arXiv subjects

Tianzhou Ma

Publications and source records attributed to Tianzhou Ma.

9 recordsLinked to original sources

arXiv2025

A novel multi-exposure-to-multi-mediator mediation model for imaging genetic study of brain disorders

Common psychiatric and brain disorders are highly heritable and affected by a number of genetic risk factors, yet the mechanism by which these genetic factors contribute to the disorders through alterations in brain structure and function remain poorly understood. Contemporary imaging genetic studies integrate genetic and neuroimaging data to investigate how genetic variation contributes to brain disorders via intermediate neuroimaging endophenotypes. However, the large number of potential exposures (genes) and mediators (neuroimaging features) pose new challenges to the traditional mediation analysis. In this paper, we propose a novel multi-exposure-to-multi-mediator mediation model that integrates genetic, neuroimaging and phenotypic data to investigate the "geneneuroimaging-brain disorder" mediation pathway. Our method jointly reduces the dimensions of exposures and mediators into low-dimensional aggregators where the mediation effect is maximized. We further introduce sparsity into the loadings to improve the interpretability. To target the bi-convex optimization problem, we implement an efficient alternating direction method of multipliers algorithm with block coordinate updates. We provide theoretical guarantees for the convergence of our algorithm and establish the asymptotic properties of the resulting estimators. Through extensive simulations, we demonstrate that our method outperforms other competing methods in recovering true loadings and true mediation proportions across a wide range of signal strengths, noise levels, and correlation structures. We further illustrate the utility of the method through a mediation analysis that integrates genetic, brain functional connectivity and smoking behavior data from UK Biobank, and identifies critical genes that impact nicotine dependence via changing the functional connectivity in specific brain regions.

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arXiv2025

The Effect of Alcohol intake on Brain White Matter Microstructural Integrity: A New Causal Inference Framework for Incomplete Phenomic Data

Although substance use, such as alcohol intake, is known to be associated with cognitive decline during aging, its direct influence on the central nervous system remains incompletely understood. In this study, we investigate the influence of alcohol intake frequency on reduction of brain white matter microstructural integrity in the fornix, a brain region considered a promising marker of age-related microstructural degeneration, using a large UK Biobank (UKB) cohort with extensive phenomic data reflecting a comprehensive lifestyle profile. Two major challenges arise: 1) potentially nonlinear confounding effects from phenomic variables and 2) a limited proportion of participants with complete phenomic data. To address these challenges, we develop a novel ensemble learning framework tailored for robust causal inference and introduce a data integration step to incorporate information from UKB participants with incomplete phenomic data, improving estimation efficiency. Our analysis reveals that daily alcohol intake may significantly reduce fractional anisotropy, a neuroimaging-derived measure of white matter structural integrity, in the fornix and increase systolic and diastolic blood pressure levels. Moreover, extensive numerical studies demonstrate the superiority of our method over competing approaches in terms of estimation bias, while outcome regression-based estimators may be preferred when minimizing mean squared error is prioritized.

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arXiv2025

Graph Canonical Correlation Analysis

Canonical correlation analysis (CCA) is a widely used technique for estimating associations between two sets of multi-dimensional variables. Recent advancements in CCA methods have expanded their application to decipher the interactions of multiomics datasets, imaging-omics datasets, and more. However, conventional CCA methods are limited in their ability to incorporate structured patterns in the cross-correlation matrix, potentially leading to suboptimal estimations. To address this limitation, we propose the graph Canonical Correlation Analysis (gCCA) approach, which calculates canonical correlations based on the graph structure of the cross-correlation matrix between the two sets of variables. We develop computationally efficient algorithms for gCCA, and provide theoretical results for finite sample analysis of best subset selection and canonical correlation estimation by introducing concentration inequalities and stopping time rule based on martingale theories. Extensive simulations demonstrate that gCCA outperforms competing CCA methods. Additionally, we apply gCCA to a multiomics dataset of DNA methylation and RNA-seq transcriptomics, identifying both positively and negatively regulated gene expression pathways by DNA methylation pathways.

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arXiv2024

Semi-Confirmatory Factor Analysis for High-Dimensional Data with Interconnected Community Structures

Confirmatory factor analysis (CFA) is a statistical method for identifying and confirming the presence of latent factors among observed variables through the analysis of their covariance structure. Compared to alternative factor models, CFA offers interpretable common factors with enhanced specificity and a more adaptable approach to covariance structure modeling. However, the application of CFA has been limited by the requirement for prior knowledge about "non-zero loadings" and by the lack of computational scalability (e.g., it can be computationally intractable for hundreds of observed variables). We propose a data-driven semi-confirmatory factor analysis (SCFA) model that attempts to alleviate these limitations. SCFA automatically specifies "non-zero loadings" by learning the network structure of the large covariance matrix of observed variables, and then offers closed-form estimators for factor loadings, factor scores, covariances between common factors, and variances between errors using the likelihood method. Therefore, SCFA is applicable to high-throughput datasets (e.g., hundreds of thousands of observed variables) without requiring prior knowledge about "non-zero loadings". Through an extensive simulation analysis benchmarking against standard packages, SCFA exhibits superior performance in estimating model parameters with a much-reduced computational time. We illustrate its practical application through factor analysis on two high-dimensional RNA-seq gene expression datasets.

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arXiv2024

Multivariate Bayesian variable selection with application to multi-trait genetic fine mapping

Variable selection has played a critical role in modern statistical learning and scientific discoveries. Numerous regularization and Bayesian variable selection methods have been developed in the past two decades for variable selection, but most of these methods consider selecting variables for only one response. As more data is being collected nowadays, it is common to analyze multiple related responses from the same study. Existing multivariate variable selection methods select variables for all responses without considering the possible heterogeneity across different responses, i.e. some features may only predict a subset of responses but not the rest. Motivated by the multi-trait fine mapping problem in genetics to identify the causal variants for multiple related traits, we developed a novel multivariate Bayesian variable selection method to select critical predictors from a large number of grouped predictors that target at multiple correlated and possibly heterogeneous responses. Our new method is featured by its selection at multiple levels, its incorporation of prior biological knowledge to guide selection and identification of best subset of responses predictors target at. We showed the advantage of our method via extensive simulations and a real fine mapping example to identify causal variants associated with different subsets of addictive behaviors.

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arXiv2022

Robust distance correlation for variable screening

High-dimensional data are commonly seen in modern statistical applications, variable selection methods play indispensable roles in identifying the critical features for scientific discoveries. Traditional best subset selection methods are computationally intractable with a large number of features, while regularization methods such as Lasso, SCAD and their variants perform poorly in ultrahigh-dimensional data due to low computational efficiency and unstable algorithm. Sure screening methods have become popular alternatives by first rapidly reducing the dimension using simple measures such as marginal correlation then applying any regularization methods. A number of screening methods for different models or problems have been developed, however, none of the methods have targeted at data with heavy tailedness, which is another important characteristics of modern big data. In this paper, we propose a robust distance correlation (``RDC'') based sure screening method to perform screening in ultrahigh-dimensional regression with heavy-tailed data. The proposed method shares the same good properties as the original model-free distance correlation based screening while has additional merit of robustly estimating the distance correlation when data is heavy-tailed and improves the model selection performance in screening. We conducted extensive simulations under different scenarios of heavy tailedness to demonstrate the advantage of our proposed procedure as compared to other existing model-based or model-free screening procedures with improved feature selection and prediction performance. We also applied the method to high-dimensional heavy-tailed RNA sequencing (RNA-seq) data of The Cancer Genome Atlas (TCGA) pancreatic cancer cohort and RDC was shown to outperform the other methods in prioritizing the most essential and biologically meaningful genes.

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arXiv2022

Bayesian response adaptive randomization design with a composite endpoint of mortality and morbidity

Allocating patients to treatment arms during a trial based on the observed responses accumulated prior to the decision point, and sequential adaptation of this allocation,, could minimize the expected number of failures or maximize total benefit to patients. In this study, we developed a Bayesian response adaptive randomization (RAR) design targeting the endpoint of organ support-free days (OSFD) for patients admitted to the intensive care units (ICU). The OSFD is a mixture of mortality and morbidity assessed by the number of days of free of organ support within a predetermined time-window post-randomization. In the past, researchers treated OSFD as an ordinal outcome variable where the lowest category is death. We propose a novel RAR design for a composite endpoint of mortality and morbidity, e.g., OSFD, by using a Bayesian mixture model with a Markov chain Monte Carlo sampling to estimate the posterior probability of OSFD and determine treatment allocation ratios at each interim. Simulations were conducted to compare the performance of our proposed design under various randomization rules and different alpha spending functions. The results show that our RAR design using Bayesian inference allocated more patients to the better performing arm(s) compared to other existing adaptive rules while assuring adequate power and type I error rate control for the across a range of plausible clinical scenarios.

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arXiv2020

A sparse negative binomial mixture model for clustering RNA-seq count data

Clustering with variable selection is a challenging yet critical task for modern small-n-large-p data. Existing methods based on sparse Gaussian mixture models or sparse K-means provide solutions to continuous data. With the prevalence of RNA-seq technology and lack of count data modeling for clustering, the current practice is to normalize count expression data into continuous measures and apply existing models with Gaussian assumption. In this paper, we develop a negative binomial mixture model with lasso or fused lasso gene regularization to cluster samples (small n) with high-dimensional gene features (large p). EM algorithm and Bayesian information criterion are used for inference and determining tuning parameters. The method is compared with existing methods using extensive simulations and two real transcriptomic applications in rat brain and breast cancer studies. The result shows superior performance of the proposed count data model in clustering accuracy, feature selection and biological interpretation in pathways.

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arXiv2017

Variable screening with multiple studies

Advancement in technology has generated abundant high-dimensional data that allows integration of multiple relevant studies. Due to their huge computational advantage, variable screening methods based on marginal correlation have become promising alternatives to the popular regularization methods for variable selection. However, all these screening methods are limited to single study so far. In this paper, we consider a general framework for variable screening with multiple related studies, and further propose a novel two-step screening procedure using a self-normalized estimator for high-dimensional regression analysis in this framework. Compared to the one-step procedure and rank-based sure independence screening (SIS) procedure, our procedure greatly reduces false negative errors while keeping a low false positive rate. Theoretically, we show that our procedure possesses the sure screening property with weaker assumptions on signal strengths and allows the number of features to grow at an exponential rate of the sample size. In addition, we relax the commonly used normality assumption and allow sub-Gaussian distributions. Simulations and a real transcriptomic application illustrate the advantage of our method as compared to the rank-based SIS method.

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