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

Suppose we have a Bayesian model that 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 prioritize 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 modeling 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 surveys, registers, and expert beliefs. This analysis shows which parameters contribute most of the uncertainty about each prevalence estimate, and the expected improvements in precision from specific amounts of additional data. These benefits can be traded with the costs of sampling to determine an optimal sample size. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

假设我们拥有一个融合多源证据的贝叶斯模型（Bayesian model）。我们希望明确哪些模型参数对模型的估计结果或决策影响最为显著，或是哪些参数的不确定性主导了决策层面的不确定性。此外，我们还需对后续数据采集工作进行优先级排序。此类问题可通过信息价值（Value of Information, VoI）分析解决：该方法通过评估针对特定参数开展研究或按既定设计采集数据时，预期带来的损失减少量。本文阐述了用于贝叶斯证据合成的信息价值分析的理论框架与实践方法，融合并拓展了卫生经济学、计算机建模及贝叶斯设计领域的相关理念。该类方法可泛化至多种决策场景，包括点估计以及离散行动间的选择。我们将此类方法应用于一个艾滋病病毒（HIV, Human Immunodeficiency Virus）感染率估计模型中，该模型整合了来自调查、登记系统及专家判断的间接信息。本次分析明确了各感染率估计结果的不确定性主要由哪些参数贡献，以及特定规模的新增数据可预期带来的精度提升幅度。可将此类收益与采样成本进行权衡，以此确定最优样本量。本文的补充材料（包括可复现研究的标准化材料说明）可通过在线补充资源获取。