Department of Biostatistics and Health Data Science, Indiana University School of Medicine, Indianapolis, Indiana, USA.
Department of Biostatistics and Bioinformatics, Rollins School of Public Health, Emory University, Atlanta, Georgia, USA.
Stat Med. 2021 Sep 30;40(22):4772-4793. doi: 10.1002/sim.9093. Epub 2021 Jun 8.
Existing missing data methods for functional data mainly focus on reconstructing missing measurements along a single function-a univariate functional data setting. Motivated by a renal study, we focus on a bivariate functional data setting, where each sampling unit is a collection of two distinct component functions, one of which may be missing. Specifically, we propose a Bayesian multiple imputation approach based on a bivariate functional latent factor model that exploits the joint changing patterns of the component functions to allow accurate and stable imputation of one component given the other. We further extend the framework to address multilevel bivariate functional data with missing components by modeling and exploiting inter-component and intra-subject correlations. We develop a Gibbs sampling algorithm that simultaneously generates multiple imputations of missing component functions and posterior samples of model parameters. For multilevel bivariate functional data, a partially collapsed Gibbs sampler is implemented to improve computational efficiency. Our simulation study demonstrates that our methods outperform other competing methods for imputing missing components of bivariate functional data under various designs and missingness rates. The motivating renal study aims to investigate the distribution and pharmacokinetic properties of baseline and post-furosemide renogram curves that provide further insights into the underlying mechanism of renal obstruction, with post-furosemide renogram curves missing for some subjects. We apply the proposed methods to impute missing post-furosemide renogram curves and obtain more refined insights.
现有的功能数据缺失数据方法主要集中于在单变量功能数据设置中重建缺失的测量值。受肾脏研究的启发，我们关注于双变量功能数据设置，其中每个采样单元是两个不同分量函数的集合，其中一个可能缺失。具体来说，我们提出了一种基于双变量功能潜在因子模型的贝叶斯多重插补方法，该方法利用分量函数的联合变化模式，允许在给定另一个分量的情况下准确和稳定地插补一个分量。我们进一步扩展了该框架，通过对组件间和主体内相关性进行建模和利用，来解决具有缺失组件的多层次双变量功能数据。我们开发了一种 Gibbs 抽样算法，该算法可以同时生成缺失组件函数的多重插补和模型参数的后验样本。对于多层次双变量功能数据，实现了部分折叠 Gibbs 抽样器以提高计算效率。我们的模拟研究表明，在各种设计和缺失率下，我们的方法在插补双变量功能数据的缺失组件方面优于其他竞争方法。该肾脏研究旨在探讨基线和速尿后肾图曲线的分布和药代动力学特性，这些特性为深入了解肾脏阻塞的潜在机制提供了进一步的见解，其中一些受试者的速尿后肾图曲线缺失。我们应用所提出的方法来插补缺失的速尿后肾图曲线，并获得更精细的见解。
