Asynchronous functional linear regression models for longitudinal data in reproducing kernel Hilbert space

Motivated by the analysis of longitudinal neuroimaging studies, we study the longitudinal functional linear regression model under asynchronous data setting for modeling the association between clinical outcomes and functional (or imaging) covariates. In the asynchronous data setting, both covariates and responses may be measured at irregular and mismatched time points, posing methodological challenges to existing statistical methods. We develop a kernel weighted loss function with roughness penalty to obtain the functional estimator and derive its representer theorem. The rate of convergence, a Bahadur representation, and the asymptotic pointwise distribution of the functional estimator are obtained under the reproducing kernel Hilbert space framework. We propose a penalized likelihood ratio test to test the nullity of the functional coefficient, derive its asymptotic distribution under the null hypothesis, and investigate the separation rate under the alternative hypotheses. Simulation studies are conducted to examine the finite-sample performance of the proposed procedure. We apply the proposed methods to the analysis of multitype data obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, which reveals significant association between 21 regional brain volume density curves and the cognitive function. Data used in preparation of this paper were obtained from the ADNI database (adni.loni.usc.edu).     

Longitudinal Analysis Is More Powerful than Cross-Sectional Analysis in Detecting Genetic Association with Neuroimaging Phenotypes

Most existing genome-wide association analyses are cross-sectional, utilizing only phenotypic data at a single time point, e.g. baseline. On the other hand, longitudinal studies, such as Alzheimer''s Disease Neuroimaging Initiative (ADNI), collect phenotypic information at multiple time points. In this article, as a case study, we conducted both longitudinal and cross-sectional analyses of the ADNI data with several brain imaging (not clinical diagnosis) phenotypes, demonstrating the power gains of longitudinal analysis over cross-sectional analysis. Specifically, we scanned genome-wide single nucleotide polymorphisms (SNPs) with 56 brain-wide imaging phenotypes processed by FreeSurfer on 638 subjects. At the genome-wide significance level () or a less stringent level (e.g. ), longitudinal analysis of the phenotypic data from the baseline to month 48 identified more SNP-phenotype associations than cross-sectional analysis of only the baseline data. In particular, at the genome-wide significance level, both SNP rs429358 in gene APOE and SNP rs2075650 in gene TOMM40 were confirmed to be associated with various imaging phenotypes in multiple regions of interests (ROIs) by both analyses, though longitudinal analysis detected more regional phenotypes associated with the two SNPs and indicated another significant SNP rs439401 in gene APOE. In light of the power advantage of longitudinal analysis, we advocate its use in current and future longitudinal neuroimaging studies.     

Genetic interactions found between calcium channel genes modulate amyloid load measured by positron emission tomography

Late-onset Alzheimer’s disease (LOAD) is known to have a complex, oligogenic etiology, with considerable genetic heterogeneity. We investigated the influence of genetic interactions between genes in the Alzheimer’s disease (AD) pathway on amyloid-beta (Aβ) deposition as measured by PiB or AV-45 ligand positron emission tomography (PET) to aid in understanding LOAD’s genetic etiology. Subsets of the Alzheimer’s Disease Neuroimaging Initiative (ADNI) cohorts were used for discovery and for two independent validation analyses. A significant interaction between RYR3 and CACNA1C was confirmed in all three of the independent ADNI datasets. Both genes encode calcium channels expressed in the brain. The results shown here support previous animal studies implicating interactions between these calcium channels in amyloidogenesis and suggest that the pathological cascade of this disease may be modified by interactions in the amyloid–calcium axis. Future work focusing on the mechanisms of such relationships may inform targets for clinical intervention.     

Heterogeneous multimodal biomarkers analysis for Alzheimer’s disease via Bayesian network

By 2050, it is estimated that the number of worldwide Alzheimer’s disease (AD) patients will quadruple from the current number of 36 million, while no proven disease-modifying treatments are available. At present, the underlying disease mechanisms remain under investigation, and recent studies suggest that the disease involves multiple etiological pathways. To better understand the disease and develop treatment strategies, a number of ongoing studies including the Alzheimer’s Disease Neuroimaging Initiative (ADNI) enroll many study participants and acquire a large number of biomarkers from various modalities including demographic, genotyping, fluid biomarkers, neuroimaging, neuropsychometric test, and clinical assessments. However, a systematic approach that can integrate all the collected data is lacking. The overarching goal of our study is to use machine learning techniques to understand the relationships among different biomarkers and to establish a system-level model that can better describe the interactions among biomarkers and provide superior diagnostic and prognostic information. In this pilot study, we use Bayesian network (BN) to analyze multimodal data from ADNI, including demographics, volumetric MRI, PET, genotypes, and neuropsychometric measurements and demonstrate our approach to have superior prediction accuracy.     

Partial least squares for functional joint models with applications to the Alzheimer's disease neuroimaging initiative study

Many biomedical studies have identified important imaging biomarkers that are associated with both repeated clinical measures and a survival outcome. The functional joint model (FJM) framework, proposed by Li and Luo in 2017, investigates the association between repeated clinical measures and survival data, while adjusting for both high-dimensional images and low-dimensional covariates based on the functional principal component analysis (FPCA). In this paper, we propose a novel algorithm for the estimation of FJM based on the functional partial least squares (FPLS). Our numerical studies demonstrate that, compared to FPCA, the proposed FPLS algorithm can yield more accurate and robust estimation and prediction performance in many important scenarios. We apply the proposed FPLS algorithm to a neuroimaging study. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.     

Bayesian latent multi‐state modeling for nonequidistant longitudinal electronic health records

Large amounts of longitudinal health records are now available for dynamic monitoring of the underlying processes governing the observations. However, the health status progression across time is not typically observed directly: records are observed only when a subject interacts with the system, yielding irregular and often sparse observations. This suggests that the observed trajectories should be modeled via a latent continuous‐time process potentially as a function of time‐varying covariates. We develop a continuous‐time hidden Markov model to analyze longitudinal data accounting for irregular visits and different types of observations. By employing a specific missing data likelihood formulation, we can construct an efficient computational algorithm. We focus on Bayesian inference for the model: this is facilitated by an expectation‐maximization algorithm and Markov chain Monte Carlo methods. Simulation studies demonstrate that these approaches can be implemented efficiently for large data sets in a fully Bayesian setting. We apply this model to a real cohort where patients suffer from chronic obstructive pulmonary disease with the outcome being the number of drugs taken, using health care utilization indicators and patient characteristics as covariates.     

On Efficiency of Constrained Longitudinal Data Analysis Versus Longitudinal Analysis of Covariance

Summary : In randomized clinical trials, measurements are often collected on each subject at a baseline visit and several post‐randomization time points. The longitudinal analysis of covariance in which the postbaseline values form the response vector and the baseline value is treated as a covariate can be used to evaluate the treatment differences at the postbaseline time points. Liang and Zeger (2000, Sankhyā: The Indian Journal of Statistics, Series B 62, 134–148) propose a constrained longitudinal data analysis in which the baseline value is included in the response vector together with the postbaseline values and a constraint of a common baseline mean across treatment groups is imposed on the model as a result of randomization. If the baseline value is subject to missingness, the constrained longitudinal data analysis is shown to be more efficient for estimating the treatment differences at postbaseline time points than the longitudinal analysis of covariance. The efficiency gain increases with the number of subjects missing baseline and the number of subjects missing all postbaseline values, and, for the pre–post design, decreases with the absolute correlation between baseline and postbaseline values.     

Estimating Subject‐Specific Dependent Competing Risk Profile with Censored Event Time Observations

Summary In a longitudinal study, suppose that the primary endpoint is the time to a specific event. This response variable, however, may be censored by an independent censoring variable or by the occurrence of one of several dependent competing events. For each study subject, a set of baseline covariates is collected. The question is how to construct a reliable prediction rule for the future subject's profile of all competing risks of interest at a specific time point for risk‐benefit decision making. In this article, we propose a two‐stage procedure to make inferences about such subject‐specific profiles. For the first step, we use a parametric model to obtain a univariate risk index score system. We then estimate consistently the average competing risks for subjects who have the same parametric index score via a nonparametric function estimation procedure. We illustrate this new proposal with the data from a randomized clinical trial for evaluating the efficacy of a treatment for prostate cancer. The primary endpoint for this study was the time to prostate cancer death, but had two types of dependent competing events, one from cardiovascular death and the other from death of other causes.     

Analysis of multivariate recurrent event data with time‐dependent covariates and informative censoring

Multivariate recurrent event data are usually encountered in many clinical and longitudinal studies in which each study subject may experience multiple recurrent events. For the analysis of such data, most existing approaches have been proposed under the assumption that the censoring times are noninformative, which may not be true especially when the observation of recurrent events is terminated by a failure event. In this article, we consider regression analysis of multivariate recurrent event data with both time‐dependent and time‐independent covariates where the censoring times and the recurrent event process are allowed to be correlated via a frailty. The proposed joint model is flexible where both the distributions of censoring and frailty variables are left unspecified. We propose a pairwise pseudolikelihood approach and an estimating equation‐based approach for estimating coefficients of time‐dependent and time‐independent covariates, respectively. The large sample properties of the proposed estimates are established, while the finite‐sample properties are demonstrated by simulation studies. The proposed methods are applied to the analysis of a set of bivariate recurrent event data from a study of platelet transfusion reactions.     

Time‐Varying Latent Effect Model for Longitudinal Data with Informative Observation Times

Summary In analysis of longitudinal data, it is not uncommon that observation times of repeated measurements are subject‐specific and correlated with underlying longitudinal outcomes. Taking account of the dependence between observation times and longitudinal outcomes is critical under these situations to assure the validity of statistical inference. In this article, we propose a flexible joint model for longitudinal data analysis in the presence of informative observation times. In particular, the new procedure considers the shared random‐effect model and assumes a time‐varying coefficient for the latent variable, allowing a flexible way of modeling longitudinal outcomes while adjusting their association with observation times. Estimating equations are developed for parameter estimation. We show that the resulting estimators are consistent and asymptotically normal, with variance–covariance matrix that has a closed form and can be consistently estimated by the usual plug‐in method. One additional advantage of the procedure is that it provides a unified framework to test whether the effect of the latent variable is zero, constant, or time‐varying. Simulation studies show that the proposed approach is appropriate for practical use. An application to a bladder cancer data is also given to illustrate the methodology.     

Proteins that mediate protein aggregation and cytotoxicity distinguish Alzheimer's hippocampus from normal controls

Neurodegenerative diseases are distinguished by characteristic protein aggregates initiated by disease‐specific ‘seed’ proteins; however, roles of other co‐aggregated proteins remain largely unexplored. Compact hippocampal aggregates were purified from Alzheimer's and control‐subject pools using magnetic‐bead immunoaffinity pulldowns. Their components were fractionated by electrophoretic mobility and analyzed by high‐resolution proteomics. Although total detergent‐insoluble aggregates from Alzheimer's and controls had similar protein content, within the fractions isolated by tau or Aβ_1–42 pulldown, the protein constituents of Alzheimer‐derived aggregates were more abundant, diverse, and post‐translationally modified than those from controls. Tau‐ and Aβ‐containing aggregates were distinguished by multiple components, and yet shared >90% of their protein constituents, implying similar accretion mechanisms. Alzheimer‐specific protein enrichment in tau‐containing aggregates was corroborated for individuals by three analyses. Five proteins inferred to co‐aggregate with tau were confirmed by precise in situ methods, including proximity ligation amplification that requires co‐localization within 40 nm. Nematode orthologs of 21 proteins, which showed Alzheimer‐specific enrichment in tau‐containing aggregates, were assessed for aggregation‐promoting roles in C. elegans by RNA‐interference ‘knockdown’. Fifteen knockdowns (71%) rescued paralysis of worms expressing muscle Aβ, and 12 (57%) rescued chemotaxis disrupted by neuronal Aβ expression. Proteins identified in compact human aggregates, bound by antibody to total tau, were thus shown to play causal roles in aggregation based on nematode models triggered by Aβ_1–42. These observations imply shared mechanisms driving both types of aggregation, and/or aggregate‐mediated cross‐talk between tau and Aβ. Knowledge of protein components that promote protein accrual in diverse aggregate types implicates common mechanisms and identifies novel targets for drug intervention.     

GWAS-Linked Loci and Neuroimaging Measures in Alzheimer’s Disease

Recently, 19 susceptibility loci for Alzheimer’s disease (AD) had been identified through AD genome-wide association studies (GWAS) meta-analysis. However, how they influence the pathogenesis of AD still remains largely unknown. We studied those loci with six MRI measures, abnormal glucose metabolism, and β-amyloid (Aβ) deposition on neuroimaging in a large cohort from Alzheimer’s Disease Neuroimaging Initiative (ADNI) database in order to provide clues of the mechanisms through which these genetic variants might be acting. As a result, single nucleotide polymorphisms (SNPs) at rs983392 within MS4A6A and rs11218343 within SOLR1 were both associated with the percentage of increase in the volume of left inferior temporal regions in the follow-up study. Meanwhile, rs11218343 at SORL1 and rs6733839 at BIN1 was associated with rate of volume change of left parahippocampal and right inferior parietal, respectively. Moreover, rs6656401 at CR1 and rs983392 at MS4A6A were both associated with smaller volume of right middle temporal at baseline. However, in addition to the APOE locus, we did not detect any influence on glucose metabolism and Aβ deposition. APOE ε4 allele was associated with almost all measures. Altogether, five loci (rs6656401 at CR1, rs983392within MS4A6A, rs11218343 at SORL1, rs6733839 at BIN1, and APOE ε4) have been detected to be associated with one or a few established AD-related neuroimaging measures.     

A Stochastic Regression Model for General Trend Analysis of Longitudinal Continuous Data

A predictive continuous time model is developed for continuous panel data to assess the effect of time‐varying covariates on the general direction of the movement of a continuous response that fluctuates over time. This is accomplished by reparameterizing the infinitesimal mean of an Ornstein–Uhlenbeck processes in terms of its equilibrium mean and a drift parameter, which assesses the rate that the process reverts to its equilibrium mean. The equilibrium mean is modeled as a linear predictor of covariates. This model can be viewed as a continuous time first‐order autoregressive regression model with time‐varying lag effects of covariates and the response, which is more appropriate for unequally spaced panel data than its discrete time analog. Both maximum likelihood and quasi‐likelihood approaches are considered for estimating the model parameters and their performances are compared through simulation studies. The simpler quasi‐likelihood approach is suggested because it yields an estimator that is of high efficiency relative to the maximum likelihood estimator and it yields a variance estimator that is robust to the diffusion assumption of the model. To illustrate the proposed model, an application to diastolic blood pressure data from a follow‐up study on cardiovascular diseases is presented. Missing observations are handled naturally with this model.     

The risk prediction of Alzheimer’s disease based on the deep learning model of brain 18F-FDG positron emission tomography

In order to predict the risks of Alzheimer’s Disease (AD) based on the deep learning model of brain 18F-FDG positron emission tomography (PET), a total of 350 mild cognitive impairment (MCI) participants from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database were selected as the research objects; in addition, the Convolutional Architecture for Fast Feature Embedding (CAFFE) was selected as the framework of the deep learning platform; the FDG PET image features of each participant were extracted by a deep convolution network model to construct the prediction and classification models; therefore, the MCI stage features were classified and the transformation was predicted. The results showed that in terms of the MCI transformation prediction, the sensitivity and specificity of conv3 classification were respectively 91.02% and 77.63%; in terms of the Late Mild Cognitive Impairment (LMCI) and Early Mild Cognitive Impairment (EMCI) classification, the accuracy of conv5 classification was 72.19%, and the sensitivity and specificity of conv5 were all 73% approximately. Thus, it was seen that the model constructed in the research could be used to solve the problems of MCI transformation prediction, which also had certain effects on the classifications of EMCI and LMCI. The risk prediction of AD based on the deep learning model of brain 18F-FDG PET discussed in the research matched the expected results. It provided a relatively accurate reference model for the prediction of AD. Despite the deficiencies of the research process, the research results have provided certain references and guidance for the future exploration of accurate AD prediction model; therefore, the research is of great significance.     

Basics of Multivariate Analysis in Neuroimaging Data

Multivariate analysis techniques for neuroimaging data have recently received increasing attention as they have many attractive features that cannot be easily realized by the more commonly used univariate, voxel-wise, techniques^1,5,6,7,8,9. Multivariate approaches evaluate correlation/covariance of activation across brain regions, rather than proceeding on a voxel-by-voxel basis. Thus, their results can be more easily interpreted as a signature of neural networks. Univariate approaches, on the other hand, cannot directly address interregional correlation in the brain. Multivariate approaches can also result in greater statistical power when compared with univariate techniques, which are forced to employ very stringent corrections for voxel-wise multiple comparisons. Further, multivariate techniques also lend themselves much better to prospective application of results from the analysis of one dataset to entirely new datasets. Multivariate techniques are thus well placed to provide information about mean differences and correlations with behavior, similarly to univariate approaches, with potentially greater statistical power and better reproducibility checks. In contrast to these advantages is the high barrier of entry to the use of multivariate approaches, preventing more widespread application in the community. To the neuroscientist becoming familiar with multivariate analysis techniques, an initial survey of the field might present a bewildering variety of approaches that, although algorithmically similar, are presented with different emphases, typically by people with mathematics backgrounds. We believe that multivariate analysis techniques have sufficient potential to warrant better dissemination. Researchers should be able to employ them in an informed and accessible manner. The current article is an attempt at a didactic introduction of multivariate techniques for the novice. A conceptual introduction is followed with a very simple application to a diagnostic data set from the Alzheimer s Disease Neuroimaging Initiative (ADNI), clearly demonstrating the superior performance of the multivariate approach.     

Thioesters for the in vitro evaluation of agents to image brain cholinesterases

Cholinesterases are associated with pathology characteristic of conditions such as Alzheimer’s disease and are therefore, considered targets for neuroimaging. Ester derivatives of N-methylpiperidinol are promising potential imaging agents; however, methodology is lacking for evaluating these compounds in vitro. Here, we report the synthesis and evaluation of a series of N-methylpiperidinyl thioesters, possessing comparable properties to their corresponding esters, which can be directly evaluated for cholinesterase kinetics and histochemical distribution in human brain tissue. N-methylpiperidinyl esters and thioesters were synthesized and they demonstrated comparable cholinesterase kinetics. Furthermore, thioesters were capable, using histochemical method, to visualize cholinesterase activity in human brain tissue. N-methylpiperidinyl thioesters can be rapidly evaluated for cholinesterase kinetics and visualization of enzyme distribution in brain tissue which may facilitate development of cholinesterase imaging agents for application to conditions such as Alzheimer’s disease.     

Analysis of secondary phenotypes in multigroup association studies

Although case-control association studies have been widely used, they are insufficient for many complex diseases, such as Alzheimer's disease and breast cancer, since these diseases may have multiple subtypes with distinct morphologies and clinical implications. Many multigroup studies, such as the Alzheimer's Disease Neuroimaging Initiative (ADNI), have been undertaken by recruiting subjects based on their multiclass primary disease status, while extensive secondary outcomes have been collected. The aim of this paper is to develop a general regression framework for the analysis of secondary phenotypes collected in multigroup association studies. Our regression framework is built on a conditional model for the secondary outcome given the multigroup status and covariates and its relationship with the population regression of interest of the secondary outcome given the covariates. Then, we develop generalized estimation equations to estimate the parameters of interest. We use both simulations and a large-scale imaging genetic data analysis from the ADNI to evaluate the effect of the multigroup sampling scheme on standard genome-wide association analyses based on linear regression methods, while comparing it with our statistical methods that appropriately adjust for the multigroup sampling scheme. Data used in preparation of this article were obtained from the ADNI database.     

Continuous time Markov models for binary longitudinal data

Longitudinal data usually consist of a number of short time series. A group of subjects or groups of subjects are followed over time and observations are often taken at unequally spaced time points, and may be at different times for different subjects. When the errors and random effects are Gaussian, the likelihood of these unbalanced linear mixed models can be directly calculated, and nonlinear optimization used to obtain maximum likelihood estimates of the fixed regression coefficients and parameters in the variance components. For binary longitudinal data, a two state, non-homogeneous continuous time Markov process approach is used to model serial correlation within subjects. Formulating the model as a continuous time Markov process allows the observations to be equally or unequally spaced. Fixed and time varying covariates can be included in the model, and the continuous time model allows the estimation of the odds ratio for an exposure variable based on the steady state distribution. Exact likelihoods can be calculated. The initial probability distribution on the first observation on each subject is estimated using logistic regression that can involve covariates, and this estimation is embedded in the overall estimation. These models are applied to an intervention study designed to reduce children's sun exposure.     

Rare variants in the splicing regulatory elements of EXOC3L4 are associated with brain glucose metabolism in Alzheimer’s disease

Background

Alzheimer’s disease (AD) is one of the most common neurodegenerative diseases that causes problems related to brain function. To some extent it is understood on a molecular level how AD arises, however there are a lack of biomarkers that can be used for early diagnosis. Two popular methods to identify AD-related biomarkers use genetics and neuroimaging. Genes and neuroimaging phenotypes have provided some insights as to the potential for AD biomarkers. While the field of imaging-genomics has identified genetic features associated with structural and functional neuroimaging phenotypes, it remains unclear how variants that affect splicing could be important for understanding the genetic etiology of AD.

Methods

In this study, rare variants (minor allele frequency?<?0.01) in splicing regulatory element (SRE) loci from whole genome sequencing (WGS) in the Alzheimer’s Disease Neuroimaging Initiative (ADNI) cohort, were used to identify genes that are associated with global brain cortical glucose metabolism in AD measured by FDG PET-scans. Gene-based associated analyses of rare variants were performed using the program BioBin and the optimal Sequence Kernel Association Test (SKAT-O).

Results

The gene, EXOC3L4, was identified as significantly associated with global cortical glucose metabolism (FDR (false discovery rate) corrected p?<?0.05) using SRE coding variants only. Three loci that may affect splicing within EXOC3L4 contribute to the association.

Conclusion

Based on sequence homology, EXOC3L4 is likely a part of the exocyst complex. Our results suggest the possibility that variants which affect proper splicing of EXOC3L4 via SREs may impact vesicle transport, giving rise to AD related phenotypes. Overall, by utilizing WGS and functional neuroimaging we have identified a gene significantly associated with an AD related endophenotype, potentially through a mechanism that involves splicing.

     

Longitudinal Studies of Binary Response Data Following Case–Control and Stratified Case–Control Sampling: Design and Analysis

Summary We discuss design and analysis of longitudinal studies after case–control sampling, wherein interest is in the relationship between a longitudinal binary response that is related to the sampling (case–control) variable, and a set of covariates. We propose a semiparametric modeling framework based on a marginal longitudinal binary response model and an ancillary model for subjects' case–control status. In this approach, the analyst must posit the population prevalence of being a case, which is then used to compute an offset term in the ancillary model. Parameter estimates from this model are used to compute offsets for the longitudinal response model. Examining the impact of population prevalence and ancillary model misspecification, we show that time‐invariant covariate parameter estimates, other than the intercept, are reasonably robust, but intercept and time‐varying covariate parameter estimates can be sensitive to such misspecification. We study design and analysis issues impacting study efficiency, namely: choice of sampling variable and the strength of its relationship to the response, sample stratification, choice of working covariance weighting, and degree of flexibility of the ancillary model. The research is motivated by a longitudinal study following case–control sampling of the time course of attention deficit hyperactivity disorder (ADHD) symptoms.