64: Estimating the Bivariate Normal Distribution from Marginal Summaries

Music City Center 

Clinical trial simulation is widely used in drug research to assess safety, efficacy, and inform trial design. Realistic simulation outcomes require careful handling of variable interrelationships. However, privacy concerns often restrict access to individual-level data or relational summaries, making correlation estimation challenging. Consequently, researchers must rely on study-level summaries (e.g., means, variances, sample sizes). We propose a novel maximum likelihood estimation (MLE)-based approach to estimate the joint distribution of two normally distributed variables using only marginal summary data. Our method leverages numerical optimization to effectively estimate the correlation coefficient under these constraints. Through simulation studies across various settings and comparison with the naive sample means method, we demonstrate the accuracy and robustness of our approach. This method enhances realistic data generation in simulations, and improves decision-making in drug development.

Marginal Summary Data

Joint Distribution Estimation

Clinical Trial Simulation (CTS)

Distributed Learning

Strict Privacy

Bivariate Normal Distribution 

Health Policy Statistics Section