Estimating the joint distribution of two binary variables from marginal summaries in clinical trials

Clinical trial simulation (CTS) is critical in new drug development, providing insight into safety and efficacy while guiding trial design before committing substantial investment. 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 obtained from publications, 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 maximum likelihood approach to estimate the joint distribution of two binary variables using only marginal summary data from multiple published studies. 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 simulation of realistic clinical trial data, thereby improving decision-making processes in drug development. To facilitate its implementation, we provide an open-source R package, ebdm, which is available on CRAN.