Net Reclassification Improvement (NRI)

NRI measures the net proportion of individuals reclassified correctly when a new marker is added to an existing risk prediction model. Unlike AUC-ROC, which only assesses discriminative ability, NRI directly evaluates whether the new model moves people into more clinically meaningful risk strata. It answers the practical question: 'Does adding this PRS actually change clinical decisions for the better?'

NRI is calculated separately for individuals who experience the event (cases) and those who do not (controls):

• Event NRI: Proportion of cases correctly reclassified upward to a higher risk category
• Non-Event NRI: Proportion of controls correctly reclassified downward to a lower risk category
• Overall NRI: Sum of event and non-event NRI

A positive NRI indicates net improvement; zero means no benefit; negative values suggest the new marker worsens classification.

Two distinct variants exist:

• Category-Based NRI: Requires pre-defined, clinically meaningful risk thresholds (e.g., <5%, 5-10%, >10% 10-year risk). Reclassification is counted only when individuals cross these boundaries.
• Category-Free (Continuous) NRI: Does not rely on arbitrary cut-points. Any upward movement in predicted risk for cases or downward movement for controls is counted, making it threshold-independent.

The category-free version avoids the limitation of choosing arbitrary risk boundaries but may overstate clinically trivial changes.

NRI complements, but does not replace, traditional metrics:

• Discrimination (AUC-ROC): Measures ranking ability; NRI measures correct re-stratification. A model can have high AUC but zero NRI if reclassifications are balanced between correct and incorrect.
• Calibration: NRI assumes the baseline model is well-calibrated. Poor calibration undermines the validity of risk categories and can produce misleading NRI values.
• Integrated Discrimination Improvement (IDI): A related metric that measures the continuous improvement in discrimination without relying on risk categories.

Consider adding a coronary artery disease PRS to the Pooled Cohort Equations (PCE):

• Among 1,000 patients who later had a cardiac event, 120 were reclassified from intermediate to high risk by the PRS-enhanced model (correct), while 30 moved from intermediate to low risk (incorrect).
• Event NRI = (120 - 30) / 1,000 = 0.09 or 9%
• If non-event NRI is 6%, the overall NRI is 0.15 or 15%

This means 15% of the cohort was more appropriately risk-stratified with the PRS added.

NRI has important caveats:

• Category dependence: Results are sensitive to the chosen risk thresholds; different cut-points yield different NRI values.
• Overestimation risk: Category-free NRI can inflate importance by counting infinitesimal probability changes as 'reclassification.'
• No magnitude weighting: A reclassification from 4.9% to 5.1% counts the same as 4.9% to 15%, despite vastly different clinical implications.
• Calibration sensitivity: Miscalibrated models produce unreliable NRI estimates.
• Sampling variability: NRI requires large sample sizes for stable estimates, particularly in low-event-rate populations.

A threshold-independent metric evaluating a model's ability to correctly rank a randomly selected case higher than a randomly selected control. While AUC-ROC measures discrimination, it is often insensitive to the addition of new biomarkers. NRI complements AUC-ROC by explicitly quantifying whether adding a PRS to a baseline model moves individuals into more clinically appropriate risk strata.

• Ranges from 0.5 (no discrimination) to 1.0 (perfect discrimination)
• Insensitive to clinically meaningful risk reclassification
• Often requires NRI to demonstrate incremental clinical value

A global measure of model discrimination equivalent to the AUC-ROC for binary outcomes. The C-statistic represents the probability that a model correctly orders pairs of individuals by risk. Like AUC-ROC, it can remain unchanged even when a new marker dramatically improves risk classification, making NRI a critical supplementary metric for demonstrating the clinical utility of polygenic scores.

• Generalization of AUC for survival and ordinal outcomes
• Harrell's C-index for censored time-to-event data
• Often reported alongside NRI in clinical prediction studies

A continuous analog of NRI that measures the improvement in discrimination slopes when a new marker is added. Unlike categorical NRI, IDI does not require arbitrary risk thresholds. It quantifies the increase in average predicted risk for cases and the decrease for controls.

• IDI = (mean predicted risk in cases_new − mean predicted risk in cases_old) − (mean predicted risk in controls_new − mean predicted risk in controls_old)
• Complements NRI by capturing magnitude of risk shifts
• Sensitive to changes across the entire risk spectrum

The agreement between predicted probabilities and observed event rates. A model with excellent discrimination and high NRI may still be poorly calibrated if predicted risks systematically overestimate or underestimate true risk. Calibration is assessed using Hosmer-Lemeshow tests and calibration plots.

• Essential for absolute risk communication to patients
• Assessed by plotting observed vs. predicted risk deciles
• NRI and calibration together provide a complete picture of clinical validity

A method for evaluating the net benefit of a prediction model across a range of clinical decision thresholds. Unlike NRI, which focuses on reclassification, decision curve analysis directly quantifies whether using a model to guide interventions leads to better outcomes than treating all or no patients.

• Incorporates the relative harm of false positives vs. false negatives
• Plots net benefit against threshold probability
• Used to demonstrate clinical utility beyond statistical metrics

The probability that an individual will develop a specific disease within a defined time window. While NRI assesses reclassification between risk categories, absolute risk combines a PRS with population-level incidence rates and clinical factors to provide actionable, patient-specific probabilities.

• Calculated using baseline hazard and individual risk factor profile
• Requires well-calibrated models for clinical decision-making
• NRI improvements in category assignment directly impact absolute risk communication