Estimation of Bivariate Normal Distributions from Marginal Summaries in Clinical Trials

2025-08-04

AI Summary

In privacy-sensitive distributed settings—such as clinical trial simulations and federated learning—individual-level data are inaccessible, rendering conventional covariance estimation infeasible. To address this, we propose a novel method for estimating the correlation coefficient of bivariate normal variables using only marginal summary statistics (means and variances) from multiple heterogeneous datasets. Our approach formulates a likelihood function that depends solely on the correlation parameter within a maximum likelihood estimation framework and solves it via numerical optimization—without requiring access to raw data, joint covariances, or data sharing. The method naturally accommodates distributional heterogeneity and unequal sample sizes, thereby strengthening privacy preservation. Extensive simulation studies demonstrate its high estimation accuracy and robustness, consistently outperforming existing summary-statistics-based alternatives.

Technology Category

• Machine Learning: Privacy
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Computer Vision: Bias, Fairness & Privacy

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

In certain privacy-sensitive scenarios within fields such as clinical trial simulations, federated learning, and distributed learning, researchers often face the challenge of estimating correlations between variables without access to individual-level data. To address this issue, we propose a novel method to estimate the correlation of bivariate normal variables using marginal information from multiple datasets. The method, based on maximum likelihood estimation (MLE), accommodates datasets with varying sample sizes and avoids reliance on sensitive information such as sample covariances, making it particularly suitable for privacy-restricted settings. Extensive simulation studies demonstrate the proposed method's effectiveness in accurately estimating correlations and its robustness across diverse data configurations.

Problem

• Estimating bivariate normal correlations without individual data
• Using marginal summaries for privacy-sensitive clinical trials
• MLE-based method handles varying sample sizes securely

Innovation

• Estimates bivariate normal correlations
• Uses marginal data without covariances
• MLE-based for privacy-sensitive settings