arXiv subjects

Thaddeus Tarpey

Publications and source records attributed to Thaddeus Tarpey.

14 recordsLinked to original sources

arXiv2026

Clarifying identification and estimation of treatment effects in the Sequential Parallel Comparison Design

Sequential parallel comparison design (SPCD) clinical trials aim to adjust active treatment effect estimates for placebo response to minimize the impact of placebo responders on the estimates. This is potentially accomplished using a two stage design by measuring treatment effects among all participants during the first stage, then classifying some placebo arm participants as placebo non-responders who will be re-randomized in the second stage. In this paper, we use causal inference tools to clarify under what assumptions treatment effects can be identified in SPCD trials and what effects the conventional estimators target at each stage of the SPCD trial. We further illustrate the highly influential impact of placebo response misclassification on the second stage estimate. We conclude that the conventional SPCD estimators do not target meaningful treatment effects.

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arXiv2025

K-Tensors: Clustering Positive Semi-Definite Matrices

This paper presents a new clustering algorithm for symmetric positive semi-definite (SPSD) matrices, called K-Tensors. The method identifies structured subsets of the SPSD cone characterized by common principal component (CPC) representations, where each subset corresponds to matrices sharing a common eigenstructure. Unlike conventional clustering approaches that rely on vectorization or transformations of SPSD matrices, thereby losing critical geometric and spectral information, K-Tensors introduces a divergence that respects the intrinsic geometry of SPSD matrices. This divergence preserves the shape and eigenstructure information and yields principal SPSD tensors, defined as a set of representative matrices that summarize the distribution of SPSD matrices. By exploring its theoretical properties, we show that the proposed clustering algorithm is self-consistent under mild distribution assumptions and converges to a local optimum. We demonstrate the use of the algorithm through an application to resting-state functional magnetic resonance imaging (rs-fMRI) data from the Human Connectome Project, where we cluster brain connectivity matrices to discover groups of subjects with shared connectivity structures.

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arXiv2025

Bayesian Mixed-Effects Models for Multilevel Two-way Functional Data: Applications to EEG Experiments

In multi-condition EEG experiments, brain activity is recorded as subjects perform various tasks or are exposed to different stimuli. The recorded signals are commonly transformed into time-frequency representations, which often display smooth variations across time and frequency dimensions. These representations are naturally structured as two-way functional data, with experimental conditions nested within subjects. Existing analytical methods fail to jointly account for the data's multilevel structure, functional nature, and dependence on subject-level covariates. To address these limitations, we propose a Bayesian mixed-effects model for two-way functional data that incorporates covariate-dependent fixed effects at the condition level and multilevel random effects. For enhanced model interpretability and parsimony, we introduce a novel covariate-dependent CANDECOMP/PARAFAC (CP) decomposition for the fixed effects, with marginally interpretable time and frequency patterns. We further propose a sparsity-inducing prior for CP rank selection and an efficient algorithm for posterior sampling. The proposed method is evaluated through extensive simulations and applied to EEG data collected to investigate the effects of alcoholism on cognitive processing in response to visual stimuli. Our analysis reveals distinct patterns of time-frequency activity associated with alcoholism, offering new insights into the neural processing differences between subject groups and experimental conditions.

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arXiv2024

Projection-pursuit Bayesian regression for symmetric matrix predictors

This paper develops a novel Bayesian approach for nonlinear regression with symmetric matrix predictors, often used to encode connectivity of different nodes. Unlike methods that vectorize matrices as predictors that result in a large number of model parameters and unstable estimation, we propose a Bayesian multi-index regression method, resulting in a projection-pursuit-type estimator that leverages the structure of matrix-valued predictors. We establish the model identifiability conditions and impose a sparsity-inducing prior on the projection directions for sparse sampling to prevent overfitting and enhance interpretability of the parameter estimates. Posterior inference is conducted through Bayesian backfitting. The performance of the proposed method is evaluated through simulation studies and a case study investigating the relationship between brain connectivity features and cognitive scores.

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arXiv2024

Trajectory-Based Individualized Treatment Rules

A core component of precision medicine research involves optimizing individualized treatment rules (ITRs) based on patient characteristics. Many studies used to estimate ITRs are longitudinal in nature, collecting outcomes over time. Yet, to date, methods developed to estimate ITRs often ignore the longitudinal structure of the data. Information available from the longitudinal nature of the data can be especially useful in mental health studies. Although treatment means might appear similar, understanding the trajectory of outcomes over time can reveal important differences between treatments and placebo effects. This longitudinal perspective is especially beneficial in mental health research, where subtle shifts in outcome patterns can hold significant implications. Despite numerous studies involving the collection of outcome data across various time points, most precision medicine methods used to develop ITRs overlook the information available from the longitudinal structure. The prevalence of missing data in such studies exacerbates the issue, as neglecting the longitudinal nature of the data can significantly impair the effectiveness of treatment rules. This paper develops a powerful longitudinal trajectory-based ITR construction method that incorporates baseline variables, via a single-index or biosignature, into the modeling of longitudinal outcomes. This trajectory-based ITR approach substantially minimizes the negative impact of missing data compared to more traditional ITR approaches. The approach is illustrated through simulation studies and a clinical trial for depression, contrasting it with more traditional ITRs that ignore longitudinal information.

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arXiv2024

Bayesian scalar-on-network regression with applications to brain functional connectivity

This paper presents a Bayesian regression model relating scalar outcomes to brain functional connectivity represented as symmetric positive definite (SPD) matrices. Unlike many proposals that simply vectorize the matrix-valued connectivity predictors thereby ignoring their geometric structure, the method presented here respects the Riemannian geometry of SPD matrices by using a tangent space modeling. Dimension reduction is performed in the tangent space, relating the resulting low-dimensional representations to the responses. The dimension reduction matrix is learned in a supervised manner with a sparsity-inducing prior imposed on a Stiefel manifold to prevent overfitting. Our method yields a parsimonious regression model that allows uncertainty quantification of all model parameters and identification of key brain regions that predict the outcomes. We demonstrate the performance of our approach in simulation settings and through a case study to predict Picture Vocabulary scores using data from the Human Connectome Project.

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arXiv2024

Extracting Scalar Measures from Curves

The ability to order outcomes is necessary to make comparisons which is complicated when there is no natural ordering on the space of outcomes, as in the case of functional outcomes. This paper examines methods for extracting a scalar summary from functional or longitudinal outcomes based on an average rate of change which can be used to compare curves. Common approaches used in practice use a change score or an analysis of covariance (ANCOVA) to make comparisons. However, these standard approaches only use a fraction of the available data and are inefficient. We derive measures of performance of an averaged rate of change of a functional outcome and compare this measure to standard measures. Simulations and data from a depression clinical trial are used to illustrate results.

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arXiv2022

Bayesian index models for heterogeneous treatment effects

The general idea of this article is to develop a Bayesian model with a flexible link function connecting an exponential family treatment response to a linear combination of covariates and a treatment indicator and the interaction between the two. Generalized linear models allowing data-driven link functions are often called "single-index models," and among popular semi-parametric modeling methods. In this article, we will focus on modeling heterogeneous treatment effects, with the goal of developing a treatment benefit index (TBI) incorporating prior information from historical data. This treatment benefit index can be useful for stratifying patients according to their predicted treatment benefit levels and can be especially useful for precision health applications. The proposed method is applied to a COVID-19 treatment study.

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arXiv2022

A Single Index Model for Longitudinal Outcomes to Optimize Individual Treatment Decision Rules

A pressing challenge in medical research is to identify optimal treatments for individual patients. This is particularly challenging in mental health settings where mean responses are often similar across multiple treatments. For example, the mean longitudinal trajectories for patients treated with an active drug and placebo may be very similar but different treatments may exhibit distinctly different individual trajectory shapes. Most precision medicine approaches using longitudinal data often ignore information from the longitudinal data structure. This paper investigates a powerful precision medicine approach by examining the impact of baseline covariates on longitudinal outcome trajectories to guide treatment decisions instead of traditional scalar outcome measures derived from longitudinal data, such as a change score. We introduce a method of estimating "biosignatures" defined as linear combinations of baseline characteristics (i.e., a single index) that optimally separate longitudinal trajectories among different treatment groups. The criterion used is to maximize the Kullback-Leibler Divergence between different treatment outcome distributions. The approach is illustrated via simulation studies and a depression clinical trial. The approach is also contrasted with more traditional methods and compares performance in the presence of missing data.

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arXiv2022

Unsupervised Bayesian classification for models with scalar and functional covariates

We consider unsupervised classification by means of a latent multinomial variable which categorizes a scalar response into one of L components of a mixture model. This process can be thought as a hierarchical model with first level modelling a scalar response according to a mixture of parametric distributions, the second level models the mixture probabilities by means of a generalised linear model with functional and scalar covariates. The traditional approach of treating functional covariates as vectors not only suffers from the curse of dimensionality since functional covariates can be measured at very small intervals leading to a highly parametrised model but also does not take into account the nature of the data. We use basis expansion to reduce the dimensionality and a Bayesian approach to estimate the parameters while providing predictions of the latent classification vector. By means of a simulation study we investigate the behaviour of our approach considering normal mixture model and zero inflated mixture of Poisson distributions. We also compare the performance of the classical Gibbs sampling approach with Variational Bayes Inference.

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arXiv2021

A single-index model with a surface-link for optimizing individualized dose rules

This paper focuses on the problem of modeling and estimating interaction effects between covariates and a continuous treatment variable on an outcome, using a single-index regression approach. The primary motivation is to estimate an optimal individualized dose rule in an observational study. To model possibly nonlinear interaction effects between patients' covariates and a continuous treatment variable, we employ a two-dimensional penalized spline regression on an index-treatment domain, where the index is defined as a linear projection of the covariates. The method is illustrated using two applications as well as simulation experiments. A unique contribution of this work is in the parsimonious (single-index) parametrization specifically defined for the interaction effect term.

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arXiv2021

Functional additive models for optimizing individualized treatment rules

A novel functional additive model is proposed which is uniquely modified and constrained to model nonlinear interactions between a treatment indicator and a potentially large number of functional and/or scalar pretreatment covariates. The primary motivation for this approach is to optimize individualized treatment rules based on data from a randomized clinical trial. We generalize functional additive regression models by incorporating treatment-specific components into additive effect components. A structural constraint is imposed on the treatment-specific components in order to provide a class of additive models with main effects and interaction effects that are orthogonal to each other. If primary interest is in the interaction between treatment and the covariates, as is generally the case when optimizing individualized treatment rules, we can thereby circumvent the need to estimate the main effects of the covariates, obviating the need to specify their form and thus avoiding the issue of model misspecification. The methods are illustrated with data from a depression clinical trial with electroencephalogram functional data as patients' pretreatment covariates.

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arXiv2020

Sufficient Dimension Reduction for Interactions

Dimension reduction lies at the heart of many statistical methods. In regression, dimension reduction has been linked to the notion of sufficiency whereby the relation of the response to a set of predictors is explained by a lower dimensional subspace in the predictor space. In this paper, we consider the notion of a dimension reduction in regression on subspaces that are sufficient to explain interaction effects between predictors and another variable of interest. The motivation for this work is from precision medicine where the performance of an individualized treatment rule, given a set of pretreatment predictors, is determined by interaction effects.

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arXiv2020

A constrained sparse additive model for treatment effect-modifier selection

Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. This paper develops a sparse additive model focused on estimation of treatment effect-modification with simultaneous treatment effect-modifier selection. We propose a version of the sparse additive model uniquely constrained to estimate the interaction effects between treatment and pretreatment covariates, while leaving the main effects of the pretreatment covariates unspecified. The proposed regression model can effectively identify treatment effect-modifiers that exhibit possibly nonlinear interactions with the treatment variable, that are relevant for making optimal treatment decisions. A set of simulation experiments and an application to a dataset from a randomized clinical trial are presented to demonstrate the method.

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