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

There is no gold standard for the diagnosis of Alzheimer's disease (AD), except from 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 3,000 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 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.