Bayesian Optimization with Additive Kernels for a Stepwise Calibration of Simulation Models for Cost-Effectiveness Analysis

Abstract A critical aspect of simulation models used in cost-effectiveness analysis lies in accurately representing the natural history of diseases, requiring parameters such as probabilities and disease burden rates. While most of these parameters can be sourced from scientific literature, they often require calibration to align with the model’s expected outcomes. Traditional optimization methods can be time-consuming and computationally expensive, as they often rely on simplistic heuristics that may not ensure feasible solutions. In this study, we explore using Bayesian optimization to enhance the calibration process by leveraging domain-specific knowledge and exploiting structural properties within the solution space. Specifically, we investigate the impact of additive kernel decomposition and a stepwise approach, which capitalizes on the sequential block structure inherent in simulation models. This approach breaks down large optimization problems into smaller ones without compromising solution quality. In some instances, parameters obtained using this methodology may exhibit less error than those derived from naive calibration techniques. We compare this approach with two state-of-the-art high-dimensional Bayesian Optimization techniques: SAASBO and BAxUS. Our findings demonstrate that Bayesian optimization significantly enhances the calibration process, resulting in faster convergence and improved solutions, particularly for larger simulation models. This improvement is most pronounced when combined with a stepwise calibration methodology.