Concordance Index (C-Index)

The C-Index is a rank correlation metric that assesses how well a model orders subjects by their predicted risk. It does not evaluate the absolute accuracy of predicted survival times, but rather the relative ordering of risk scores.

• Compares all possible patient pairs with comparable event times
• A value of 1.0 indicates perfect ordering of risk predictions
• A value of 0.5 indicates random guessing, equivalent to a coin flip
• Values below 0.5 suggest the model is systematically ranking patients inversely

The C-Index incorporates right-censored observations through specific comparability rules. A pair is considered comparable only if the patient with the shorter observed time experienced the event.

• If both patients are censored, the pair is non-comparable and excluded
• If the event occurs before the other's censoring time, the pair is usable
• This ensures the metric is not biased by incomplete follow-up data
• Harrell's C-Index and Uno's C-Index differ in how they weight these comparable pairs

A C-Index of 0.70 means that for 70% of randomly selected patient pairs, the model correctly identifies which patient experiences the event first. This provides an intuitive measure of discriminative power.

• Values above 0.80 are generally considered strong discrimination
• Values between 0.70–0.80 indicate moderate clinical utility
• The metric is widely reported in oncology prognostic models and cardiovascular risk scores
• It is analogous to the Area Under the ROC Curve (AUC) for binary classification, extended to time-to-event data

Two primary formulations exist, addressing different statistical properties. Harrell's C-Index is the original formulation but can be biased when censoring patterns differ between risk groups.

• Harrell's C-Index: Uses only pairs where the shorter time is an event; simple but sensitive to censoring distribution
• Uno's C-Index: Applies inverse probability censoring weighting (IPCW) to correct for dependent censoring
• Uno's version provides a consistent estimator regardless of censoring patterns
• The choice between them depends on whether censoring is assumed to be independent of covariates

The standard C-Index provides a global summary of discrimination over the entire study period. Time-dependent variants evaluate discrimination at specific time points of clinical interest.

• Time-dependent C-Index assesses how well the model discriminates at a fixed horizon, such as 5-year survival
• Useful when the proportional hazards assumption is violated
• Allows comparison of model performance at early vs. late follow-up periods
• Often reported alongside time-dependent ROC curves for a complete picture of dynamic predictive accuracy

The C-Index alone is insufficient for comprehensive model evaluation. It measures discrimination but not calibration—the agreement between predicted and observed event probabilities.

• A well-calibrated model can have a low C-Index if risk scores are tightly clustered
• Conversely, a poorly calibrated model can achieve a high C-Index
• Should be reported alongside the Brier Score for overall accuracy
• Calibration plots and decision curve analysis provide necessary context for clinical deployment decisions

Extends the standard Receiver Operating Characteristic curve to survival data by evaluating how well a model discriminates between subjects who will and will not experience an event by a specific time horizon. Unlike the C-index, which provides a global rank-based measure, time-dependent AUC quantifies discrimination at clinically relevant time points. The Heagerty, Zheng, and Lumley methods handle censoring through inverse probability weighting or nearest neighbor estimation. This metric is essential for assessing how a prognostic model's discriminative power changes over the follow-up period.

A strictly proper scoring rule that measures the mean squared difference between predicted survival probabilities and observed event status at a specific time point. While the C-index evaluates only discrimination (ranking), the Brier Score assesses calibration and sharpness simultaneously. A lower score indicates better predictive accuracy. The integrated Brier Score (IBS) summarizes performance across all time points, providing a single overall measure of probabilistic forecast quality that complements rank-based metrics.

Graphical diagnostics that compare predicted survival probabilities against observed event rates across risk groups at a specified time horizon. Subjects are binned by predicted risk, and the mean prediction is plotted against the Kaplan-Meier estimate for each bin. A perfectly calibrated model follows the 45-degree diagonal line. Calibration is critical for clinical decision-making: a model with high C-index but poor calibration may systematically overestimate or underestimate risk, leading to inappropriate treatment decisions.

Diagnostic residuals used to test the proportional hazards assumption underlying the Cox model from which many C-index calculations derive. These residuals plot the difference between observed and expected covariate values at each event time. A systematic trend over time indicates a violation of proportional hazards, meaning the C-index may misrepresent model performance. The Grambsch-Therneau test provides a formal statistical test, and smoothed residual plots reveal which covariates require time-varying coefficient extensions.

The area under the survival curve up to a specified time point τ, providing a clinically interpretable summary of treatment benefit without requiring the proportional hazards assumption. While the C-index measures relative ranking, RMST difference quantifies the absolute gain in event-free time between groups. This metric is increasingly favored in oncology trials when the hazard ratio is not constant, offering a robust alternative that directly answers the question: 'How much longer do patients live on average?'

The process of updating a patient's survival prognosis as new longitudinal data becomes available, such as repeated lab measurements or imaging results. Unlike the static C-index calculated at baseline, dynamic prediction uses landmarking or joint modeling to incorporate biomarker trajectories. The dynamic C-index evaluates discrimination at multiple landmark times, assessing how well a model re-ranks patients as their clinical profiles evolve. This is essential for real-time clinical decision support systems.