Granger mediation analysis of multiple time series with an application to functional magnetic resonance imaging

This paper presents Granger mediation analysis, a new framework for causal mediation analysis of multiple time series. This framework is motivated by a functional magnetic resonance imaging (fMRI) experiment where we are interested in estimating the mediation effects between a randomized stimulus time series and brain activity time series from two brain regions. The independent observation assumption is thus unrealistic for this type of time‐series data. To address this challenge, our framework integrates two types of models: causal mediation analysis across the mediation variables, and vector autoregressive (VAR) models across the temporal observations. We use “Granger” to refer to VAR correlations modeled in this paper. We further extend this framework to handle multilevel data, in order to model individual variability and correlated errors between the mediator and the outcome variables. Using Rubin's potential outcome framework, we show that the causal mediation effects are identifiable under our time‐series model. We further develop computationally efficient algorithms to maximize our likelihood‐based estimation criteria. Simulation studies show that our method reduces the estimation bias and improves statistical power, compared with existing approaches. On a real fMRI data set, our approach quantifies the causal effects through a brain pathway, while capturing the dynamic dependence between two brain regions.     

Modeling the Spatial and Temporal Dependence in fMRI Data

Summary Functional magnetic resonance imaging (fMRI) data sets are large and characterized by complex dependence structures driven by highly sophisticated neurophysiology and aspects of the experimental designs. Typical analyses investigating task‐related changes in measured brain activity use a two‐stage procedure in which the first stage involves subject‐specific models and the second‐stage specifies group (or population) level parameters. Customarily, the first‐level accounts for temporal correlations between the serial scans acquired during one scanning session. Despite accounting for these correlations, fMRI studies often include multiple sessions and temporal dependencies may persist between the corresponding estimates of mean neural activity. Further, spatial correlations between brain activity measurements in different locations are often unaccounted for in statistical modeling and estimation. We propose a two‐stage, spatio‐temporal, autoregressive model that simultaneously accounts for spatial dependencies between voxels within the same anatomical region and for temporal dependencies between a subject's estimates from multiple sessions. We develop an algorithm that leverages the special structure of our covariance model, enabling relatively fast and efficient estimation. Using our proposed method, we analyze fMRI data from a study of inhibitory control in cocaine addicts.     

Reconstruction of molecular network evolution from cross‐sectional omics data

Cross‐sectional studies may shed light on the evolution of a disease like cancer through the comparison of patient traits among disease stages. This problem is especially challenging when a gene–gene interaction network needs to be reconstructed from omics data, and, in addition, the patients of each stage need not form a homogeneous group. Here, the problem is operationalized as the estimation of stage‐wise mixtures of Gaussian graphical models (GGMs) from high‐dimensional data. These mixtures are fitted by a (fused) ridge penalized EM algorithm. The fused ridge penalty shrinks GGMs of contiguous stages. The (fused) ridge penalty parameters are chosen through cross‐validation. The proposed estimation procedures are shown to be consistent and their performance in other respects is studied in simulation. The down‐stream exploitation of the fitted GGMs is outlined. In a data illustration the methodology is employed to identify gene–gene interaction network changes in the transition from normal to cancer prostate tissue.     

Parameter estimation of a monod-type model. Part II: Use of a neural network with associative memories

Summary On the basis of a previous study related with parameter identifiability and sensitivity analysis of a Monod-type model, a parameter estimation method based on Artificial Neural Networks (ANN) with Associative Memories (AMs) is presented. A combination of an iterative procedure and a convergence index given by AMs allows to confirm the nature of relations existing between state variables and parameters which were found in the first part of the study. The convergence criterion is particularly well adapted to showing various influences of state variables on parameter estimation of such a model.     

A deep learning approach to conflating heterogeneous geospatial data for corn yield estimation: A case study of the US Corn Belt at the county level

Understanding large‐scale crop growth and its responses to climate change are critical for yield estimation and prediction, especially under the increased frequency of extreme climate and weather events. County‐level corn phenology varies spatially and interannually across the Corn Belt in the United States, where precipitation and heat stress presents a temporal pattern among growth phases (GPs) and vary interannually. In this study, we developed a long short‐term memory (LSTM) model that integrates heterogeneous crop phenology, meteorology, and remote sensing data to estimate county‐level corn yields. By conflating heterogeneous phenology‐based remote sensing and meteorological indices, the LSTM model accounted for 76% of yield variations across the Corn Belt, improved from 39% of yield variations explained by phenology‐based meteorological indices alone. The LSTM model outperformed least absolute shrinkage and selection operator (LASSO) regression and random forest (RF) approaches for end‐of‐the‐season yield estimation, as a result of its recurrent neural network structure that can incorporate cumulative and nonlinear relationships between corn yield and environmental factors. The results showed that the period from silking to dough was most critical for crop yield estimation. The LSTM model presented a robust yield estimation under extreme weather events in 2012, which reduced the root‐mean‐square error to 1.47 Mg/ha from 1.93 Mg/ha for LASSO and 2.43 Mg/ha for RF. The LSTM model has the capability to learn general patterns from high‐dimensional (spectral, spatial, and temporal) input features to achieve a robust county‐level crop yield estimation. This deep learning approach holds great promise for better understanding the global condition of crop growth based on publicly available remote sensing and meteorological data.     

Partly functional temporal process regression with semiparametric profile estimating functions

Summary .  Marginal mean models of temporal processes in event time data analysis are gaining more attention for their milder assumptions than the traditional intensity models. Recent work on fully functional temporal process regression (TPR) offers great flexibility by allowing all the regression coefficients to be nonparametrically time varying. The existing estimation procedure, however, prevents successive goodness-of-fit test for covariate coefficients in comparing a sequence of nested models. This article proposes a partly functional TPR model in the line of marginal mean models. Some covariate effects are time independent while others are completely unspecified in time. This class of models is very rich, including the fully functional model and the semiparametric model as special cases. To estimate the parameters, we propose semiparametric profile estimating equations, which are solved via an iterative algorithm, starting at a consistent estimate from a fully functional model in the existing work. No smoothing is needed, in contrast to other varying-coefficient methods. The weak convergence of the resultant estimators are developed using the empirical process theory. Successive tests of time-varying effects and backward model selection procedure can then be carried out. The practical usefulness of the methodology is demonstrated through a simulation study and a real example of recurrent exacerbation among cystic fibrosis patients.     

Parameter Estimation for the Compartmental Model

An estimation procedure is obtained for a stochastic compartmental model. Compartmental analysis assumes that a system may be divided into homogeneous components, or compartments. The main theory for the compartmental system was studied by Matis and Hartley (1971) with a discrete population in a steady state. All the transitions among the particles are considered to be stochastic in nature. An estimation procedure, Regular Best Asymptotic Normal (RBAN), discussed by Chiang (1956) is investigated for a stochastic m-compartmental system. The detailed proof of the procedure is provided here. Asymptotic properties for the estimator has been studied and computation has been carried out on our proposed nonlinear model. The downhill simplex search method, originally developed by Nelder and Mead (1965), and applied to minimize our quadratic form is inherently nonlinear in nature, thus avoiding the need to evaluate any derivative for point estimation of the parameters. The procedure applied to an experimental situation involving two compartments gives very encouraging results.     

Species co‐occurrence analysis: pairwise versus matrix‐level approaches

Veech (2013, Global Ecology and Biogeography, 22 , 252–260) introduced a formula to calculate the probability of two species co‐occurring in various sites under the assumption of statistical independence between the two distributional patterns. He presented his model as a new procedure, a ‘pairwise approach’, different from analyses of whole presence–absence matrices to examine patterns of co‐occurrence. Here I show that: (1) Veech's method is identical to Fisher's exact test, a standard procedure for measuring the statistical association between two discrete variables; (2) in a broad sense, the pairwise approach is very similar to early analyses of spatial association, such as the one advanced by Forbes in 1907; (3) implicit in Veech's formula is a sampling scheme that is indistinguishable from well‐known matrix‐level null models that randomize the distribution of species among equiprobable sites; (4) pairwise co‐occurrence patterns can be analysed using any matrix‐level null model, so pairwise comparisons are not limited to using Veech's formula. The methodological distinction that Veech proposed between pairwise and matrix‐level approaches does not in fact exist, although the conceptual distinction between the two approaches is still a debated topic.     

Gradients in richness and turnover of a forest passerine's diet prior to breeding: A mixed model approach applied to faecal metabarcoding data

Rather little is known about the dietary richness and variation of generalist insectivorous species, including birds, due primarily to difficulties in prey identification. Using faecal metabarcoding, we provide the most comprehensive analysis of a passerine's diet to date, identifying the relative magnitudes of biogeographic, habitat and temporal trends in the richness and turnover in diet of Cyanistes caeruleus (blue tit) along a 39 site and 2° latitudinal transect in Scotland. Faecal samples were collected in 2014–2015 from adult birds roosting in nestboxes prior to nest building. DNA was extracted from 793 samples and we amplified COI and 16S minibarcodes. We identified 432 molecular operational taxonomic units that correspond to putative dietary items. Most dietary items were rare, with Lepidoptera being the most abundant and taxon‐rich prey order. Here, we present a statistical approach for estimation of gradients and intersample variation in taxonomic richness and turnover using a generalised linear mixed model. We discuss the merits of this approach over existing tools and present methods for model‐based estimation of repeatability, taxon richness and Jaccard indices. We found that dietary richness increases significantly as spring advances, but changes little with elevation, latitude or local tree composition. In comparison, dietary composition exhibits significant turnover along temporal and spatial gradients and among sites. Our study shows the promise of faecal metabarcoding for inferring the macroecology of food webs, but we also highlight the challenge posed by contamination and make recommendations of laboratory and statistical practices to minimise its impact on inference.     

A beta‐binomial mixed‐effects model approach for analysing longitudinal discrete and bounded outcomes

Patient‐reported outcomes (PROs) are currently being increasingly used as primary outcome measures in observational and experimental studies since they inform clinicians and researchers about the health‐status of patients and generate data to facilitate improved care. PROs usually appear as discrete and bounded with U, J, or inverse J shapes, and hence, exponential family members offer inadequate distributional fits. The beta‐binomial distribution has been proposed in the literature to fit PROs. However, the fact that the beta‐binomial distribution does not belong to the exponential family limits its applicability in the regression model context, and classical estimation approaches are not straightforward. Moreover, PROs are usually measured in a longitudinal framework in which individuals are followed up for a certain period. Hence, each individual obtains several scores of the PRO over time, which leads to the repeated measures and defines the correlation structure in the data. In this work, we have developed and proposed an estimation procedure for the analysis of correlated discrete and bounded outcomes, particularly PROs, by a beta‐binomial mixed‐effects model. Additionally, we have implemented the methodology in the PROreg package in R. Because there are similar approaches in the literature to address the same issue, this work also incorporates a comparison study between our proposal and alternative methodologies commonly implemented in R and shows the superior performance of our estimation procedure. This paper was motivated by the analysis of the health‐status of patients with chronic obstructive pulmonary disease, where the main objective is the assessment of risk factors that may affect the evolution of the disease. The application of the proposed approach in the study leads to clinically relevant results.     

Macroevolution of hoverflies (Diptera: Syrphidae): the effect of using higher‐level taxa in studies of biodiversity,and correlates of species richness

We test a near‐complete genus level phylogeny of hoverflies (Diptera: Syrphidae) for consistency with a null model of clade growth having uniform probabilities of speciation and extinction among contemporaneous species. The phylogeny is too unbalanced for this null model. Importantly, the degree of imbalance in the phylogeny depends on whether the phylogeny is analysed at the genus level or species level, suggesting that genera ought not to be used uncritically as surrogates for species in large‐scale evolutionary analyses. Tests for a range of morphological, life‐history and ecological correlates of diversity give equivocal results, but suggest that high species‐richness may be associated with sexual selection and diet breadth. We find no correlation between species‐richness and either body size or reproductive rate.     

Trendtests with adaptive scoring

The concept of adaptive two‐stage designs is applied to the problem of testing the equality of several normal means against an ordered (monotone) alternative. The likelihood‐ratio‐test proposed by Bartholomew is known to have favorable power properties when testing against a monotonic trend. Tests based on contrasts provide a flexible way to incorporate available information regarding the pattern of the unknown true means through appropriate specification of the scores. The basic idea of the presented concept is the combination of Bartholomew 's test (first stage) with an “adaptive score test” (second stage) which utilizes the information resulting from isotonic regression estimation at the first stage. In a Monte Carlo simulation study the adaptive scoring procedure is compared to the non‐adaptive two‐stage procedure using the Bartholomew test at both stages. We found that adaptive scoring may improve the power of the two stage design, in particular if the sample size at the first stage is considerably larger than at the second stage.     

Identifyability measures to select the parameters to be estimated in a solid‐state fermentation distributed parameter model

Process modeling can lead to of advantages such as helping in process control, reducing process costs and product quality improvement. This work proposes a solid‐state fermentation distributed parameter model composed by seven differential equations with seventeen parameters to represent the process. Also, parameters estimation with a parameters identifyability analysis (PIA) is performed to build an accurate model with optimum parameters. Statistical tests were made to verify the model accuracy with the estimated parameters considering different assumptions. The results have shown that the model assuming substrate inhibition better represents the process. It was also shown that eight from the seventeen original model parameters were nonidentifiable and better results were obtained with the removal of these parameters from the estimation procedure. Therefore, PIA can be useful to estimation procedure, since it may reduce the number of parameters that can be evaluated. Further, PIA improved the model results, showing to be an important procedure to be taken. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:905–917, 2016     

Double‐wavelet transform for multisubject task‐induced functional magnetic resonance imaging data

The goal of this article is to model multisubject task‐induced functional magnetic resonance imaging (fMRI) response among predefined regions of interest (ROIs) of the human brain. Conventional approaches to fMRI analysis only take into account temporal correlations, but do not rigorously model the underlying spatial correlation due to the complexity of estimating and inverting the high dimensional spatio‐temporal covariance matrix. Other spatio‐temporal model approaches estimate the covariance matrix with the assumption of stationary time series, which is not always feasible. To address these limitations, we propose a double‐wavelet approach for modeling the spatio‐temporal brain process. Working with wavelet coefficients simplifies temporal and spatial covariance structure because under regularity conditions, wavelet coefficients are approximately uncorrelated. Different wavelet functions were used to capture different correlation structures in the spatio‐temporal model. The main advantages of the wavelet approach are that it is scalable and that it deals with nonstationarity in brain signals. Simulation studies showed that our method could reduce false‐positive and false‐negative rates by taking into account spatial and temporal correlations simultaneously. We also applied our method to fMRI data to study activation in prespecified ROIs in the prefontal cortex. Data analysis showed that the result using the double‐wavelet approach was more consistent than the conventional approach when sample size decreased.     

The population ecology of male gametophytes: the link between pollination and seed production

The fate of male gametophytes after pollen reaches stigmas links pollination to ovule fertilisation, governing subsequent siring success and seed production. Although male gametophyte performance primarily involves cellular processes, an ecological analogy may expose insights into the nature and implications of male gametophyte success. We elaborate this analogy theoretically and present empirical examples that illustrate associated insights. Specifically, we consider pollen loads on stigmas as localised populations subject to density‐independent mortality and density‐dependent processes as they traverse complex stylar environments. Different combinations of the timing of pollen‐tube access to limiting stylar resources (simultaneous or sequential), the tube distribution among resources (repulsed or random) and the timing of density‐independent mortality relative to competition (before or after) create signature relations of mean pollen‐tube success and its variation among pistils to pollen receipt. Using novel nonlinear regression analyses (two‐moment regression), we illustrate contrasting relations for two species, demonstrating that variety in these relations is a feature of reproductive diversity among angiosperms, rather than merely a theoretical curiosity. Thus, the details of male gametophyte ecology should shape sporophyte reproductive success and hence the dynamics and structure of angiosperm populations.     

ESTIMATING HIERARCHICAL F-STATISTICS

This paper presents an analysis of variance (ANOVA) approach by which estimation of F-statistics can be made from data with an arbitrary s-level hierarchical population structure. Assuming a complete random-effect model, a general ANOVA procedure is developed to estimate F-statistics as ratios of different variance components for all levels of population subdivision in the hierarchy. A generalized relationship among F-statistics is also derived to extend the well-known relationship originally found by Sewall Wright. Although not entirely free from the bias particular to small number of subdivisions at each hierarchy and extreme gene frequencies, the ANOVA estimators of F-statistics consider sampling effects at each level of hierarchy, thus removing the bias incurred in the other estimators that are commonly based on direct substitution of unknown gene frequencies by their sample estimates. Therefore, the ANOVA estimation procedure presented here may become increasingly useful in analyzing complex population structure because of increasing use of the estimated hierarchical F-statistics to infer genetic and demographic structures of natural populations within and among species.     

Temporal proteomic analysis of IGF‐1R signalling in MCF‐7 breast adenocarcinoma cells

Dysregulation of the insulin‐like growth factor 1 receptor signalling network is implicated in tumour growth and resistance to chemotherapy. We explored proteomic changes resulting from insulin‐like growth factor 1 stimulation of MCF‐7 adenocarcinoma cells as a function of time. Quantitative analysis using iTRAQ? reagents and 2‐D LC‐MS/MS analysis of three biological replicates resulted in the identification of 899 proteins (p≤0.05) with an estimated mean false‐positive rate of 2.6%. Quantitative protein expression was obtained from 681 proteins. Further analysis by supervised k‐means clustering identified five temporal clusters, which were submitted to the FuncAssociate server to assign overrepresented gene ontology terms. Proteins associated with vesicle transport were significantly overrepresented. We further analyzed our data set for proteins showing temporal significance using the software, extraction and analysis of differential gene expression, resulting in 20 significantly and temporally changing proteins (p≤0.1). These significant proteins play roles in, among others, altered glucose metabolism (lactate dehydrogenase A and pyruvate kinase M1/M2) and cellular stress (nascent polypeptide‐associated complex subunit α and heat shock (HSC70) proteins). We used multiple reaction monitoring to validate these interesting proteins and have revealed several differences in relative peptide expression corresponding to protein isoforms and variants.     

Joint estimation of migration rate and effective population size using the island model

Using the island model of population demography, I report that the demographic parameters migration rate and effective population size can be jointly estimated with equilibrium probabilities of identity in state calculated using a sample of genotypes collected at a single point in time from a single generation. The method, which uses moment-type estimators, applies to dioecious populations in which females and males have identical demography and monoecious populations with no selfing and requires that offspring genotypes are sampled following reproduction and prior to migration. I illustrate the estimation procedure using the infinite-island model with no mutation and the finite-island model with three kinds of mutation models. In the infinite-island model with no mutation, the estimators can be expressed as simple functions of estimates of the F-statistic parameters F(IT) and F(ST). In the finite-island model with mutation among k alleles, mutation rate, migration rate, and effective population size can be simultaneously estimated. The estimates of migration rate and effective population size are somewhat robust to violations in assumptions that may arise in empirical applications such as different kinds of mutation models and deviations from temporal equilibrium.     

Bayesian Total Internal Reflection Fluorescence Correlation Spectroscopy Reveals hIAPP-Induced Plasma Membrane Domain Organization in Live Cells

Amyloid fibril deposition of human islet amyloid polypeptide (hIAPP) in pancreatic islet cells is implicated in the pathogenesis of type II diabetes. A growing number of studies suggest that small peptide aggregates are cytotoxic via their interaction with the plasma membrane, which leads to membrane permeabilization or disruption. A recent study using imaging total internal reflection-fluorescence correlation spectroscopy (ITIR-FCS) showed that monomeric hIAPP induced the formation of cellular plasma membrane microdomains containing dense lipids, in addition to the modulation of membrane fluidity. However, the spatial organization of microdomains and their temporal evolution were only partially characterized due to limitations in the conventional analysis and interpretation of imaging FCS datasets. Here, we apply a previously developed Bayesian analysis procedure to ITIR-FCS data to resolve hIAPP-induced microdomain spatial organization and temporal dynamics. Our analysis enables the visualization of the temporal evolution of multiple diffusing species in the spatially heterogeneous cell membrane, lending support to the carpet model for the association mode of hIAPP aggregates with the plasma membrane. The presented Bayesian analysis procedure provides an automated and general approach to unbiased model-based interpretation of imaging FCS data, with broad applicability to resolving the heterogeneous spatial-temporal organization of biological membrane systems.