arXiv subjects

Scott Zeger

Publications and source records attributed to Scott Zeger.

11 recordsLinked to original sources

arXiv2026

Sufficient conditions for proper posteriors in fully-Bayesian Functional PCA

In a fully-Bayesian Functional Principal Components Analysis (FPCA) the principal components are treated as unknown infinite-dimensional parameters. By projecting the functional principal components on a rich orthonormal spline basis, we show that orthonormality of the principal components is equivalent to orthonormality of the spline coefficients. A penalty on the integral of the second derivative of the functional principal components can be induced on the spline coefficients, where each function has its own smoothing parameter. Finally, each smoothing parameter is treated as an inverse variance component in the associated mixed effects model. In this work, we demonstrate that no additional conditions are required to ensure that the corresponding smoothing prior, and thus the posterior distribution, is proper. This allows the choice of less informative priors, such that smoothing is driven by the data.

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arXiv2025

Bayesian Multivariate Sparse Functional Principal Components Analysis

Functional Principal Components Analysis (FPCA) provides a parsimonious, semi-parametric model for multivariate, sparsely-observed functional data. Frequentist FPCA approaches estimate principal components (PCs) from the data, then condition on these estimates in subsequent analyses. As an alternative, we propose a fully-Bayesian inferential framework for multivariate, sparse functional data (MSFAST) which explicitly models the PCs and incorporates their uncertainty. MSFAST builds upon the FAST approach to FPCA for univariate, densely-observed functional data. Like FAST, MSFAST represents PCs using orthonormal splines and samples the orthonormal spline coefficients using parameter expansion. MSFAST extends FAST to multivariate, sparsely-observed data by (1) standardizing each functional covariate to mitigate poor posterior conditioning due to disparate scales; (2) using a better-suited orthogonal spline basis; (3) updating parameterizations for computational stability; (4) introducing routines that leverage multiple cores and threads to accelerate compute; (5) using a Procrustes-based posterior PC alignment procedure; and (6) providing efficient prediction routines. We evaluate MSFAST alongside existing implementations using simulations. MSFAST produces uniquely valid inferences and accurate estimates, particularly in smaller signal-to-noise regimes. MSFAST is motivated by and applied to a study of child growth, with an accompanying vignette illustrating the implementation step-by-step.

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arXiv2024

Fast Bayesian Functional Principal Components Analysis

Functional Principal Components Analysis (FPCA) is a widely used analytic tool for dimension reduction of functional data. Traditional implementations of FPCA estimate the principal components from the data, then treat these estimates as fixed in subsequent analyses. To account for the uncertainty of PC estimates, we propose FAST, a fully-Bayesian FPCA with three core components: (1) projection of eigenfunctions onto an orthonormal spline basis; (2) efficient sampling of the orthonormal spline coefficient matrix using a parameter expansion scheme based on polar decomposition; and (3) ordering eigenvalues during sampling. Extensive simulation studies show that FAST is very stable and performs better compared to existing methods. FAST is motivated by and applied to a study of the variability in mealtime glucose from the Dietary Approaches to Stop Hypertension for Diabetes Continuous Glucose Monitoring (DASH4D CGM) study. All relevant STAN code and simulation routines are available as supplementary material.

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arXiv2024

Probabilistic Clustering using Shared Latent Variable Model for Assessing Alzheimers Disease Biomarkers

The preclinical stage of many neurodegenerative diseases can span decades before symptoms become apparent. Understanding the sequence of preclinical biomarker changes provides a critical opportunity for early diagnosis and effective intervention prior to significant loss of patients' brain functions. The main challenge to early detection lies in the absence of direct observation of the disease state and the considerable variability in both biomarkers and disease dynamics among individuals. Recent research hypothesized the existence of subgroups with distinct biomarker patterns due to co-morbidities and degrees of brain resilience. Our ability to early diagnose and intervene during the preclinical stage of neurodegenerative diseases will be enhanced by further insights into heterogeneity in the biomarker-disease relationship. In this paper, we focus on Alzheimer's disease (AD) and attempt to identify the systematic patterns within the heterogeneous AD biomarker-disease cascade. Specifically, we quantify the disease progression using a dynamic latent variable whose mixture distribution represents patient subgroups. Model estimation uses Hamiltonian Monte Carlo with the number of clusters determined by the Bayesian Information Criterion (BIC). We report simulation studies that investigate the performance of the proposed model in finite sample settings that are similar to our motivating application. We apply the proposed model to the BIOCARD data, a longitudinal study that was conducted over two decades among individuals who were initially cognitively normal. Our application yields evidence consistent with the hypothetical model of biomarker dynamics presented in Jack et al. (2013). In addition, our analysis identified two subgroups with distinct disease-onset patterns. Finally, we develop a dynamic prediction approach to improve the precision of prognoses.

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arXiv2023

Modeling Structure and Country-specific Heterogeneity in Misclassification Matrices of Verbal Autopsy-based Cause of Death Classifiers

Verbal autopsy (VA) algorithms are routinely used to determine individual-level causes of death (COD) in many low-and-middle-income countries, which are then aggregated to derive population-level cause-specific mortality fractions (CSMF), essential to informing public health policies. However, VA algorithms frequently misclassify COD and introduce bias in CSMF estimates. A recent method, VA-calibration, can correct for this bias using a VA misclassification matrix estimated from paired data on COD from both VA and minimally invasive tissue sampling (MITS) from the Child Health and Mortality Prevention Surveillance (CHAMPS) Network. Due to the limited sample size, CHAMPS data are pooled across all countries, implicitly assuming that the misclassification rates are homogeneous. In this research, we show that the VA misclassification matrices are substantially heterogeneous across countries, thereby biasing the VA-calibration. We develop a coherent framework for modeling country-specific misclassification matrices in data-scarce settings. We first introduce a novel base model based on two latent mechanisms: intrinsic accuracy and systematic preference to parsimoniously characterize misclassifications. We prove that they are identifiable from the data and manifest as a form of invariance in certain misclassification odds, a pattern evident in the CHAMPS data. Then we expand from this base model, adding higher complexity and country-specific heterogeneity via interpretable effect sizes. Shrinkage priors balance the bias-variance tradeoff by adaptively favoring simpler models. We publish uncertainty-quantified estimates of VA misclassification rates for 6 countries. This effort broadens VA-calibration's future applicability and strengthens ongoing efforts of using VA for mortality surveillance.

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arXiv2023

Causal Inference using Multivariate Generalized Linear Mixed-Effects Models with Longitudinal Data

Dynamic prediction of causal effects under different treatment regimes conditional on an individual's characteristics and longitudinal history is an essential problem in precision medicine. This is challenging in practice because outcomes and treatment assignment mechanisms are unknown in observational studies, an individual's treatment efficacy is a counterfactual, and the existence of selection bias is often unavoidable. We propose a Bayesian framework for identifying subgroup counterfactual benefits of dynamic treatment regimes by adapting Bayesian g-computation algorithm (J. Robins, 1986; Zhou, Elliott, & Little, 2019) to incorporate multivariate generalized linear mixed-effects models. Unmeasured time-invariant factors are identified as subject-specific random effects in the assumed joint distribution of outcomes, time-varying confounders, and treatment assignments. Existing methods mostly assume no unmeasured confounding and focus on balancing the observed confounder distributions between different treatments, while our method allows the presence of time-invariant unmeasured confounding. We propose a sequential ignorability assumption based on treatment assignment heterogeneity, which is analogous to balancing the latent tendency toward each treatment due to unmeasured time-invariant factors beyond the observables. We use simulation studies to assess the sensitivity of the proposed method's performance to various model assumptions. The method is applied to observational clinical data to investigate the efficacy of continuously using mycophenolate in different subgroups of scleroderma patients who were treated with the drug.

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arXiv2021

Generalized Bayes Quantification Learning under Dataset Shift

Quantification learning is the task of prevalence estimation for a test population using predictions from a classifier trained on a different population. Quantification methods assume that the sensitivities and specificities of the classifier are either perfect or transportable from the training to the test population. These assumptions are inappropriate in the presence of dataset shift, when the misclassification rates in the training population are not representative of those for the test population. Quantification under dataset shift has been addressed only for single-class (categorical) predictions and assuming perfect knowledge of the true labels on a small subset of the test population. We propose generalized Bayes quantification learning (GBQL) that uses the entire compositional predictions from probabilistic classifiers and allows for uncertainty in true class labels for the limited labeled test data. Instead of positing a full model, we use a model-free Bayesian estimating equation approach to compositional data based only on a first-moment assumption. The idea will be useful in Bayesian compositional data analysis in general as it is robust to different generating mechanisms for compositional data and includes categorical outputs as a special case. We show how our method yields existing quantification approaches as special cases. Extension to an ensemble GBQL that uses predictions from multiple classifiers yielding inference robust to inclusion of a poor classifier is discussed. We outline a fast and efficient Gibbs sampler using a rounding and coarsening approximation to the loss functions. We also establish posterior consistency, asymptotic normality and valid coverage of interval estimates from GBQL, as well as finite sample posterior concentration rate. Empirical performance of GBQL is demonstrated through simulations and analysis of real data with evident dataset shift.

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arXiv2020

A Transformation-free Linear Regression for Compositional Outcomes and Predictors

Compositional data are common in many fields, both as outcomes and predictor variables. The inventory of models for the case when both the outcome and predictor variables are compositional is limited and the existing models are difficult to interpret, due to their use of complex log-ratio transformations. We develop a transformation-free linear regression model where the expected value of the compositional outcome is expressed as a single Markov transition from the compositional predictor. Our approach is based on generalized method of moments thereby not requiring complete specification of data likelihood and is robust to different data generating mechanism. Our model is simple to interpret, allows for 0s and 1s in both the compositional outcome and covariates, and subsumes several interesting subcases of interest. We also develop a permutation test for linear independence. Finally, we show that despite its simplicity, our model accurately captures the relationship between compositional data from education and medical research.

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arXiv2019

Regularized Bayesian transfer learning for population level etiological distributions

Computer-coded verbal autopsy (CCVA) algorithms predict cause of death from high-dimensional family questionnaire data (verbal autopsies) of a deceased individual. CCVA algorithms are typically trained on non-local data, then used to generate national and regional estimates of cause-specific mortality fractions. These estimates may be inaccurate if the non-local training data is different from the local population of interest. This problem is a special case of transfer learning. However, most transfer learning classification approaches are concerned with individual (e.g. a person's) classification within a target domain (e.g. a particular population) with training performed in data from a source domain. Epidemiologists are often more interested in estimating population-level etiological distributions, using datasets much smaller than those used in common transfer learning applications. We present a parsimonious hierarchical Bayesian transfer learning framework to directly estimate population-level class probabilities in a target domain. To address small sample sizes, we introduce a novel shrinkage prior for the transfer error rates guaranteeing that, in absence of any labeled target domain data or when the baseline classifier has zero transfer error, the calibrated estimate of class probabilities coincides with the naive estimates from the baseline classifier, thereby subsuming the default practice as a special case. A novel Gibbs sampler using data-augmentation enables fast implementation. We extend our approach to use not one, but an ensemble of baseline classifiers. Theoretical and empirical results demonstrate how the ensemble model favors the most accurate baseline classifier. We present extensions allowing class probabilities to vary with covariates, and an EM-algorithm-based MAP estimation. An R-package implementing this method is developed.

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arXiv2017

Estimating AutoAntibody Signatures to Detect Autoimmune Disease Patient Subsets

Autoimmune diseases are characterized by highly specific immune responses against molecules in self-tissues. Different autoimmune diseases are characterized by distinct immune responses, making autoantibodies useful for diagnosis and prediction. In many diseases, the targets of autoantibodies are incompletely defined. Although the technologies for autoantibody discovery have advanced dramatically over the past decade, each of these techniques generates hundreds of possibilities, which are onerous and expensive to validate. We set out to establish a method to greatly simplify autoantibody discovery, using a pre-filtering step to define subgroups with similar specificities based on migration of radiolabeled, immunoprecipitated proteins on sodium dodecyl sulfate (SDS) gels and autoradiography [$\textbf{G}$el $\textbf{E}$lectrophoresis and band detection on $\textbf{A}$utoradiograms (GEA)]. Human recognition of patterns is not optimal when the patterns are complex or scattered across many samples. Multiple sources of errors - including irrelevant intensity differences and warping of gels - have challenged automation of pattern discovery from autoradiograms. In this paper, we address these limitations using a Bayesian hierarchical model with shrinkage priors for pattern alignment and spatial dewarping. The Bayesian model combines information from multiple gel sets and corrects spatial warping for coherent estimation of autoantibody signatures defined by presence or absence of a grid of landmark proteins. We show the pre-processing creates more clearly separated clusters and improves the accuracy of autoantibody subset detection via hierarchical clustering. Finally, we demonstrate the utility of the proposed methods with GEA data from scleroderma patients.

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arXiv2015

Nested Partially-Latent Class Models for Dependent Binary Data; Estimating Disease Etiology

The Pneumonia Etiology Research for Child Health (PERCH) study seeks to use modern measurement technology to infer the causes of pneumonia for which gold-standard evidence is unavailable. The paper describes a latent variable model designed to infer from case-control data the etiology distribution for the population of cases, and for an individual case given his or her measurements. We assume each observation is drawn from a mixture model for which each component represents one cause or disease class. The model addresses a major limitation of the traditional latent class approach by taking account of residual dependence among multivariate binary outcome given disease class, hence reduces estimation bias, retains efficiency and offers more valid inference. Such "local dependence" on a single subject is induced in the model by nesting latent subclasses within each disease class. Measurement precision and covariation can be estimated using the control sample for whom the class is known. In a Bayesian framework, we use stick-breaking priors on the subclass indicators for model-averaged inference across different numbers of subclasses. Assessment of model fit and individual diagnosis are done using posterior samples drawn by Gibbs sampling. We demonstrate the utility of the method on simulated and on the motivating PERCH data.

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