Longwen Shang

Topic

Reconstructing Joint Distributions from Marginal Summaries in Clinical Trials: Methods and Applications

Department of Mathematics and Statistics

Date & location

• Tuesday, April 28, 2026
• 4:00 P.M.
• Virtual Defence

Examining Committee

Supervisory Committee

• Dr. Xuekui Zhang, Department of Mathematics and Statistics, University of Victoria (Co-Supervisor)
• Dr. Min Tsao, Department of Mathematics and Statistics, UVic (Co-Supervisor)
• Dr. Lin Cai, Department of Electrical and Computer Engineering, UVic (Outside Member)

External Examiner

• Dr. Yue Zhang, Department of Mathematics and Statistics, Thompson Rivers University

Chair of Oral Examination

• Dr. Stephen Lindsay, Department of Psychology, UVic

Abstract

Clinical trial simulation (CTS) has become a core component of modern drug development, providing a quantitative framework to evaluate candidate designs, decision rules, and operating characteristics before committing substantial resources. Realistic CTS requires access to the joint distribution of key covariates and outcomes, yet in many privacy-sensitive settings only marginal, study-level summaries are available from publications or trial registries. This dissertation develops a suite of methods for reconstructing low-dimensional joint distributions from such marginal summaries, with a focus on applications in CTS, model-informed drug development, and privacy-preserving evidence synthesis.

In Chapter 2, we consider two binary variables for which multiple studies report only marginal totals. We formulate a bivariate binomial likelihood that treats the unreported joint cell counts as latent and derive maximum likelihood estimators that accommodate heterogeneous sample sizes across studies. In Chapter 3, we address two continuous variables assumed to follow a bivariate normal distribution. Here, each study contributes only sample means, variances, and sample sizes. We develop a maximum likelihood method to estimate the correlation coefficient using only these marginal summaries, again allowing for varying sample sizes and avoiding reliance on within-study covariances. In Chapter 4, we study the mixed binary–continuous case. We model the continuous outcome as a two-component Gaussian mixture conditional on the binary variable, with study-specific mixing proportions. Using closed-form expressions for conditional moments, we construct a generalized method of moments estimator that requires only binary event counts and the reported mean and variance of the continuous outcome from each study. Across all three settings, we conduct extensive simulation studies and analyze real-world datasets to evaluate finite-sample performance, robustness, and practical utility.

Collectively, these methods provide modular building blocks for simulating synthetic patients and learning dependence structures when only marginal summaries can be shared, thereby enabling more realistic CTS, cross-study evidence synthesis, and federated analyses under stringent privacy and data-sharing constraints. The methods are implemented in the open-source R package ebdm, available on CRAN, facilitating their integration into model-informed drug development workflows.