# Value of Information: Sensitivity Analysis and Research Design in Bayesian Evidence Synthesis

## TL;DR

This paper develops methods for Value of Information analysis in Bayesian evidence synthesis, helping identify key parameters and optimal data collection strategies to improve decision-making accuracy.

## Contribution

It extends VoI techniques to Bayesian evidence synthesis, providing a framework for prioritizing data collection and understanding parameter influence in complex models.

## Key findings

- Identified key parameters affecting HIV prevalence estimates.
- Quantified expected improvements from additional data collection.
- Demonstrated applicability to real-world health data synthesis.

## Abstract

Suppose we have a Bayesian model which combines evidence from several different sources. We want to know which model parameters most affect the estimate or decision from the model, or which of the parameter uncertainties drive the decision uncertainty. Furthermore we want to prioritise what further data should be collected. These questions can be addressed by Value of Information (VoI) analysis, in which we estimate expected reductions in loss from learning specific parameters or collecting data of a given design. We describe the theory and practice of VoI for Bayesian evidence synthesis, using and extending ideas from health economics, computer modelling and Bayesian design. The methods are general to a range of decision problems including point estimation and choices between discrete actions. We apply them to a model for estimating prevalence of HIV infection, combining indirect information from several surveys, registers and expert beliefs. This analysis shows which parameters contribute most of the uncertainty about each prevalence estimate, and provides the expected improvements in precision from collecting specific amounts of additional data.