A structured brain‐wide and genome‐wide association study using ADNI PET images

A multistage variable selection method is introduced for detecting association signals in structured brain‐wide and genome‐wide association studies (brain‐GWAS). Compared to conventional methods that link one voxel to one single nucleotide polymorphism (SNP), our approach is more efficient and powerful in selecting the important signals by integrating anatomic and gene grouping structures in the brain and the genome, respectively. It avoids resorting to a large number of multiple comparisons while effectively controlling the false discoveries. Validity of the proposed approach is demonstrated by both theoretical investigation and numerical simulations. We apply our proposed method to a brain‐GWAS using Alzheimer's Disease Neuroimaging Initiative positron emission tomography (ADNI PET) imaging and genomic data. We confirm previously reported association signals and also uncover several novel SNPs and genes that are either associated with brain glucose metabolism or have their association significantly modified by Alzheimer's disease status.     

A Potts‐mixture spatiotemporal joint model for combined magnetoencephalography and electroencephalography 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, magnetic resonance imaging (MRI), MEG and EEG, together. We propose a new Bayesian spatial finite mixture model that builds on the mesostate‐space model developed by Daunizeau & Friston [Daunizeau and Friston, NeuroImage 2007; 38, 67–81]. 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 . The Canadian Journal of Statistics 47: 688–711; 2019 © 2019 Statistical Society of Canada     

A review of statistical methods in imaging genetics

With the rapid growth of modern technology, many biomedical studies are being conducted to collect massive datasets with 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's disease). However, the development of analytical methods for the joint analysis of both high‐dimensional imaging phenotypes and high‐dimensional genetic data, a big data squared (BD²) problem, presents major computational and theoretical challenges for existing analytical methods. Besides the high‐dimensional nature of BD², 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 imaging genetics, 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. The Canadian Journal of Statistics 47: 108–131; 2019 © 2019 Statistical Society of Canada     

Physically constrained spatiotemporal modeling: generating clear-sky constructions of land surface temperature from sparse,remotely sensed satellite data

Satellite remote-sensing is used to collect important atmospheric and geophysical data at various spatial resolutions, providing insight into spatiotemporal surface and climate variability globally. These observations are often plagued with missing spatial and temporal information of Earth''s surface due to (1) cloud cover at the time of a satellite passing and (2) infrequent passing of polar-orbiting satellites. While many methods are available to model missing data in space and time, in the case of land surface temperature (LST) from thermal infrared remote sensing, these approaches generally ignore the temporal pattern called the ‘diurnal cycle’ which physically constrains temperatures to peak in the early afternoon and reach a minimum at sunrise. In order to infill an LST dataset, we parameterize the diurnal cycle into a functional form with unknown spatiotemporal parameters. Using multiresolution spatial basis functions, we estimate these parameters from sparse satellite observations to reconstruct an LST field with continuous spatial and temporal distributions. These estimations may then be used to better inform scientists of spatiotemporal thermal patterns over relatively complex domains. The methodology is demonstrated using data collected by MODIS on NASA''s Aqua and Terra satellites over both Houston, TX and Phoenix, AZ USA.     

Statistical Modelling of Brain Morphological Measures Within Family Pedigrees

Large, family-based imaging studies can provide a better understanding of the interactions of environmental and genetic influences on brain structure and function. The interpretation of imaging data from large family studies, however, has been hindered by the paucity of well-developed statistical tools for that permit the analysis of complex imaging data together with behavioral and clinical data. In this paper, we propose to use two methods for these analyses. First, a variance components model along with score statistics is used to test linear hypotheses of unknown parameters, such as the associations of brain measures (e.g., cortical and subcortical surfaces) with their potential genetic determinants. Second, we develop a test procedure based on a resampling method to assess simultaneously the statistical significance of linear hypotheses across the entire brain. The value of these methods lies in their computational simplicity and in their applicability to a wide range of imaging data. Simulation studies show that our test procedure can accurately control the family-wise error rate. We apply our methods to the detection of statistical significance of gender-by-age interactions and of the effects of genetic variation on the thickness of the cerebral cortex in a family study of major depressive disorder.     

Statistical disease mapping for heterogeneous neuroimaging studies

Many cancers and neuro‐related diseases display significant phenotypic and genetic heterogeneity across subjects and subpopulations. Characterizing such heterogeneity could transform our understanding of the etiology of these conditions and inspire new approaches to urgently needed prevention, diagnosis, treatment, and prognosis. However, most existing statistical methods face major challenges in delineating such heterogeneity at both the group and individual levels. The aim of this article is to propose a novel statistical disease‐mapping (SDM) framework to address some of these challenges. We develop an efficient estimation method to estimate unknown parameters in SDM and delineate individual and group disease maps. Statistical inference procedures such as hypothesis‐testing problems are also investigated for parameters of interest. Both simulation studies and real data analysis on the ADNI hippocampal surface dataset show that our SDM not only effectively detects diseased regions in each patient but also provides a group disease‐mapping analysis of Alzheimer subgroups.     

Variable selection for high-dimensional generalized linear model with block-missing data

In modern scientific research, multiblock missing data emerges with synthesizing information across multiple studies. However, existing imputation methods for handling block-wise missing data either focus on the single-block missing pattern or heavily rely on the model structure. In this study, we propose a single regression-based imputation algorithm for multiblock missing data. First, we conduct a sparse precision matrix estimation based on the structure of block-wise missing data. Second, we impute the missing blocks with their means conditional on the observed blocks. Theoretical results about variable selection and estimation consistency are established in the context of a generalized linear model. Moreover, simulation studies show that compared with existing methods, the proposed imputation procedure is robust to various missing mechanisms because of the good properties of regression imputation. An application to Alzheimer's Disease Neuroimaging Initiative data also confirms the superiority of our proposed method.     

Minimax powerful functional analysis of covariance tests with application to longitudinal genome-wide association studies

We model the Alzheimer's disease-related phenotype response variables observed on irregular time points in longitudinal Genome-Wide Association Studies as sparse functional data and propose nonparametric test procedures to detect functional genotype effects while controlling the confounding effects of environmental covariates. Our new functional analysis of covariance tests are based on a seemingly unrelated kernel smoother, which takes into account the within-subject temporal correlations, and thus enjoy improved power over existing functional tests. We show that the proposed test combined with a uniformly consistent nonparametric covariance function estimator enjoys the Wilks phenomenon and is minimax most powerful. Data used in the preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative database, where an application of the proposed test lead to the discovery of new genes that may be related to Alzheimer's disease.     

Joint confidence region estimation on predictive values

For evaluating diagnostic accuracy of inherently continuous diagnostic tests/biomarkers, sensitivity and specificity are well-known measures both of which depend on a diagnostic cut-off, which is usually estimated. Sensitivity (specificity) is the conditional probability of testing positive (negative) given the true disease status. However, a more relevant question is “what is the probability of having (not having) a disease if a test is positive (negative)?”. Such post-test probabilities are denoted as positive predictive value (PPV) and negative predictive value (NPV). The PPV and NPV at the same estimated cut-off are correlated, hence it is desirable to make the joint inference on PPV and NPV to account for such correlation. Existing inference methods for PPV and NPV focus on the individual confidence intervals and they were developed under binomial distribution assuming binary instead of continuous test results. Several approaches are proposed to estimate the joint confidence region as well as the individual confidence intervals of PPV and NPV. Simulation results indicate the proposed approaches perform well with satisfactory coverage probabilities for normal and non-normal data and, additionally, outperform existing methods with improved coverage as well as narrower confidence intervals for PPV and NPV. The Alzheimer's Disease Neuroimaging Initiative (ADNI) data set is used to illustrate the proposed approaches and compare them with the existing methods.     

A smoothed Q‐learning algorithm for estimating optimal dynamic treatment regimes

In this paper, we propose a smoothed Q‐learning algorithm for estimating optimal dynamic treatment regimes. In contrast to the Q‐learning algorithm in which nonregular inference is involved, we show that, under assumptions adopted in this paper, the proposed smoothed Q‐learning estimator is asymptotically normally distributed even when the Q‐learning estimator is not and its asymptotic variance can be consistently estimated. As a result, inference based on the smoothed Q‐learning estimator is standard. We derive the optimal smoothing parameter and propose a data‐driven method for estimating it. The finite sample properties of the smoothed Q‐learning estimator are studied and compared with several existing estimators including the Q‐learning estimator via an extensive simulation study. We illustrate the new method by analyzing data from the Clinical Antipsychotic Trials of Intervention Effectiveness–Alzheimer's Disease (CATIE‐AD) study.     

Multiscale Adaptive Regression Models for Neuroimaging Data

Neuroimaging studies aim to analyze imaging data with complex spatial patterns in a large number of locations (called voxels) on a two-dimensional (2D) surface or in a 3D volume. Conventional analyses of imaging data include two sequential steps: spatially smoothing imaging data and then independently fitting a statistical model at each voxel. However, conventional analyses suffer from the same amount of smoothing throughout the whole image, the arbitrary choice of smoothing extent, and low statistical power in detecting spatial patterns. We propose a multiscale adaptive regression model (MARM) to integrate the propagation-separation (PS) approach (Polzehl and Spokoiny, 2000, 2006) with statistical modeling at each voxel for spatial and adaptive analysis of neuroimaging data from multiple subjects. MARM has three features: being spatial, being hierarchical, and being adaptive. We use a multiscale adaptive estimation and testing procedure (MAET) to utilize imaging observations from the neighboring voxels of the current voxel to adaptively calculate parameter estimates and test statistics. Theoretically, we establish consistency and asymptotic normality of the adaptive parameter estimates and the asymptotic distribution of the adaptive test statistics. Our simulation studies and real data analysis confirm that MARM significantly outperforms conventional analyses of imaging data.     

Evaluating paired categorical data when the pairing is lost

We encountered a problem in which a study's experimental design called for the use of paired data, but the pairing between subjects had been lost during the data collection procedure. Thus we were presented with a data set consisting of pre and post responses but with no way of determining the dependencies between our observed pre and post values. The aim of the study was to assess whether an intervention called Self-Revelatory Performance had an impact on participant's perceptions of Alzheimer's disease. The participant's responses were measured on an Affect grid before the intervention and on a separate grid after. To address the underlying question in light of the lost pairing we utilized a modified bootstrap approach to create a null hypothesized distribution for our test statistic, which was the distance between the two Affect Grids' Centers of Mass. Using this approach we were able to reject our null hypothesis and conclude that there was evidence the intervention influenced perceptions about the disease.     

On weighted composite scores for early Alzheimer's trials

Recent research on finding appropriate composite endpoints for preclinical Alzheimer's disease has focused considerable effort on finding “optimized” weights in the construction of a weighted composite score. In this paper, several proposed methods are reviewed. Our results indicate no evidence that these methods will increase the power of the test statistics, and some of these weights will introduce biases to the study. Our recommendation is to focus on identifying more sensitive items from clinical practice and appropriate statistical analyses of a large Alzheimer's data set. Once a set of items has been selected, there is no evidence that adding weights will generate more sensitive composite endpoints.     

Rejoinder: “Statistical disease mapping for heterogeneous neuroimaging studies”

We thank all the discussants for sharing their valuable viewpoints on the proposed statistical disease mapping (SDM) framework. In our article, we addressed the issue of imaging heterogeneity at both the global and local scales by efficiently borrowing common information shared among a large number of diseased and normal subjects. Understanding such imaging heterogeneity is critical in the development of urgently needed analytic approaches to the prevention, diagnosis, treatment, and prognosis of many diseases (e.g., Alzheimer's disease, brain cancer, and lung cancer), as well as precision medicine broadly. The discussants emphasized improvements to disease mapping by introducing some alternative modelling strategies and many possible future directions in this research topic. The sections of this rejoinder are organized by discussant to address each of their comments separately.     

Bayesian analysis of spatial data using different variance and neighbourhood structures

In disease mapping, the overall goal is to study the incidence or mortality risk caused by a specific disease in a number of geographical regions. It is common to assume that the response variable follows a Poisson distribution, whose average rate can be explained by a group of covariates and a random effect. For this random effect, it is considered conditional autoregressive (CAR) models, which carry information about the neighbourhood relationship between the regions. The focus of this paper was to explore and compare some CAR models proposed in the literature. An application with epidemiological data was conducted to model the risk of death due to Crohn's Disease and Ulcerative Colitis in the State of São Paulo – Brazil. Finally, a simulation study was done to strengthen the results and assess the performance of the models in the presence of various levels of spatial dependence.     

Adaptive Gaussian Markov random fields with applications in human brain mapping

Summary.  Functional magnetic resonance imaging has become a standard technology in human brain mapping. Analyses of the massive spatiotemporal functional magnetic resonance imaging data sets often focus on parametric or non-parametric modelling of the temporal component, whereas spatial smoothing is based on Gaussian kernels or random fields. A weakness of Gaussian spatial smoothing is underestimation of activation peaks or blurring of high curvature transitions between activated and non-activated regions of the brain. To improve spatial adaptivity, we introduce a class of inhomogeneous Markov random fields with stochastic interaction weights in a space-varying coefficient model. For given weights, the random field is conditionally Gaussian, but marginally it is non-Gaussian. Fully Bayesian inference, including estimation of weights and variance parameters, can be carried out through efficient Markov chain Monte Carlo simulation. Although motivated by the analysis of functional magnetic resonance imaging data, the methodological development is general and can also be used for spatial smoothing and regression analysis of areal data on irregular lattices. An application to stylized artificial data and to real functional magnetic resonance imaging data from a visual stimulation experiment demonstrates the performance of our approach in comparison with Gaussian and robustified non-Gaussian Markov random-field models.     

The Role of Risk and Risk Aversion in an Individual's Migration Decision

Abstract

This paper proposes a simple, partial equilibrium model for studying an individual's migration decisions. It shows that an individual may choose to delay migration when the condition appears to be favorable, giving rise to the “waiting” behavior observed in the data. Using a closed-form solution, it also examines how the duration of the waiting is affected by a number of economic factors such as the risks associated with the wages in regions of origin and destination, the individual's attitude toward risk, etc.     

Robust logistic regression of family data in the presence of missing genotypes

Large cohort studies are commonly launched to study the risk effect of genetic variants or other risk factors on a chronic disorder. In these studies, family data are often collected to provide additional information for the purpose of improving the inference results. Statistical analysis of the family data can be very challenging due to the missing observations of genotypes, incomplete records of disease occurrences in family members, and the complicated dependence attributed to the shared genetic background and environmental factors. In this article, we investigate a class of logistic models with family-shared random effects to tackle these challenges, and develop a robust regression method based on the conditional logistic technique for statistical inference. An expectation–maximization (EM) algorithm with fast computation speed is developed to handle the missing genotypes. The proposed estimators are shown to be consistent and asymptotically normal. Additionally, a score test based on the proposed method is derived to test the genetic effect. Extensive simulation studies demonstrate that the proposed method performs well in finite samples in terms of estimate accuracy, robustness and computational speed. The proposed procedure is applied to an Alzheimer's disease study.     

Disaggregated spatial modelling for areal unit categorical data

Summary.  We consider joint spatial modelling of areal multivariate categorical data assuming a multiway contingency table for the variables, modelled by using a log-linear model, and connected across units by using spatial random effects. With no distinction regarding whether variables are response or explanatory, we do not limit inference to conditional probabilities, as in customary spatial logistic regression. With joint probabilities we can calculate arbitrary marginal and conditional probabilities without having to refit models to investigate different hypotheses. Flexible aggregation allows us to investigate subgroups of interest; flexible conditioning enables not only the study of outcomes given risk factors but also retrospective study of risk factors given outcomes. A benefit of joint spatial modelling is the opportunity to reveal disparities in health in a richer fashion, e.g. across space for any particular group of cells, across groups of cells at a particular location, and, hence, potential space–group interaction. We illustrate with an analysis of birth records for the state of North Carolina and compare with spatial logistic regression.     

Predictive Inference for Big,Spatial, Non‐Gaussian Data: MODIS Cloud Data and its Change‐of‐Support

Remote sensing of the earth with satellites yields datasets that can be massive in size, nonstationary in space, and non‐Gaussian in distribution. To overcome computational challenges, we use the reduced‐rank spatial random effects (SRE) model in a statistical analysis of cloud‐mask data from NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) instrument on board NASA's Terra satellite. Parameterisations of cloud processes are the biggest source of uncertainty and sensitivity in different climate models’ future projections of Earth's climate. An accurate quantification of the spatial distribution of clouds, as well as a rigorously estimated pixel‐scale clear‐sky‐probability process, is needed to establish reliable estimates of cloud‐distributional changes and trends caused by climate change. Here we give a hierarchical spatial‐statistical modelling approach for a very large spatial dataset of 2.75 million pixels, corresponding to a granule of MODIS cloud‐mask data, and we use spatial change‐of‐Support relationships to estimate cloud fraction at coarser resolutions. Our model is non‐Gaussian; it postulates a hidden process for the clear‐sky probability that makes use of the SRE model, EM‐estimation, and optimal (empirical Bayes) spatial prediction of the clear‐sky‐probability process. Measures of prediction uncertainty are also given.