Demographic Parity

Demographic parity is a statistical independence metric, meaning it evaluates the model's prediction rate alone, without requiring access to the true labels. This makes it uniquely suited for federated model evaluation where ground truth validation data may be siloed or unavailable. A model satisfies demographic parity if the probability of a positive prediction is identical across all protected groups, formally expressed as:

• Formula: P(ŷ=1 | A=a) = P(ŷ=1 | A=b) for all groups a, b
• Key Implication: The metric ignores whether predictions are correct, focusing solely on outcome distribution
• Federated Advantage: Can be computed securely by aggregating only prediction counts and group membership tallies, not individual labels

The standard operationalization of demographic parity is the Disparate Impact Ratio (DIR), which quantifies the relative difference in positive prediction rates between a privileged and unprivileged group. In a federated context, this is computed by securely summing the positive prediction counts per group across all nodes.

• Calculation: DIR = P(ŷ=1 | unprivileged) / P(ŷ=1 | privileged)
• Threshold: A model is typically considered fair if 0.8 ≤ DIR ≤ 1.25, following the EEOC's 80% rule
• Federated Aggregation: Each institution computes local positive rates per group; the global DIR is derived from the sum of numerators and denominators, never exposing patient-level predictions

A critical limitation of demographic parity is its inherent conflict with calibrated risk prediction. When base rates of a condition differ across demographic groups due to genuine epidemiological factors, enforcing equal positive prediction rates forces the model to:

• Over-predict the condition in the group with a lower natural prevalence
• Under-predict the condition in the group with a higher natural prevalence
• Violate calibration: The predicted probability no longer reflects the true likelihood of the outcome

This tension is particularly acute in federated healthcare settings where disease prevalence varies significantly across geographic or socioeconomic client nodes.

Computing demographic parity across a decentralized network requires a privacy-preserving aggregation protocol to avoid exposing per-institution group statistics. The standard approach uses Secure Aggregation (SecAgg) to sum the following atomic counts from each client:

• Count of positive predictions for each demographic group
• Total count of individuals in each demographic group
• No raw predictions or labels are ever transmitted

The central server then divides the aggregated sums to compute the global positive prediction rate per group. This ensures that no single institution's demographic distribution is revealed, satisfying HIPAA minimum necessary requirements.

To address the limitations of standard demographic parity, a refined variant called Conditional Demographic Parity incorporates legitimate risk factors. This metric requires equal positive prediction rates across groups only after controlling for a set of resolving variables—features that justify differential treatment.

• Example: In a cardiac risk model, age and smoking status may be legitimate resolving variables; gender and race are not
• Federated Implementation: Requires stratified computation of positive rates within each resolving variable stratum, then aggregation across strata
• Regulatory Alignment: More closely aligns with EEOC guidance that permits business necessity defenses for statistical disparities

Demographic parity serves as a primary audit metric for demonstrating compliance with anti-discrimination regulations in automated clinical decision systems. In a federated evaluation framework, the audit trail must include:

• Cryptographic proof that only aggregated counts were shared, not individual records
• Versioned snapshots of the demographic parity calculation at each evaluation round
• Threshold breach alerts when the Disparate Impact Ratio falls outside the acceptable range

This supports FDA SaMD and EU AI Act requirements for continuous bias monitoring of high-risk medical AI systems deployed across multiple institutions.