What is the C-Statistic?
The C-statistic (concordance statistic) is a measure of a prediction model's ability to discriminate between patients who will and will not experience a specific outcome—essentially quantifying how well the model distinguishes higher-risk from lower-risk individuals. 1
Core Definition and Interpretation
The C-statistic represents the probability that a randomly selected person who experiences the outcome will have a higher predicted risk score than a randomly selected person who does not experience the outcome. 1
- Mathematically, the C-statistic is analogous to the area under the receiver operating characteristic (ROC) curve 1
- For binary outcomes, the C-statistic and area under the ROC curve are identical measures 1
- For survival data, specialized versions exist including Harrell's C-index or time-dependent C-statistics that account for censoring and time-to-event components 1
Interpreting C-Statistic Values
Values above 0.7 are typically considered to constitute good evidence for discriminative ability, while values between 0.5 and 0.7 must be interpreted in the context of the clinical scenario and representativeness of the sample. 1
- C = 0.50: No discrimination—predictions are no better than chance alone 1
- C = 0.5-0.7: Modest discrimination—clinical utility depends heavily on context 1
- C > 0.7: Good discriminative ability 1
- C = 1.0: Perfect discrimination (theoretical maximum) 1
A C-statistic with confidence limits overlapping 0.5 implies that decisions based on risk estimation may be no better than chance alone. 1
Critical Distinction: Discrimination vs. Calibration
The C-statistic measures discrimination only—it does not assess calibration, which is a separate and equally important concept. 1
- Discrimination (C-statistic): Can the model distinguish who is at higher vs. lower risk? 1
- Calibration: Do predicted probabilities match observed event rates? (e.g., if the model predicts 10% risk, do 10% of those patients actually experience the event?) 1
These two concepts do not necessarily track with each other—a model can have good discrimination but poor calibration, or vice versa. 1
Important Clinical Caveats
Population Heterogeneity Affects C-Statistics
C-statistic values vary with the characteristics of the data sample in ways that relative risk estimates do not. 1
- In more homogeneous populations (e.g., restricted surgical cohorts), C-statistics will be lower regardless of the model's true discriminatory ability 1, 2
- In more heterogeneous populations, C-statistics will be higher 2
- The discriminative ability of a continuous variable cannot be judged by its odds ratio alone, but must be considered in relation to population heterogeneity 3
Statistical vs. Clinical Significance
Differences in C-statistics between models can be statistically significant without necessarily being clinically significant. 1
- Small improvements in C-statistics may not translate to meaningful clinical benefit 1
- The clinical context, disease severity, and potential for harm with misclassification must guide interpretation 1
Validation Requirements
Discrimination should be assessed in both internal validation (in the derivation data) and external validation (in an independent study). 1
- Internal validation requires allowance for optimism in the C-statistic 1
- External validation tests whether the model's discriminative ability generalizes to other populations 1
Complementary Performance Measures
While the C-statistic is essential, comprehensive model evaluation requires additional metrics:
- Calibration plots: Visual assessment of predicted vs. observed risks 1
- Decision curve analysis: Evaluates net benefit at different risk thresholds 1
- Net reclassification improvement: Assesses correct reclassifications when adding new predictors 1
- Brier score: Overall accuracy measure for probability predictions 1