Fusion Pursuit for Pattern-Mixture Models with Application to Longitudinal Studies with Nonignorable Missing Data

缺失数据在科学研究中无处不在，这对统计分析的准确性提出了挑战，统计分析的结果最终将产生知识并指导政策或决策。该项目旨在开发一套新的统计工具，以应对在分析具有不可忽视的遗漏的纵向研究中的挑战，例如信息性辍学。首席研究员将把一种称为融合追踪的机器学习方法纳入模式混合建模框架，以在纵向关联分析中实现更有效的估计和推理。这些方法将被广泛用于调查、医学和政策研究，以及其他涉及大量缺失数据的纵向研究的领域。该项目还将把研究与研究生的培训结合起来，通过研究参与和教学来培养受训人员。该项目将扩展模式混合模型在分析非随机缺失的纵向数据方面的估计和推理能力。该研究在广义估计方程的框架下，提出了一种分层后融合追踪策略，以克服模式混合模型在分析大规模数据集时的瓶颈--缺失模式造成的过度分层。该项目将首先开发一种正则化方法，以同时折叠冗余的缺失数据模式层并估计感兴趣的参数。为了确保有效的统计推断，该项目随后将开发一种融合后推理方法，以得出有效和可推广的置信度区域。最后，该项目将在真实世界纵向研究的三种情况下演示所开发的方法，包括缺失访问、缺失协变量和分布式数据。该研究项目预计将扩大模式混合模型在分析缺少数据的纵向研究中的用例。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Missing data is ubiquitous in scientific research, challenging the accuracy of statistical analyses, the results of which will ultimately generate knowledge and guide policy or decision making. This project aims to develop a suite of new statistical tools to address the challenges in analyzing longitudinal studies with nonignorable missingness, such as informative dropout. The principal investigator will incorporate a machine learning approach termed fusion pursuit into the pattern-mixture modeling framework to achieve more efficient estimation and inference in longitudinal association analyses. The methods will find broad use in survey, medical, and policy research, and in other areas that involve longitudinal studies with a heavy presence of missing data. The project will also integrate research with the training of graduate students, developing trainees in the topics proposed through research involvement and teaching.The project will extend the estimation and inference capabilities of pattern-mixture models in analyzing longitudinal data that are subject to missing not at random. Formulated in the framework of generalized estimating equations, this research develops a post-stratification fusion pursuit strategy to overcome over-stratification by missing-data patterns, which is the bottleneck of pattern-mixture models in analyzing large-scale data sets. The project will first develop a regularization approach to simultaneously collapse redundant missing-data pattern strata and estimate parameters of interest. To ensure valid statistical inference, the project will then develop a post-fusion inference approach to derive valid and generalizable confidence regions. Finally, the project will demonstrate the developed approaches in three situations of real-world longitudinal studies, including missing visits, missing covariates, and distributed data. The research project is expected to broaden the use cases of pattern-mixture models in analyzing longitudinal studies with missing data.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.