Approximating Binary–Continuous Joint Distributions from Marginal Summaries: Application to Clinical Trial Simulation

Clinical trial simulation (CTS) is increasingly used in modern drug development to optimize design, evaluate decision rules, and support regulatory assessment. To generate realistic synthetic patients, simulations should reflect key marginal features and dependencies among variables. When individual-level data are available, this is straightforward; however, privacy, regulatory, and proprietary restrictions often limit access to such data, leaving only summary-level statistics reported in publications or trial registries. We propose a method for approximating the joint structure of a continuous and a binary variable by estimating low-order features, using only marginal summaries from multiple independent studies. The continuous variable is modeled as a two-component Gaussian mixture conditional on the binary outcome, allowing study-specific mixing proportions. We derive closed-form conditional moments and use these to construct a generalized method of moments (GMM) estimator. Simulation studies demonstrate accurate and well-calibrated estimation of the component-specific means and variances across a wide range of scenarios, and an application to UK Biobank summary data illustrates the method’s ability to approximate these key distributional features without access to individual records. The proposed method enables privacy-preserving parameterization of CTS models and supports model-informed drug development, cross-study evidence synthesis, and federated analyses in data-restricted environments. To facilitate its implementation, we provide an open-source R package, ebdm, which is available on CRAN.