Estimating the Joint Distribution of Two Binary Variables with Marginal Statistics

TL;DR

This paper introduces a maximum likelihood-based method to estimate the joint distribution of two binary variables using only marginal summary data, addressing privacy and data access issues in clinical trial simulation.

Contribution

It presents a novel approach that accurately estimates joint distributions from marginal data, enabling realistic clinical trial simulations without requiring individual-level data.

Findings

Method achieves high accuracy in diverse simulation scenarios

Robustness demonstrated across varying sample sizes and data conditions

Application to real data shows practical utility and improved simulation realism

Abstract

Clinical trial simulation (CTS) is critical in new drug development, providing insight into safety and efficacy while guiding trial design. Achieving realistic outcomes in CTS requires an accurately estimated joint distribution of the underlying variables. However, privacy concerns and data availability issues often restrict researchers to marginal summary-level data of each variable, making it challenging to estimate the joint distribution due to the lack of access to individual-level data or relational summaries between variables. We propose a novel approach based on the method of maximum likelihood that estimates the joint distribution of two binary variables using only marginal summary data. By leveraging numerical optimization and accommodating varying sample sizes across studies, our method preserves privacy while bypassing the need for granular or relational data. Through an extensive simulation study covering a diverse range of scenarios and an application to a real-world dataset, we demonstrate the accuracy, robustness, and practicality of our method. This method enhances the generation of realistic simulated data, thereby improving decision-making processes in drug development.