Distributed Estimation and Inference for the Analysis of Big Biomedical Data

Abstract

This thesis focuses on developing and implementing new statistical methods to address some of the current difficulties encountered in the analysis of high-dimensional correlated biomedical data. Following the divide-and-conquer paradigm, I develop a theoretically sound and computationally tractable class of distributed statistical methods that are made accessible to practitioners through R statistical software. This thesis aims to establish a class of distributed statistical methods for regression analyses with very large outcome variables arising in many biomedical fields, such as in metabolomic or imaging research. The general distributed procedure divides data into blocks that are analyzed on a parallelized computational platform and combines these separate results via Hansen’s (1982) generalized method of moments. These new methods provide distributed and efficient statistical inference in many different regression settings. Computational efficiency is achieved by leveraging recent developments in large scale computing, such as the MapReduce paradigm on the Hadoop platform. In the first project presented in Chapter III, I develop a divide-and-conquer procedure implemented in a parallelized computational scheme for statistical estimation and inference of regression parameters with high-dimensional correlated responses. This project is motivated by an electroencephalography study whose goal is to determine the effect of iron deficiency on infant auditory recognition memory. The proposed method (published as Hector and Song (2020a)), the Distributed and Integrated Method of Moments (DIMM), divides responses into subvectors to be analyzed in parallel using pairwise composite likelihood, and combines results using an optimal one-step meta-estimator. In the second project presented in Chapter IV, I develop an extended theoretical framework of distributed estimation and inference to incorporate a broad range of classical statistical models and biomedical data types. To reduce computational speed and meet data privacy demands, I propose to divide data by outcomes and subjects, leading to a doubly divide-and-conquer paradigm. I also address parameter heterogeneity explicitly for added flexibility. I establish a new theoretical framework for the analysis of a broad class of big data problems to facilitate valid statistical inference for biomedical researchers. Possible applications include genomic data, metabolomic data, longitudinal and spatial data, and many more. In the third project presented in Chapter V, I propose a distributed quadratic inference function framework to jointly estimate regression parameters from multiple potentially heterogeneous data sources with correlated vector outcomes. This project is motivated by the analysis of the association between smoking and metabolites in a large cohort study. The primary goal of this joint integrative analysis is to estimate covariate effects on all outcomes through a marginal regression model in a statistically and computationally efficient way. To overcome computational and modeling challenges arising from the high-dimensional likelihood of the correlated vector outcomes, I propose to analyze each data source using Qu et al.’s quadratic inference funtions, and then to jointly reestimate parameters from each data source by accounting for correlation between data sources.