JuliaCon 2026

Virtual Populations (VPops) are widely used in Quantitative Systems Pharmacology (QSP) to represent variability in patient responses to therapy using parameterized dynamical models. Unlike traditional modeling approaches that focus on average treatment effects, VPop methods aim to reproduce the full distribution of clinical outcomes observed in trials.
We introduce VPopMIP, a Julia package implementing a Mixed-Integer Programming (MIP) formulation for generating VPops that match clinical endpoints. In contrast to many existing approaches that require individual-level patient data, VPopMIP enables calibration to published clinical summary statistics (e.g., response rates, medians, and confidence intervals), which are more commonly available in practice.
The method formulates virtual patient selection as a constrained optimization problem that enforces agreement with multiple outcome measures across therapies.
We demonstrate the methodology using a solid tumor model with multiple efficacy endpoints across treatment regimens. The results illustrate how MIP-based selection provides an efficient way to construct clinically consistent virtual populations.