An Effective Methodology for Combining Information from Independent Sources with Applications to Social and Behavioral Sciences and Medical Research

在信息爆炸式增长的现代时代，以有效和有意义的方式处理信息非常重要。荟萃分析的统计方法学是实现这一点的技术。它在社会和行为科学以及医学研究等领域具有广泛的影响和应用。事实上，将来自独立来源的数据信息结合起来的正式和有意义的方法在理论和实践上都很重要。多项研究的综合结果总结了整体关联，由此得出的推论比任何单一研究的推论更稳健和可靠，本提案的目标是开发一个统一的框架和新的方法，用于结合来自独立来源的信息，并展示这些方法在广泛应用中的有用性。所提出的框架的基础工具是置信分布（CD）。虽然CD是一个历史悠久的基本统计推断概念，但最近的发展重新定义了它，重点是解决更复杂的现实问题。该框架可以统一目前实践中使用的大多数信息组合方法，包括经典的p值组合和基于模型的荟萃分析方法。此外，这种CD组合的框架可以导致新方法的发展，例如：a）稳健的荟萃分析方法，其可以消除当前实践中要求所有研究都是相同类型并且具有完全相同的参数值的关键约束;以及B）将专家意见与观测数据中的信息相结合的频率主义贝叶斯折衷方法，这在常规频率论推断中是不可能的。统一的发展可能会导致一个共同的计算程序的各种荟萃分析方法。它不仅具有理论价值，而且可以促进元分析的更广泛应用。该项目的进展将有助于解决本文提出的一系列具体问题，并刺激统计方法发展方面的新研究和应用。

In the modern era with explosive growth of information, it is important to process information in an efficient and meaningful manner. Statistical methodology of meta-analysis is a technique for enabling this. It has broad impacts and applications in social and behavioral sciences and medical research, among other fields. Indeed, formal and meaningful ways of combining data information from independent sources are important both theoretically and practically. Combined results from multiple studies summarize overall associations, and inferences from this are more robust and reliable than inferences from any single study.The goals of this proposal are to develop a unifying framework and new methodologies for combining information from independent sources, and to demonstrate the usefulness of the methodologies in a broad range of applications. The underlying tool of the proposed framework is confidence distributions (CDs). Although CD is a fundamental statistical inference concept with a long history, recent developments have redefined it with a focus on solving more complex real-life problems. The proposed framework based on CDs can unify most information combination methods used in the current practice, including both the classical p-value combination and the model based meta-analysis approaches. Furthermore, this framework of CD combination can lead to developments of new methodologies, such as: a) a robust meta-analysis approach, which can remove a critical constraint in current practice requiring all studies be of the same type and with the exact same parameter values; and b) a frequentist Bayes compromise approach to combining expert opinions with information in observed data, which is otherwise not possible in regular frequentist inference. The unifying development can potentially lead to a common computing program for various meta-analysis approaches. It not only has theoretical values, but can also promote broader applications of meta-analysis. Advances emerging from this project will help solve the specific set of problems set forth herein, and stimulate new research and applications in statistical methodological developments.