstrap resampling.

Interpretation: values range from 0.5 (no discrimination, random) to 1.0 (perfect discrimination). Common heuristic ranges label 0.7–0.8 as acceptable, 0.8–0.9 as good, and >0.9 as excellent, though clinical relevance depends on context. Values below 0.5 indicate worse-than-random discrimination and suggest model miscalibration or reversed prediction.

Limitations and considerations: AUC/c-statistic assesses discrimination but not calibration or clinical utility. It is insensitive to changes in predicted probabilities that do not affect ranking, can be affected by class imbalance, and requires alternative formulations (e.g., Harrell’s c-index) for censored survival data. It is widely used in medicine, epidemiology, and machine learning as a summary measure of predictive performance.