arXiv subjects

Farouk S. Nathoo

Publications and source records attributed to Farouk S. Nathoo.

16 recordsLinked to original sources

arXiv2026

A Wavelet-Based Framework for Mapping Long Memory in Resting-State fMRI: Age-Related Changes in the Hippocampus from the ADHD-200 Dataset

Functional magnetic resonance imaging (fMRI) time series are known to exhibit long-range temporal dependencies that challenge traditional modeling approaches. In this study, we propose a novel computational pipeline to characterize and interpret these dependencies using a long-memory (LM) framework, which captures the slow, power-law decay of autocorrelation in resting-state fMRI (rs-fMRI) signals. The pipeline involves voxelwise estimation of LM parameters via a wavelet-based Bayesian method, yielding spatial maps that reflect temporal dependence across the brain. These maps are then projected onto a lower-dimensional space via a composite basis and are then related to individual-level covariates through group-level regression. We applied this approach to the ADHD-200 dataset and found significant positive associations between age in children and the LM parameter in the hippocampus, after adjusting for ADHD symptom severity and medication status. These findings complement prior neuroimaging work by linking long-range temporal dependence to developmental changes in memory-related brain regions. Overall, the proposed methodology enables detailed mapping of intrinsic temporal dynamics in rs-fMRI and offers new insights into the relationship between functional signal memory and brain development.

stat.AP↗

arXiv2025

Generalized Jeffreys's approximate objective Bayes factor: Model-selection consistency, finite-sample accuracy, and statistical evidence in 71,126 clinical trial findings

Concerns about the misuse and misinterpretation of p-values and statistical significance have motivated alternatives for quantifying evidence. We define a generalized form of Jeffreys's approximate objective Bayes factor (eJAB), a one-line calculation that is a function of the p-value, sample size, and parameter dimension. We establish conditions under which eJAB is model-selection consistent and verify them for ten statistical tests. We assess finite-sample accuracy by comparing eJAB with Markov chain Monte Carlo computed Bayes factors in 12 simulation studies. We then apply eJAB to 71,126 results from ClinicalTrials.gov (CTG) and find that the proportion of findings with $\text{p-value} \le α$ yet $eJAB_{01}>1$ (favoring the null) closely tracks the significance level $α$, suggesting that such contradictions are pointing to the type I errors. We catalog 4,088 such candidate type I errors and provide details for 131 with reported $\text{p-value} \le 0.01$. We also identify 487 instances of the Jeffreys-Lindley paradox. Finally, we estimate that 75% (6%) of clinical trial plans from CTG set $α\ge 0.05$ as the target evidence threshold, and that 35.5% (0.22%) of results significant at $α=0.05$ correspond to evidence that is no stronger than anecdotal under eJAB.

stat.ME↗

arXiv2025

Survival Analysis with Discrete Biomarkers Under a Semiparametric Bayesian Conditional Poisson Model

Discrete biomarkers derived as cell densities or counts from tissue microarrays and immunostaining are widely used to study immune signatures in relation to survival outcomes in cancer. Although routinely collected, these signatures are not measured with exact precision because the sampling mechanism involves examination of small tissue cores from a larger section of interest. We model these error-prone biomarkers as Poisson processes with latent rates, inducing heteroscedasticity in their conditional variance. While critical for tumor histology, such measurement error frameworks remain understudied for conditionally Poisson-distributed covariates. To address this, we propose a Bayesian joint model that incorporates a Dirichlet process (DP) mixture to flexibly characterize the latent covariate distribution. The proposed approach is evaluated using simulation studies which demonstrate a superior bias reduction and robustness to the underlying model in realistic settings when compared to existing methods. We further incorporate Bayes factors for hypothesis testing in the Bayesian semiparametric joint model. The methodology is applied to a survival study of high-grade serous carcinoma where comparisons are made between the proposed and existing approaches. Accompanying R software is available at the GitHub repository listed in the Web Appendices.

stat.ME↗

arXiv2025

POI-SIMEX for Conditionally Poisson Distributed Biomarkers from Tissue Histology

Covariate measurement error in regression analysis is an important issue that has been studied extensively under the classical additive and the Berkson error models. Here, we consider cases where covariates are derived from tumor tissue histology, and in particular tissue microarrays. In such settings, biomarkers are evaluated from tissue cores that are subsampled from a larger tissue section so that these biomarkers are only estimates of the true cell densities. The resulting measurement error is non-negligible but is seldom accounted for in the analysis of cancer studies involving tissue microarrays. To adjust for this type of measurement error, we assume that these discrete-valued biomarkers are conditionally Poisson distributed, based on a Poisson process model governing the spatial locations of marker-positive cells. Existing methods for addressing conditional Poisson surrogates, particularly in the absence of internal validation data, are limited. We extend the simulation extrapolation (SIMEX) algorithm to accommodate the conditional Poisson case (POI-SIMEX), where measurement errors are non-Gaussian with heteroscedastic variance. The proposed estimator is shown to be strongly consistent in a linear regression model under the assumption of a conditional Poisson distribution for the observed biomarker. Simulation studies evaluate the performance of POI-SIMEX, comparing it with the naive method and an alternative corrected likelihood approach in linear regression and survival analysis contexts. POI-SIMEX is then applied to a study of high-grade serous cancer, examining the association between survival and the presence of triple-positive biomarker (CD3+CD8+FOXP3+ cells)

stat.ME↗

arXiv2025

Strong Consistency of the SIMEX Estimator in Linear Regression with a Conditionally Poisson Covariate

This paper considers estimation for linear regression analysis with covariate measurement error arising from Poisson surrogates. We consider cases where covariates follow a conditional Poisson distribution, capturing non-Gaussian and heteroscedastic error structures. To address this, we extend the simulation extrapolation (SIMEX) algorithm to the conditional Poisson setting (POI-SIMEX), enabling robust adjustment in the absence of internal validation data. Theoretical analysis establishes strong consistency of the POI-SIMEX estimator under a linear regression framework.

math.ST↗

arXiv2022

Neuroimaging Feature Extraction using a Neural Network Classifier for Imaging Genetics

A major issue in the association of genes to neuroimaging phenotypes is the high dimension of both genetic data and neuroimaging data. In this article, we tackle the latter problem with an eye toward developing solutions that are relevant for disease prediction. Supported by a vast literature on the predictive power of neural networks, our proposed solution uses neural networks to extract from neuroimaging data features that are relevant for predicting Alzheimer's Disease (AD) for subsequent relation to genetics. Our neuroimaging-genetic pipeline is comprised of image processing, neuroimaging feature extraction and genetic association steps. We propose a neural network classifier for extracting neuroimaging features that are related with disease and a multivariate Bayesian group sparse regression model for genetic association. We compare the predictive power of these features to expert selected features and take a closer look at the SNPs identified with the new neuroimaging features.

q-bio.QM↗

arXiv2020

Spectral Dynamic Causal Modelling of Resting-State fMRI: Relating Effective Brain Connectivity in the Default Mode Network to Genetics

We conduct an imaging genetics study to explore how effective brain connectivity in the default mode network (DMN) may be related to genetics within the context of Alzheimer's disease and mild cognitive impairment. We develop an analysis of longitudinal resting-state functional magnetic resonance imaging (rs-fMRI) and genetic data obtained from a sample of 111 subjects with a total of 319 rs-fMRI scans from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. A Dynamic Causal Model (DCM) is fit to the rs-fMRI scans to estimate effective brain connectivity within the DMN and related to a set of single nucleotide polymorphisms (SNPs) contained in an empirical disease-constrained set which is obtained out-of-sample from 663 ADNI subjects having only genome-wide data. We examine longitudinal data in both a 4-region and an 6-region network and relate longitudinal effective brain connectivity networks estimated using spectral DCM to SNPs using both linear mixed effect (LME) models as well as function-on-scalar regression (FSR). In the former case we implement a parametric bootstrap for testing SNP coefficients and make comparisons with p-values obtained from the chi-squared null distribution. We also implement a parametric bootstrap approach for testing regression functions in FSR and we make comparisons between p-values obtained from the parametric bootstrap to p-values obtained using the F-distribution with degrees-of-freedom based on Satterthwaite's approximation. In both networks we report on exploratory patterns of associations with relatively high ranks that exhibit stability to the differing assumptions made by both FSR and LME.

q-bio.NC↗

arXiv2020

A Bayesian Spatial Model for Imaging Genetics

We develop a Bayesian bivariate spatial model for multivariate regression analysis applicable to studies examining the influence of genetic variation on brain structure. Our model is motivated by an imaging genetics study of the Alzheimer's Disease Neuroimaging Initiative (ADNI), where the objective is to examine the association between images of volumetric and cortical thickness values summarizing the structure of the brain as measured by magnetic resonance imaging (MRI) and a set of 486 SNPs from 33 Alzheimer's Disease (AD) candidate genes obtained from 632 subjects. A bivariate spatial process model is developed to accommodate the correlation structures typically seen in structural brain imaging data. First, we allow for spatial correlation on a graph structure in the imaging phenotypes obtained from a neighbourhood matrix for measures on the same hemisphere of the brain. Second, we allow for correlation in the same measures obtained from different hemispheres (left/right) of the brain. We develop a mean-field variational Bayes algorithm and a Gibbs sampling algorithm to fit the model. We also incorporate Bayesian false discovery rate (FDR) procedures to select SNPs. We implement the methodology in a new release of the R package bgsmtr. We show that the new spatial model demonstrates superior performance over a standard model in our application. Data used in the preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu).

stat.ME↗

arXiv2019

A Potts-Mixture Spatiotemporal Joint Model for Combined MEG and EEG Data

We develop a new methodology for determining the location and dynamics of brain activity from combined magnetoencephalography (MEG) and electroencephalography (EEG) data. The resulting inverse problem is ill-posed and is one of the most difficult problems in neuroimaging data analysis. In our development we propose a solution that combines the data from three different modalities, MRI, MEG, and EEG, together. We propose a new Bayesian spatial finite mixture model that builds on the mesostate-space model developed by Daunizeau and Friston (2007). Our new model incorporates two major extensions: (i) We combine EEG and MEG data together and formulate a joint model for dealing with the two modalities simultaneously; (ii) we incorporate the Potts model to represent the spatial dependence in an allocation process that partitions the cortical surface into a small number of latent states termed mesostates. The cortical surface is obtained from MRI. We formulate the new spatiotemporal model and derive an efficient procedure for simultaneous point estimation and model selection based on the iterated conditional modes algorithm combined with local polynomial smoothing. The proposed method results in a novel estimator for the number of mixture components and is able to select active brain regions which correspond to active variables in a high-dimensional dynamic linear model. The methodology is investigated using synthetic data and simulation studies and then demonstrated on an application examining the neural response to the perception of scrambled faces. R software implementing the methodology along with several sample datasets are available at the following GitHub repository https://github.com/v2south/PottsMix.

stat.AP↗

arXiv2018

A Better (Bayesian) Interval Estimate for Within-Subject Designs

We develop a Bayesian highest-density interval (HDI) for use in within-subject designs. This credible interval is based on a standard noninformative prior and a modified posterior distribution that conditions on both the data and point estimates of the subject-specific random effects. Conditioning on the estimated random effects removes between-subject variance and produces intervals that are the Bayesian analogue of the within-subject confidence interval proposed in Loftus and Masson (1994). We show that the latter interval can also be derived as a Bayesian within-subject HDI under a certain improper prior. We argue that the proposed new interval is superior to the original within-subject confidence interval, on the grounds of (a) it being based on a more sensible prior, (b) it having a clear and intuitively appealing interpretation, and (c) because its length is always smaller. A generalization of the new interval that can be applied to heteroscedastic data is also derived, and we show that the resulting interval is numerically equivalent to the normalization method discussed in Franz and Loftus (2012); however, our work provides a Bayesian formulation for the normalization method, and in doing so we identify the associated prior distribution.

stat.ME↗

arXiv2018

A Review of Statistical Methods in Imaging Genetics

With the rapid growth of modern technology, many large-scale biomedical studies have been/are being/will be conducted to collect massive datasets with large volumes of multi-modality imaging, genetic, neurocognitive, and clinical information from increasingly large cohorts. Simultaneously extracting and integrating rich and diverse heterogeneous information in neuroimaging and/or genomics from these big datasets could transform our understanding of how genetic variants impact brain structure and function, cognitive function, and brain-related disease risk across the lifespan. Such understanding is critical for diagnosis, prevention, and treatment of numerous complex brain-related disorders (e.g., schizophrenia and Alzheimer). However, the development of analytical methods for the joint analysis of both high-dimensional imaging phenotypes and high-dimensional genetic data, called big data squared (BD$^2$), presents major computational and theoretical challenges for existing analytical methods. Besides the high-dimensional nature of BD$^2$, various neuroimaging measures often exhibit strong spatial smoothness and dependence and genetic markers may have a natural dependence structure arising from linkage disequilibrium. We review some recent developments of various statistical techniques for the joint analysis of BD$^2$, including massive univariate and voxel-wise approaches, reduced rank regression, mixture models, and group sparse multi-task regression. By doing so, we hope that this review may encourage others in the statistical community to enter into this new and exciting field of research.

stat.ME↗

arXiv2017

Bayesian Analysis of fMRI data with Spatially-Varying Autoregressive Orders

Statistical modeling of fMRI data is challenging as the data are both spatially and temporally correlated. Spatially, measurements are taken at thousands of contiguous regions, called voxels, and temporally measurements are taken at hundreds of time points at each voxel. Recent advances in Bayesian hierarchical modeling have addressed the challenges of spatiotemproal structure in fMRI data with models incorporating both spatial and temporal priors for signal and noise. While there has been extensive research on modeling the fMRI signal (i.e., the covolution of the experimental design with the functional choice for the hemodynamic response function) and its spatial variability, less attention has been paid to realistic modeling of the temporal dependence that typically exists within the fMRI noise, where a low order autoregressive process is typically adopted. Furthermore, the AR order is held constant across voxels (e.g. AR(1) at each voxel). Motivated by an event-related fMRI experiment, we propose a novel hierarchical Bayesian model with automatic selection of the autoregressive orders of the noise process that vary spatially over the brain. With simulation studies we show that our model has improved accuracy and apply it to our motivating example.

stat.CO↗

arXiv2017

Bayesian Computation for Log-Gaussian Cox Processes--A Comparative Analysis of Methods

The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point patterns. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the first level and a Gaussian Process at the second level. Different methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulations studies as well as through applications examining both ecological data and neuroimaging data.

stat.CO↗

arXiv2016

A Bayesian Group Sparse Multi-Task Regression Model for Imaging Genetics

Motivation: Recent advances in technology for brain imaging and high-throughput genotyping have motivated studies examining the influence of genetic variation on brain structure. Wang et al. (Bioinformatics, 2012) have developed an approach for the analysis of imaging genomic studies using penalized multi-task regression with regularization based on a novel group $l_{2,1}$-norm penalty which encourages structured sparsity at both the gene level and SNP level. While incorporating a number of useful features, the proposed method only furnishes a point estimate of the regression coefficients; techniques for conducting statistical inference are not provided. A new Bayesian method is proposed here to overcome this limitation. Results: We develop a Bayesian hierarchical modeling formulation where the posterior mode corresponds to the estimator proposed by Wang et al. (Bioinformatics, 2012), and an approach that allows for full posterior inference including the construction of interval estimates for the regression parameters. We show that the proposed hierarchical model can be expressed as a three-level Gaussian scale mixture and this representation facilitates the use of a Gibbs sampling algorithm for posterior simulation. Simulation studies demonstrate that the interval estimates obtained using our approach achieve adequate coverage probabilities that outperform those obtained from the nonparametric bootstrap. Our proposed methodology is applied to the analysis of neuroimaging and genetic data collected as part of the Alzheimer's Disease Neuroimaging Initiative (ADNI), and this analysis of the ADNI cohort demonstrates clearly the value added of incorporating interval estimation beyond only point estimation when relating SNPs to brain imaging endophenotypes.

stat.ME↗

arXiv2016

Regularization Parameter Selection for a Bayesian Multi-Level Group Lasso Regression Model with Application to Imaging Genomics

We investigate the choice of tuning parameters for a Bayesian multi-level group lasso model developed for the joint analysis of neuroimaging and genetic data. The regression model we consider relates multivariate phenotypes consisting of brain summary measures (volumetric and cortical thickness values) to single nucleotide polymorphism (SNPs) data and imposes penalization at two nested levels, the first corresponding to genes and the second corresponding to SNPs. Associated with each level in the penalty is a tuning parameter which corresponds to a hyperparameter in the hierarchical Bayesian formulation. Following previous work on Bayesian lassos we consider the estimation of tuning parameters through either hierarchical Bayes based on hyperpriors and Gibbs sampling or through empirical Bayes based on maximizing the marginal likelihood using a Monte Carlo EM algorithm. For the specific model under consideration we find that these approaches can lead to severe overshrinkage of the regression parameter estimates in the high-dimensional setting or when the genetic effects are weak. We demonstrate these problems through simulation examples and study an approximation to the marginal likelihood which sheds light on the cause of this problem. We then suggest an alternative approach based on the widely applicable information criterion (WAIC), an asymptotic approximation to leave-one-out cross-validation that can be computed conveniently within an MCMC framework.

stat.ML↗

arXiv2015

High-Dimensional Classification for Brain Decoding

Brain decoding involves the determination of a subject's cognitive state or an associated stimulus from functional neuroimaging data measuring brain activity. In this setting the cognitive state is typically characterized by an element of a finite set, and the neuroimaging data comprise voluminous amounts of spatiotemporal data measuring some aspect of the neural signal. The associated statistical problem is one of classification from high-dimensional data. We explore the use of functional principal component analysis, mutual information networks, and persistent homology for examining the data through exploratory analysis and for constructing features characterizing the neural signal for brain decoding. We review each approach from this perspective, and we incorporate the features into a classifier based on symmetric multinomial logistic regression with elastic net regularization. The approaches are illustrated in an application where the task is to infer, from brain activity measured with magnetoencephalography (MEG), the type of video stimulus shown to a subject.

stat.ML↗