arXiv subjects

Jeremy T. Gaskins

Publications and source records attributed to Jeremy T. Gaskins.

9 recordsLinked to original sources

arXiv2026

Linked-Tucker Factorized Individualized Regression for Paired Multivariate Categorical Outcomes

We propose a joint individualized hurdle-ordinal regression model for paired zero-inflated ordinal outcomes with subject-specific, spatially varying, and time-varying covariate effects, motivated by the Iowa Fluoride Study (IFS). The two outcomes, dental caries and dental fluorosis, are measured repeatedly across ages at fine spatial resolution, yielding nested longitudinal data with substantial zero inflation, ordinality, and heterogeneity across individuals and locations. For each outcome, a hurdle component models disease presence, while a proportional-odds component models severity among positive observations. To parsimoniously represent the high-dimensional coefficient arrays, we introduce a linked Tucker tensor factorization. Shared subject-mode factors induce dependence between the caries and fluorosis coefficient tensors, while separate spatial factors accommodate the distinct measurement grids of tooth surfaces and tooth zones. A horseshoe prior on the core tensor elements encourages sparsity, and posterior computation is performed using the No-U-Turn Sampler in NumPyro. Population-level effect summaries are obtained by projecting individualized posterior linear predictors onto the design space, and Wasserstein barycenters aggregate these summaries across tooth locations and anatomical classes. Applied to the IFS, the model reveals spatially heterogeneous associations between early-life fluoride and dietary exposures and both outcomes. Fluoride exposure is associated with increased odds and severity of fluorosis, while soda intake consistently increases caries risk. These associations differ between presence and severity components and vary across tooth locations, ages, and subpopulations defined by prior caries status, highlighting the importance of the joint hurdle-ordinal framework for disentangling disease occurrence from disease progression in multilevel dental data.

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arXiv2026

Covariate Informed Identification of Heterogeneity and Outliers in Longitudinal Data

We often observe heterogeneity in longitudinal data, where the mean and variance for certain profiles meaningfully differ from the rest. Some profiles may also exhibit outliers at a limited number of measurements. Using a standard mixed effects model, which assumes homogeneity, can lead to overestimating the residual variance and inefficient estimation. In this work, we identify and account for three sources of heterogeneity in longitudinal data: incompatible mean trajectories, increased residual variance, and outliers at individual measurements. Our Bayesian mixture model incorporates binary indicators of heterogeneity for each of these features, modeled through logistic regression using covariates. We perform statistical inference using Markov chain Monte Carlo and implement model selection to evaluate the inclusion of various heterogeneous components. Simulations demonstrate that our model can accurately identify heterogeneity and produce efficient estimates of the fixed effects parameters. We further validate our approach using the DHEAS hormone data from the SWAN study.

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arXiv2025

Predictor-Informed Bayesian Nonparametric Clustering

In this project we are interested in performing clustering of observations such that the cluster membership is influenced by a set of predictors. To that end, we employ the Bayesian nonparameteric Common Atoms Model, which is a nested clustering algorithm that utilizes a (fixed) group membership for each observation to encourage more similar clustering of members of the same group. CAM operates by assuming each group has its own vector of cluster probabilities, which are themselves clustered to allow similar clustering for some groups. We extend this approach by treating the group membership as an unknown latent variable determined as a flexible nonparametric form of the covariate vector. Consequently, observations with similar predictor values will be in the same latent group and are more likely to be clustered together than observations with disparate predictors. We propose a pyramid group model that flexibly partitions the predictor space into these latent group memberships. This pyramid model operates similarly to a Bayesian regression tree process except that it uses the same splitting rule for at all nodes at the same tree depth which facilitates improved mixing. We outline a block Gibbs sampler to perform posterior inference from our model. Our methodology is demonstrated in simulation and real data examples. In the real data application, we utilize the RAND Health and Retirement Study to cluster and predict patient outcomes in terms of the number of overnight hospital stays.

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arXiv2025

Analyzing zero-inflated clustered longitudinal ordinal outcomes using GEE-type models with an application to dental fluorosis studies

Motivated by the Iowa Fluoride Study (IFS), which tracked fluoride intake and dental outcomes from childhood to young adulthood (ages 9, 13, 17, and 23), we analyze dental fluorosis - a condition caused by excessive fluoride exposure during enamel formation. In this context, fluorosis scores across tooth surfaces present as zero-inflated, clustered, and longitudinal ordinal outcomes, prompting the development of a unified modeling framework. Leveraging generalized estimating equations (GEEs), we construct separate models for the presence and severity of fluorosis and propose a combined model that links these components though shared covariates. To improve estimation efficiency and borrowing strength across timepoints, we incorporate James-Stein shrinkage estimators. We compare several working correlation structures, including a data-driven jackknifed structure, and perform model selection via rank aggregation. Simulation studies validate the finite-sample performance of the proposed models, and a bootstrap-based power analysis further confirms the validity of the testing procedure. In our analysis of the IFS data, early-life total daily fluoride intake, average home water fluoride concentration, and specific teeth and zones emerge as significant risk factors for dental fluorosis. Maxillary lateral incisors and zones closer to the gum show protective effects across different ages. These findings reveal novel age-specific associations between early-life exposures and the progression of dental fluorosis through early adulthood.

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arXiv2024

Modeling Zero-Inflated Correlated Dental Data through Gaussian Copulas and Approximate Bayesian Computation

We develop a new longitudinal count data regression model that accounts for zero-inflation and spatio-temporal correlation across responses. This project is motivated by an analysis of Iowa Fluoride Study (IFS) data, a longitudinal cohort study with data on caries (cavity) experience scores measured for each tooth across five time points. To that end, we use a hurdle model for zero-inflation with two parts: the presence model indicating whether a count is non-zero through logistic regression and the severity model that considers the non-zero counts through a shifted Negative Binomial distribution allowing overdispersion. To incorporate dependence across measurement occasion and teeth, these marginal models are embedded within a Gaussian copula that introduces spatio-temporal correlations. A distinct advantage of this formulation is that it allows us to determine covariate effects with population-level (marginal) interpretations in contrast to mixed model choices. Standard Bayesian sampling from such a model is infeasible, so we use approximate Bayesian computing for inference. This approach is applied to the IFS data to gain insight into the risk factors for dental caries and the correlation structure across teeth and time.

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arXiv2023

A Bayesian Methodology for Estimation for Sparse Canonical Correlation

It can be challenging to perform an integrative statistical analysis of multi-view high-dimensional data acquired from different experiments on each subject who participated in a joint study. Canonical Correlation Analysis (CCA) is a statistical procedure for identifying relationships between such data sets. In that context, Structured Sparse CCA (ScSCCA) is a rapidly emerging methodological area that aims for robust modeling of the interrelations between the different data modalities by assuming the corresponding CCA directional vectors to be sparse. Although it is a rapidly growing area of statistical methodology development, there is a need for developing related methodologies in the Bayesian paradigm. In this manuscript, we propose a novel ScSCCA approach where we employ a Bayesian infinite factor model and aim to achieve robust estimation by encouraging sparsity in two different levels of the modeling framework. Firstly, we utilize a multiplicative Half-Cauchy process prior to encourage sparsity at the level of the latent variable loading matrices. Additionally, we promote further sparsity in the covariance matrix by using graphical horseshoe prior or diagonal structure. We conduct multiple simulations to compare the performance of the proposed method with that of other frequently used CCA procedures, and we apply the developed procedures to analyze multi-omics data arising from a breast cancer study.

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arXiv2023

Fast Bayesian High-Dimensional Gaussian Graphical Model Estimation

Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the precision matrix. However, in high dimensional cases, standard covariance estimates are typically unstable. Moreover, it is natural to expect only a few significant associations to be present in many realistic applications. This necessitates the injection of sparsity techniques into the estimation. Classical frequentist methods use penalization for this purpose; in contrast, fully Bayesian methods are computationally slow, typically requiring iterative sampling over a quadratic number of parameters in a space constrained by positive definiteness. We propose a Bayesian graph estimation method based on an ensemble of Bayesian neighborhood regressions. An attractive feature of our methods is the ability for easy parallelization across separate graphical neighborhoods, invoking computational efficiency greater than most existing methods. Our strategy induces sparsity with a Horseshoe shrinkage prior and includes a novel variable selection step based on the marginal likelihood from the predictors ranks. Our method appropriately combines the estimated regression coefficients to produce a graph estimate and a matrix of partial correlation estimates for inference. Performance of various methods are assessed using measures like FDR and TPR. Competitive performance across a variety of cases is demonstrated through extensive simulations. Lastly, we apply these methods to investigate the dependence structure across genetic expressions for women with triple negative breast cancer.

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arXiv2019

Bayesian Variable Selection for Multi-Outcome Models Through Shared Shrinkage

Variable selection over a potentially large set of covariates in a linear model is quite popular. In the Bayesian context, common prior choices can lead to a posterior expectation of the regression coefficients that is a sparse (or nearly sparse) vector with a few non-zero components, those covariates that are most important. This article extends the global-local shrinkage idea to a scenario where one wishes to model multiple response variables simultaneously. Here, we have developed a variable selection method for a K-outcome model (multivariate regression) that identifies the most important covariates across all outcomes. The prior for all regression coefficients is a mean zero normal with coefficient-specific variance term that consists of a predictor-specific factor (shared local shrinkage parameter) and a model-specific factor (global shrinkage term) that differs in each model. The performance of our modeling approach is evaluated through simulation studies and a data example.

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arXiv2017

A Bayesian Nonparametric Model for Predicting Pregnancy Outcomes Using Longitudinal Profiles

Across several medical fields, developing an approach for disease classification is an important challenge. The usual procedure is to fit a model for the longitudinal response in the healthy population, a different model for the longitudinal response in disease population, and then apply the Bayes' theorem to obtain disease probabilities given the responses. Unfortunately, when substantial heterogeneity exists within each population, this type of Bayes classification may perform poorly. In this paper, we develop a new approach by fitting a Bayesian nonparametric model for the joint outcome of disease status and longitudinal response, and then use the clustering induced by the Dirichlet process in our model to increase the flexibility of the method, allowing for multiple subpopulations of healthy, diseased, and possibly mixed membership. In addition, we introduce an MCMC sampling scheme that facilitates the assessment of the inference and prediction capabilities of our model. Finally, we demonstrate the method by predicting pregnancy outcomes using longitudinal profiles on the $β$--HCG hormone levels in a sample of Chilean women being treated with assisted reproductive therapy.

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