Informing Health Economic Decisions: A Framework for Model Calibration and Value of Information Analysis for Target Data

Decision-analytic models (DAMs) are vital tools in public health economics for evaluating healthcare strategies under uncertainty. Their credibility hinges on robust calibration of unobservable parameters. However, the comparative effectiveness of diverse calibration methods—spanning Bayesian (e.g., Incremental Mixture Importance Sampling [IMIS], Hamiltonian Monte Carlo [HMC]) and non-Bayesian (e.g., Random Search, Latin Hypercube Sampling, Nelder-Mead, Simulated Annealing) approaches—and the economic value of improving calibration data remain understudied.

This thesis addresses these gaps through two objectives. First, it evaluates calibration methods using a natural history model across varying complexities, assessing their accuracy in recovering known parameters, influence on cost-effectiveness outcomes, and characterisation of decision uncertainty. Second, it develops a Value of Information (VOI) framework to quantify the economic worth of calibration data, examining how data availability (none, expert-elicited, empirical), richness (number of data points), and calibration method affect the value of acquiring improved data. The VOI framework is theoretically illustrated and then applied to cancer and infectious disease case studies.

Results indicate Bayesian methods, particularly IMIS and HMC, achieve superior parameter estimation and uncertainty quantification in high-dimensional scenarios, offering robust cost-effectiveness conclusions. Non-Bayesian optimisation methods (e.g., Nelder-Mead), while computationally efficient, risk bias and inadequate uncertainty representation, potentially distorting decision uncertainty metrics. Unguided sampling methods (e.g., Random Search) retain substantial residual uncertainty. VOI analyses demonstrate that data value is contingent on data quality, quantity, and calibration approaches.

Ultimately, this work delivers clear evidence favouring Bayesian techniques for calibrating complex health economic models, offering a crucial guide for researchers. It also equips policymakers with a novel analytic framework to formally evaluate and justify expenditure on data collection for calibration. By providing this methodological direction and a tool for strategic data investment, this research directly enhances the transparency, reliability, and decision-relevance of DAMs, fostering more defensible and efficient health resource allocation.