WAVELET-DOMAIN REGRESSION AND PREDICTIVE INFERENCE IN PSYCHIATRIC NEUROIMAGING

Identifying causal subsequent memory effects

Over 40 y of accumulated research has detailed associations between neuroimaging signals measured during a memory encoding task and later memory performance, across a variety of brain regions, measurement tools, statistical approaches, and behavioral tasks. But the interpretation of these subsequent memory effects (SMEs) remains unclear: if the identified signals reflect cognitive and neural mechanisms of memory encoding, then the underlying neural activity must be causally related to future memory. However, almost all previous SME analyses do not control for potential confounders of this causal interpretation, such as serial position and item effects. We collect a large fMRI dataset and use an experimental design and analysis approach that allows us to statistically adjust for nearly all known exogenous confounding variables. We find that, using standard approaches without adjustment, we replicate several univariate and multivariate subsequent memory effects and are able to predict memory performance across people. However, we are unable to identify any signal that reliably predicts subsequent memory after adjusting for confounding variables, bringing into doubt the causal status of these effects. We apply the same approach to subjects' judgments of learning collected following an encoding period and show that these behavioral measures of mnemonic status do predict memory after adjustments, suggesting that it is possible to measure signals near the time of encoding that reflect causal mechanisms but that existing neuroimaging measures, at least in our data, may not have the precision and specificity to do so.

Multi-task Learning with High-Dimensional Noisy Images

Recent medical imaging studies have given rise to distinct but inter-related datasets corresponding to multiple experimental tasks or longitudinal visits. Standard scalar-on-image regression models that fit each dataset separately are not equipped to leverage information across inter-related images, and existing multi-task learning approaches are compromised by the inability to account for the noise that is often observed in images. We propose a novel joint scalar-on-image regression framework involving wavelet-based image representations with grouped penalties that are designed to pool information across inter-related images for joint learning, and which explicitly accounts for noise in high-dimensional images via a projection-based approach. In the presence of non-convexity arising due to noisy images, we derive non-asymptotic error bounds under non-convex as well as convex grouped penalties, even when the number of voxels increases exponentially with sample size. A projected gradient descent algorithm is used for computation, which is shown to approximate the optimal solution via well-defined non-asymptotic optimization error bounds under noisy images. Extensive simulations and application to a motivating longitudinal Alzheimer's disease study illustrate significantly improved predictive ability and greater power to detect true signals, that are simply missed by existing methods without noise correction due to the attenuation to null phenomenon.

Estimating the effect of friction on crash risk: Reducing the effect of omitted variable bias that results from spatial correlation

Omitted variable bias is one of the main factors that lead to incorrect estimates of the effect of a variable on the expected number of crashes using regression modeling. We propose to use differencing of the (spatially adjacent) variables to reduce the effect of omitted variable bias. Differencing is a linear transformation that preserves the structure of the (generalized) linear model but can often result in significantly reducing the correlation between the variables. It is special case of (generalized) partial linear model regression which itself is a special case of a generalized additive model (GAM). In the spatial context used in this paper, differencing is similar to the well-known approach of including a spatial correlation structure (spatial error term) in the analysis of crash data. It is generally not clear how to interpret the results of models that include a spatial correlation structure and whether and how the added spatial correlation structure reduces the bias in the estimated regression parameters. However, for the case of differencing, it becomes clear how the effect of omitted variable bias is reduced by reducing the correlation between the variable of interest and the omitted variables. The order of differencing determines the dominant spatial scales of the variables considered in the model which affect how much the correlation is reduced. This reveals that omitted variable bias can be reduced when there are spatial scales at which the covariate of interest varies but the omitted variables either 1) are relatively homogeneous or 2) have variations that are not correlated to those of the variable of interest.

A New Adaptive Spatial Filtering Method in the Wavelet Domain for Medical Images

Although there are many methods in the literature to eliminate noise from images, finding new methods remains a challenge in the field and, despite the complexity of existing methods, many of the methods do not reach a sufficient level of applicability, most often due to the relatively high calculation time. In addition, most existing methods perform well when the processed image is adapted to the algorithm, but otherwise fail or results in significant artifacts. The context of eliminating noise from images is similar to that of improving images and for this reason some notions necessary to understand the proposed method will be repeated. An adaptive spatial filter in the wavelet domain is proposed by soft truncation of the wavelet coefficients with threshold value adapted to the local statistics of the image and correction based on the hierarchical correlation map. The filter exploits, in a new way, both the inter-band and the bandwidth dependence of the wavelet coefficients, considering the minimization of computational resources.

A Spatio-Temporal Model for Longitudinal Image-on-Image Regression

Neurologists and radiologists often use magnetic resonance imaging (MRI) in the management of subjects with multiple sclerosis (MS) because it is sensitive to inflammatory and demyelinative changes in the white matter of the brain and spinal cord. Two conventional modalities used for identifying lesions are T1-weighted (T1) and T2-weighted fluid-attenuated inversion recovery (FLAIR) imaging, which are used clinically and in research studies. Magnetization transfer ratio (MTR), which is available only in research settings, is an advanced MRI modality that has been used extensively for measuring disease-related demyelination both in white matter lesions as well across normal-appearing white matter. Acquiring MTR is not standard in clinical practice, due to the increased scan time and cost. Hence, prediction of MTR based on the modalities T1 and FLAIR could have great impact on the availability of these promising measures for improved patient management. We propose a spatio-temporal regression model for image response and image predictors that are acquired longitudinally, with images being co-registered within the subject but not across subjects. The model is additive, with the response at a voxel being dependent on the available covariates not only through the current voxel but also on the imaging information from the voxels within a neighboring spatial region as well as their temporal gradients. We propose a dynamic Bayesian estimation procedure that updates the parameters of the subject-specific regression model as data accummulates. To bypass the computational challenges associated with a Bayesian approach for high-dimensional imaging data, we propose an approximate Bayesian inference technique. We assess the model fitting and the prediction performance using longitudinally acquired MRI images from 46 MS patients.

The impact of model assumptions in scalar-on-image regression

Complex statistical models such as scalar-on-image regression often require strong assumptions to overcome the issue of nonidentifiability. While in theory, it is well understood that model assumptions can strongly influence the results, this seems to be underappreciated, or played down, in practice. This article gives a systematic overview of the main approaches for scalar-on-image regression with a special focus on their assumptions. We categorize the assumptions and develop measures to quantify the degree to which they are met. The impact of model assumptions and the practical usage of the proposed measures are illustrated in a simulation study and in an application to neuroimaging data. The results show that different assumptions indeed lead to quite different estimates with similar predictive ability, raising the question of their interpretability. We give recommendations for making modeling and interpretation decisions in practice based on the new measures and simulations using hypothetic coefficient images and the observed data.

A Bayesian Spatial Model to Predict Disease Status Using Imaging Data From Various Modalities

Relating disease status to imaging data stands to increase the clinical significance of neuroimaging studies. Many neurological and psychiatric disorders involve complex, systems-level alterations that manifest in functional and structural properties of the brain and possibly other clinical and biologic measures. We propose a Bayesian hierarchical model to predict disease status, which is able to incorporate information from both functional and structural brain imaging scans. We consider a two-stage whole brain parcellation, partitioning the brain into 282 subregions, and our model accounts for correlations between voxels from different brain regions defined by the parcellations. Our approach models the imaging data and uses posterior predictive probabilities to perform prediction. The estimates of our model parameters are based on samples drawn from the joint posterior distribution using Markov Chain Monte Carlo (MCMC) methods. We evaluate our method by examining the prediction accuracy rates based on leave-one-out cross validation, and we employ an importance sampling strategy to reduce the computation time. We conduct both whole-brain and voxel-level prediction and identify the brain regions that are highly associated with the disease based on the voxel-level prediction results. We apply our model to multimodal brain imaging data from a study of Parkinson's disease. We achieve extremely high accuracy, in general, and our model identifies key regions contributing to accurate prediction including caudate, putamen, and fusiform gyrus as well as several sensory system regions.

Scalar-on-Image Regression via the Soft-Thresholded Gaussian Process

This work concerns spatial variable selection for scalar-on-image regression. We propose a new class of Bayesian nonparametric models and develop an efficient posterior computational aigorithm. The proposed soft-thresholded Gaussian process provides large prior support over the class of piecewise-smooth, sparse, and continuous spatially-varying regression coefficient functions. In addition, under some mild regularity conditions the soft-thresholded Gaussian proess prior leads to the posterior consistency for parameter estimation and variable selection for scalar-on-image regression, even when the number of predictors is larger than the sample size. The proposed method is compared to alternatives via simulation and applied to an electroen-cephalography study of alcoholism.

Methods for scalar-on-function regression

Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images, etc. are considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorizing the basic model types as linear, nonlinear and nonparametric. We discuss publicly available software packages, and illustrate some of the procedures by application to a functional magnetic resonance imaging dataset.

Generalized Scalar-on-Image Regression Models via Total Variation

The use of imaging markers to predict clinical outcomes can have a great impact in public health. The aim of this paper is to develop a class of generalized scalar-on-image regression models via total variation (GSIRM-TV), in the sense of generalized linear models, for scalar response and imaging predictor with the presence of scalar covariates. A key novelty of GSIRM-TV is that it is assumed that the slope function (or image) of GSIRM-TV belongs to the space of bounded total variation in order to explicitly account for the piecewise smooth nature of most imaging data. We develop an efficient penalized total variation optimization to estimate the unknown slope function and other parameters. We also establish nonasymptotic error bounds on the excess risk. These bounds are explicitly specified in terms of sample size, image size, and image smoothness. Our simulations demonstrate a superior performance of GSIRM-TV against many existing approaches. We apply GSIRM-TV to the analysis of hippocampus data obtained from the Alzheimers Disease Neuroimaging Initiative (ADNI) dataset.

Classification of ADNI PET Images via Regularized 3D Functional Data Analysis

We propose a penalized Haar wavelet approach for the classification of 3D brain images in the framework of functional data analysis, which treats each entire 3D brain image as a single functional input thus automatically takes into account the spatial correlations of voxel level imaging measures. We validate the proposed approach through extensive simulations and compare its classification performance with other commonly used machine learning methods, which show that the proposed method outperforms other methods in both classification accuracy and identification of the relevant voxels. We then apply the proposed method to the practical classification problems for Alzheimer's disease using PET images obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database to highlight the advantages of our approach.

The Neuro Bureau ADHD-200 Preprocessed repository

In 2011, the "ADHD-200 Global Competition" was held with the aim of identifying biomarkers of attention-deficit/hyperactivity disorder from resting-state functional magnetic resonance imaging (rs-fMRI) and structural MRI (s-MRI) data collected on 973 individuals. Statisticians and computer scientists were potentially the most qualified for the machine learning aspect of the competition, but generally lacked the specialized skills to implement the necessary steps of data preparation for rs-fMRI. Realizing this barrier to entry, the Neuro Bureau prospectively collaborated with all competitors by preprocessing the data and sharing these results at the Neuroimaging Informatics Tools and Resources Clearinghouse (NITRC) (http://www.nitrc.org/frs/?group_id=383). This "ADHD-200 Preprocessed" release included multiple analytical pipelines to cater to different philosophies of data analysis. The processed derivatives included denoised and registered 4D fMRI volumes, regional time series extracted from brain parcellations, maps of 10 intrinsic connectivity networks, fractional amplitude of low frequency fluctuation, and regional homogeneity, along with grey matter density maps. The data was used by several teams who competed in the ADHD-200 Global Competition, including the winning entry by a group of biostaticians. To the best of our knowledge, the ADHD-200 Preprocessed release was the first large public resource of preprocessed resting-state fMRI and structural MRI data, and remains to this day the only resource featuring a battery of alternative processing paths.

WAVELET-DOMAIN REGRESSION AND PREDICTIVE INFERENCE IN PSYCHIATRIC NEUROIMAGING

An increasingly important goal of psychiatry is the use of brain imaging data to develop predictive models. Here we present two contributions to statistical methodology for this purpose. First, we propose and compare a set of wavelet-domain procedures for fitting generalized linear models with scalar responses and image predictors: sparse variants of principal component regression and of partial least squares, and the elastic net. Second, we consider assessing the contribution of image predictors over and above available scalar predictors, in particular via permutation tests and an extension of the idea of confounding to the case of functional or image predictors. Using the proposed methods, we assess whether maps of a spontaneous brain activity measure, derived from functional magnetic resonance imaging, can meaningfully predict presence or absence of attention deficit/hyperactivity disorder (ADHD). Our results shed light on the role of confounding in the surprising outcome of the recent ADHD-200 Global Competition, which challenged researchers to develop algorithms for automated image-based diagnosis of the disorder.

Cross-validation and hypothesis testing in neuroimaging: An irenic comment on the exchange between Friston and Lindquist et al

The "ten ironic rules for statistical reviewers" presented by Friston (2012) prompted a rebuttal by Lindquist et al. (2013), which was followed by a rejoinder by Friston (2013). A key issue left unresolved in this discussion is the use of cross-validation to test the significance of predictive analyses. This note discusses the role that cross-validation-based and related hypothesis tests have come to play in modern data analyses, in neuroimaging and other fields. It is shown that such tests need not be suboptimal and can fill otherwise-unmet inferential needs.