Mixtures of factor analyzers with covariates for modeling multiply censored dependent variables

Lower Prevalence of Asymptomatic Alzheimer's Disease Among Healthy African Americans

OBJECTIVE

Alzheimer's disease (AD) is believed to be more common in African Americans (AA), but biomarker studies in AA populations are limited. This report represents the largest study to date examining cerebrospinal fluid AD biomarkers in AA individuals.

METHODS

We analyzed 3,006 cerebrospinal fluid samples from controls, AD cases, and non-AD cases, including 495 (16.5%) self-identified black/AA and 2,456 (81.7%) white/European individuals using cutoffs derived from the Alzheimer's Disease Neuroimaging Initiative, and using a data-driven multivariate Gaussian mixture of regressions.

RESULTS

Distinct effects of race were found in different groups. Total Tauand phospho181-Tau were lower among AA individuals in all groups (p < 0.0001), and Aβ42 was markedly lower in AA controls compared with white controls (p < 0.0001). Gaussian mixture of regressions modeling of cerebrospinal fluid distributions incorporating adjustments for covariates revealed coefficient estimates for AA race comparable with 2-decade change in age. Using Alzheimer's Disease Neuroimaging Initiative cutoffs, fewer AA controls were classified as biomarker-positive asymptomatic AD (8.0% vs 13.4%). After adjusting for covariates, our Gaussian mixture of regressions model reduced this difference, but continued to predict lower prevalence of asymptomatic AD among AA controls (9.3% vs 13.5%).

INTERPRETATION

Although the risk of dementia is higher, data-driven modeling indicates lower frequency of asymptomatic AD in AA controls, suggesting that dementia among AA populations may not be driven by higher rates of AD. ANN NEUROL 2024;96:463-475.

Mixtures of t $$ t $$ factor analysers with censored responses and external covariates: An application to educational data from Peru

Analysing data from educational tests allows governments to make decisions for improving the quality of life of individuals in a society. One of the key responsibilities of statisticians is to develop models that provide decision-makers with pertinent information about the latent process that educational tests seek to represent. Mixtures oft $$ t $$ factor analysers (MtFA) have emerged as a powerful device for model-based clustering and classification of high-dimensional data containing one or several groups of observations with fatter tails or anomalous outliers. This paper considers an extension of MtFA for robust clustering of censored data, referred to as the MtFAC model, by incorporating external covariates. The enhanced flexibility of including covariates in MtFAC enables cluster-specific multivariate regression analysis of dependent variables with censored responses arising from upper and/or lower detection limits of experimental equipment. An alternating expectation conditional maximization (AECM) algorithm is developed for maximum likelihood estimation of the proposed model. Two simulation experiments are conducted to examine the effectiveness of the techniques presented. Furthermore, the proposed methodology is applied to Peruvian data from the 2007 Early Grade Reading Assessment, and the results obtained from the analysis provide new insights regarding the reading skills of Peruvian students.

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.