Mixture of Regressions with Multivariate Responses for Discovering Subtypes in Alzheimer’s Biomarkers with Detection Limits

• Type of Material: Article
• Authors: Ganzhong Tian, Emory University; John Hanfelt, Emory University; James J Lah, Emory University; Benjamin Risk, Emory University
• Language: English
• Date: 2024-03-06
• Publisher: Taylor & Francis
• Publication Version: Final Published Version
• Copyright Statement: © 2024 The Author(s). Published with license by Taylor & Francis Group, LLC
• License: Creative Commons Attribution 4.0 International
• Final Published Version (URL): https://doi.org/10.1080/26941899.2024.2309403
• Title of Journal or Parent Work: Data Science in Science
• Volume: 3
• Issue: 1
• Start Page: 2309403
• Grant/Funding Information: G.T. was supported by R01 AG055634 and R01 AG070937. B.B.R. was supported by R21 AG066970. J.H. was supported by R01 AG055634 and P30 AG066511. J.L. was supported by R01 AG070937 and P30 AG066511. Funding for materials for Roche Elecsys assays were supported by a Roche IIS grant RD004723 to J.L. Additional funding for this work was provided by a generous gift from the Goizueta Foundation.
• Keywords: truncated normal; Tobit model; latent class analysis; unsupervised learning; censored Gaussian mixture of regressions; finite mixture model; Alzheimer's disease; clustering
• Research Categories: Biology, Neuroscience; Psychology, Cognitive

Abstract

There is no gold standard for the diagnosis of Alzheimer’s disease (AD), except for autopsies, which motivates the use of unsupervised learning. A mixture of regressions is an unsupervised method that can simultaneously identify clusters from multiple biomarkers while learning within-cluster demographic effects. Cerebrospinal fluid (CSF) biomarkers for AD have detection limits, which create additional challenges. We apply a mixture of regressions with a multivariate truncated Gaussian distribution (also called a censored multivariate Gaussian mixture of regressions or a mixture of multivariate Tobit regressions) to over 3000 participants from the Emory Goizueta Alzheimer’s Disease Research Center and Emory Healthy Brain Study to examine amyloid-beta peptide 1–42 (Abeta42), total tau protein and phosphorylated tau protein in CSF with known detection limits. We address three gaps in the literature on the mixture of regressions with a truncated multivariate Gaussian distribution: software availability; inference; and clustering accuracy. We discovered three clusters that tend to align with an AD group, a normal control profile, and non-AD pathology. The CSF profiles differed by race, gender, and the genetic marker ApoE4, highlighting the importance of considering demographic factors in unsupervised learning with detection limits. Notably, African American participants in the AD-like group had significantly lower tau burden.