Estimation of Bivariate Normal Distributions from Marginal Summaries in Clinical Trials

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.