Generalized n-dimensional biomechanical field analysis using statistical parametric mapping

A variety of biomechanical data are sampled from smooth n-dimensional spatiotemporal fields. These data are usually analyzed discretely, by extracting summary metrics from particular points or regions in the continuum. It has been shown that, in certain situations, such schemes can compromise the spatiotemporal integrity of the original fields. An alternative methodology called statistical parametric mapping (SPM), designed specifically for continuous field analysis, constructs statistical images that lie in the original, biomechanically meaningful sampling space. The current paper demonstrates how SPM can be used to analyze both experimental and simulated biomechanical field data of arbitrary spatiotemporal dimensionality. Firstly, 0-, 1-, 2-, and 3-dimensional spatiotemporal datasets derived from a pedobarographic experiment were analyzed using a common linear model to emphasize that SPM procedures are (practically) identical irrespective of the data's physical dimensionality. Secondly two probabilistic finite element simulation studies were conducted, examining heel pad stress and femoral strain fields, respectively, to demonstrate how SPM can be used to probe the significance of field-wide simulation results in the presence of uncontrollable or induced modeling uncertainty. Results were biomechanically intuitive and suggest that SPM may be suitable for a wide variety of mechanical field applications. SPM's main theoretical advantage is that it avoids problems associated with a priori assumptions regarding the spatiotemporal foci of field signals. SPM's main practical advantage is that a unified framework, encapsulated by a single linear equation, affords comprehensive statistical analyses of smooth scalar fields in arbitrarily bounded n-dimensional spaces.     

The Impact of Spatial Scales and Spatial Smoothing on the Outcome of Bayesian Spatial Model

Discretization of a geographical region is quite common in spatial analysis. There have been few studies into the impact of different geographical scales on the outcome of spatial models for different spatial patterns. This study aims to investigate the impact of spatial scales and spatial smoothing on the outcomes of modelling spatial point-based data. Given a spatial point-based dataset (such as occurrence of a disease), we study the geographical variation of residual disease risk using regular grid cells. The individual disease risk is modelled using a logistic model with the inclusion of spatially unstructured and/or spatially structured random effects. Three spatial smoothness priors for the spatially structured component are employed in modelling, namely an intrinsic Gaussian Markov random field, a second-order random walk on a lattice, and a Gaussian field with Matérn correlation function. We investigate how changes in grid cell size affect model outcomes under different spatial structures and different smoothness priors for the spatial component. A realistic example (the Humberside data) is analyzed and a simulation study is described. Bayesian computation is carried out using an integrated nested Laplace approximation. The results suggest that the performance and predictive capacity of the spatial models improve as the grid cell size decreases for certain spatial structures. It also appears that different spatial smoothness priors should be applied for different patterns of point data.     

Pedobarographic statistical parametric mapping (pSPM): a pixel-level approach to foot pressure image analysis

Traditional pedobarographic analyses conduct statistical tests on single pressure values extracted from discrete anatomical regions, a process which yields a low-resolution view of the continuous foot-ground interaction and which can involve substantial user interaction for region definition. Using image processing techniques derived from a cerebral imaging methodology called 'statistical parametric mapping' (SPM), we describe a fully automatic method that requires no anatomical assumptions or region definitions and that generates high-resolution continuous statistical maps across the entire plantar foot surface. Here, we demonstrate both pedobarographic SPM (pSPM) and its robustness to arbitrary foot postures by producing statistical maps for a sample of nine healthy young adults walking: normally, with everted feet, and with inverted feet. After spatially smoothing pedobarographic images, within-subjects (WS) and between-subjects (BS) registration were performed using an optimal rigid body transformation and an optimum affine transformation, respectively. Statistical tests were performed over all 742 foot pixels of the 270 registered images using a linear mass-univariate model and the resulting SPMs were compared qualitatively with results obtained using a traditional ten-region technique. SPMs were found to provide a qualitatively improved view of pedobarographic changes, but the more important finding was that regional pedobarographic statistics can misrepresent the trends of their constituent pixels and thus potentially lead to misinterpretations of foot function. Since pSPM is fully non-interactive, is robust to arbitrary foot posture, and provides rapid and easily interpretable results, it appears to be a suitable alternative to regionalization for routine pedobarographic analyses in both laboratory and clinic.     

Emergence, spread, persistence and fade-out of sylvatic plague in Kazakhstan

Predicting the dynamics of zoonoses in wildlife is important not only for prevention of transmission to humans, but also for improving the general understanding of epidemiological processes. A large dataset on sylvatic plague in the Pre-Balkhash area of Kazakhstan (collected for surveillance purposes) provides a rare opportunity for detailed statistical modelling of an infectious disease. Previous work using these data has revealed a host abundance threshold for epizootics, and climatic influences on plague prevalence. Here, we present a model describing the local space-time dynamics of the disease at a spatial scale of 20 × 20 km(2) and a biannual temporal scale, distinguishing between invasion and persistence events. We used a Bayesian imputation method to account for uncertainties resulting from poor data in explanatory variables and response variables. Spatial autocorrelation in the data was accounted for in imputations and analyses through random effects. The results show (i) a clear effect of spatial transmission, (ii) a high probability of persistence compared with invasion, and (iii) a stronger influence of rodent abundance on invasion than on persistence. In particular, there was a substantial probability of persistence also at low host abundance.     

Functional architecture of long-range perceptual interactions

The pattern of lateral interactions in the primary visual cortex, which has emerged from recent studies, conforms to the grouping rules of similarity, proximity, smoothness and closure. The goal of this paper is to understand the perceptual salience of oriented elements that are specifically organized to form a smooth contour. An overview of recent studies, in combination with new experimental results, is presented here to emphasis the idea that visual responses depend on input from both the center and the surround of the classical receptive field (CRF). It is assumed that normal lateral interactions produce a neuronal network that is formed by two antagonistic mechanisms: (i) excitation, that is spatially organized along the optimal orientation (collinear), and is predominant near the contrast threshold of the neuron, and (ii) inhibition, that is less selective and is distributed diffusely around the cell's response field. Thus, the inputs from the CRF and the anisotropic surround are summated non-linearly. The specificity of the facilitation and suppression along the collinear direction suggests the existence of second-order elongated collinear filters, which may increase the response similarity between neurons responding to elongated stimulus, thus may enhance the perceptual salience of anisotropic configurations such as contours. This causal connection is particularly evident in amblyopes, where abnormal development of the network results in the abnormal perception of contours.     

Smooth individual level covariates adjustment in disease mapping

Spatial models for disease mapping should ideally account for covariates measured both at individual and area levels. The newly available “indiCAR” model fits the popular conditional autoregresssive (CAR) model by accommodating both individual and group level covariates while adjusting for spatial correlation in the disease rates. This algorithm has been shown to be effective but assumes log‐linear associations between individual level covariates and outcome. In many studies, the relationship between individual level covariates and the outcome may be non‐log‐linear, and methods to track such nonlinearity between individual level covariate and outcome in spatial regression modeling are not well developed. In this paper, we propose a new algorithm, smooth‐indiCAR, to fit an extension to the popular conditional autoregresssive model that can accommodate both linear and nonlinear individual level covariate effects while adjusting for group level covariates and spatial correlation in the disease rates. In this formulation, the effect of a continuous individual level covariate is accommodated via penalized splines. We describe a two‐step estimation procedure to obtain reliable estimates of individual and group level covariate effects where both individual and group level covariate effects are estimated separately. This distributed computing framework enhances its application in the Big Data domain with a large number of individual/group level covariates. We evaluate the performance of smooth‐indiCAR through simulation. Our results indicate that the smooth‐indiCAR method provides reliable estimates of all regression and random effect parameters. We illustrate our proposed methodology with an analysis of data on neutropenia admissions in New South Wales (NSW), Australia.     

Regional spatial modeling of topsoil geochemistry

Summary .  Geographic information about the levels of toxics in environmental media is commonly used in regional environmental health studies when direct measurements of personal exposure is limited or unavailable. In this article, we propose a statistical framework for analyzing the spatial distribution of topsoil geochemical properties, including the concentrations of various toxicants. Due to the small-scale heterogeneity of most geochemical topsoil processes, direct measurements of the processes themselves only provide highly localized information; it is thus financially prohibitive to study the spatial patterns of these processes across a large region using traditional geostatistical analyses of point-referenced topsoil data. Instead, it is standard practice to assess geochemical patterns at a regional scale using point-referenced measurements collected in stream sediment because, unlike topsoil data, individual stream sediment geochemical measurements are representative of the surrounding area. We propose a novel multiscale soils (MSS) model that formally synthesizes data collected in topsoil and stream sediment and allows the richer stream sediment information to inform about the topsoil process, which in environmental health studies is typically more relevant. Our model accommodates the small-scale heterogeneity of topsoil geochemical processes by modeling spatial dependence at an aggregate resolution corresponding to hydrologically similar regions known as watersheds. We present an analysis of the levels of arsenic, a toxic heavy metal, in topsoil across the midwestern United States using the MSS model and show that this model has better predictive abilities than alternative approaches using more conventional statistical models for point-referenced spatial data.     

A General Framework for Longitudinal Data through Marked Point Processes

This paper reviews a general framework for the modelling of longitudinal data with random measurement times based on marked point processes and presents a worked example. We construct a quite general regression models for longitudinal data, which may in particular include censoring that only depend on the past and outside random variation, and dependencies between measurement times and measurements. The modelling also generalises statistical counting process models. We review a non-parametric Nadarya-Watson kernel estimator of the regression function, and a parametric analysis that is based on a conditional least squares (CLS) criterion. The parametric analysis presented, is a conditional version of the generalised estimation equations of LIANG and ZEGER (1986). We conclude that the usual nonparametric and parametric regression modelling can be applied to this general set-up, with some modifications. The presented framework provides an easily implemented and powerful tool for model building for repeated measurements.     

A framework for list representation, enabling list stabilization through incorporation of gene exchangeabilities

Analysis of multivariate data sets from, for example, microarray studies frequently results in lists of genes which are associated with some response of interest. The biological interpretation is often complicated by the statistical instability of the obtained gene lists, which may partly be due to the functional redundancy among genes, implying that multiple genes can play exchangeable roles in the cell. In this paper, we use the concept of exchangeability of random variables to model this functional redundancy and thereby account for the instability. We present a flexible framework to incorporate the exchangeability into the representation of lists. The proposed framework supports straightforward comparison between any 2 lists. It can also be used to generate new more stable gene rankings incorporating more information from the experimental data. Using 2 microarray data sets, we show that the proposed method provides more robust gene rankings than existing methods with respect to sampling variations, without compromising the biological significance of the rankings.     

Smoothness without Smoothing: Why Gaussian Naive Bayes Is Not Naive for Multi-Subject Searchlight Studies

Spatial smoothness is helpful when averaging fMRI signals across multiple subjects, as it allows different subjects'' corresponding brain areas to be pooled together even if they are slightly misaligned. However, smoothing is usually not applied when performing multivoxel pattern-based analyses (MVPA), as it runs the risk of blurring away the information that fine-grained spatial patterns contain. It would therefore be desirable, if possible, to carry out pattern-based analyses which take unsmoothed data as their input but which produce smooth images as output. We show here that the Gaussian Naive Bayes (GNB) classifier does precisely this, when it is used in “searchlight” pattern-based analyses. We explain why this occurs, and illustrate the effect in real fMRI data. Moreover, we show that analyses using GNBs produce results at the multi-subject level which are statistically robust, neurally plausible, and which replicate across two independent data sets. By contrast, SVM classifiers applied to the same data do not generate a replication, even if the SVM-derived searchlight maps have smoothing applied to them. An additional advantage of GNB classifiers for searchlight analyses is that they are orders of magnitude faster to compute than more complex alternatives such as SVMs. Collectively, these results suggest that Gaussian Naive Bayes classifiers may be a highly non-naive choice for multi-subject pattern-based fMRI studies.     

A conceptual framework for mapping quantitative trait Loci regulating ontogenetic allometry

Although ontogenetic changes in body shape and its associated allometry has been studied for over a century, essentially nothing is known about their underlying genetic and developmental mechanisms. One of the reasons for this ignorance is the unavailability of a conceptual framework to formulate the experimental design for data collection and statistical models for data analyses. We developed a framework model for unraveling the genetic machinery for ontogenetic changes of allometry. The model incorporates the mathematical aspects of ontogenetic growth and allometry into a maximum likelihood framework for quantitative trait locus (QTL) mapping. As a quantitative platform, the model allows for the testing of a number of biologically meaningful hypotheses to explore the pleiotropic basis of the QTL that regulate ontogeny and allometry. Simulation studies and real data analysis of a live example in soybean have been performed to investigate the statistical behavior of the model and validate its practical utilization. The statistical model proposed will help to study the genetic architecture of complex phenotypes and, therefore, gain better insights into the mechanistic regulation for developmental patterns and processes in organisms.     

Spatial multistate transitional models for longitudinal event data

Summary .   Follow-up medical studies often collect longitudinal data on patients. Multistate transitional models are useful for analysis in such studies where at any point in time, individuals may be said to occupy one of a discrete set of states and interest centers on the transition process between states. For example, states may refer to the number of recurrences of an event, or the stage of a disease. We develop a hierarchical modeling framework for the analysis of such longitudinal data when the processes corresponding to different subjects may be correlated spatially over a region. Continuous-time Markov chains incorporating spatially correlated random effects are introduced. Here, joint modeling of both spatial dependence as well as dependence between different transition rates is required and a multivariate spatial approach is employed. A proportional intensities frailty model is developed where baseline intensity functions are modeled using parametric Weibull forms, piecewise-exponential formulations, and flexible representations based on cubic B-splines. The methodology is developed within the context of a study examining invasive cardiac procedures in Quebec. We consider patients admitted for acute coronary syndrome throughout the 139 local health units of the province and examine readmission and mortality rates over a 4-year period.     

Statistical methods in spatial genetics

The joint analysis of spatial and genetic data is rapidly becoming the norm in population genetics. More and more studies explicitly describe and quantify the spatial organization of genetic variation and try to relate it to underlying ecological processes. As it has become increasingly difficult to keep abreast with the latest methodological developments, we review the statistical toolbox available to analyse population genetic data in a spatially explicit framework. We mostly focus on statistical concepts but also discuss practical aspects of the analytical methods, highlighting not only the potential of various approaches but also methodological pitfalls.     

Bayesian analysis of mass spectrometry proteomic data using wavelet-based functional mixed models

Summary .   In this article, we apply the recently developed Bayesian wavelet-based functional mixed model methodology to analyze MALDI-TOF mass spectrometry proteomic data. By modeling mass spectra as functions, this approach avoids reliance on peak detection methods. The flexibility of this framework in modeling nonparametric fixed and random effect functions enables it to model the effects of multiple factors simultaneously, allowing one to perform inference on multiple factors of interest using the same model fit, while adjusting for clinical or experimental covariates that may affect both the intensities and locations of peaks in the spectra. For example, this provides a straightforward way to account for systematic block and batch effects that characterize these data. From the model output, we identify spectral regions that are differentially expressed across experimental conditions, in a way that takes both statistical and clinical significance into account and controls the Bayesian false discovery rate to a prespecified level. We apply this method to two cancer studies.     

Genetic mapping of developmental instability: design, model and algorithm

Developmental instability or noise, defined as the phenotypic imprecision of an organism in the face of internal or external stochastic disturbances, has been thought to play an important role in shaping evolutionary processes and patterns. The genetic studies of developmental instability have been based on fluctuating asymmetry (FA) that measures random differences between the left and the right sides of bilateral traits. In this article, we frame an experimental design characterized by a spatial autocorrelation structure for determining the genetic control of developmental instability for those traits that cannot be bilaterally measured. This design allows the residual environmental variance of a quantitative trait to be dissolved into two components due to permanent and random environmental factors. The degree of developmental instability is quantified by the relative proportion of the random residual variance to the total residual variance. We formulate a mixture model to estimate and test the genetic effects of quantitative trait loci (QTL) on the developmental instability of the trait. The genetic parameters including the QTL position, the QTL effects, and spatial autocorrelations are estimated by implementing the EM algorithm within the mixture model framework. Simulation studies were performed to investigate the statistical behavior of the model. A live example for poplar trees was used to map the QTL that control root length growth and its developmental instability from cuttings in water culture.     

Current caveats and further directions in the analysis of density-dependent population regulation

An important issue in population ecology is to disentangle different density-dependent mechanisms that may limit or regulate animal populations. This goal is further complicated when studying long-lived species for which experimental approaches are not feasible, in whose cases density-dependence hypotheses are tested using long-term monitored populations. Here we respond to some criticisms and identify additional problems associated with these kinds of observational studies. Current caveats are related to the temporal and spatial scales covered by population monitoring data, which may question its suitability for density-dependence tests, and to statistical flaws such as the incorrect control for confounding variables, low statistical power, the distribution of demographic variables, the interpretation of spurious correlations, and the often used stepwise series of univariate analyses. Generalised linear mixed models are recommended over other more traditional approaches, since they help to solve the above statistical problems and, more importantly, allow to properly test several hypotheses simultaneously. Finally, several management actions aimed to recover endangered species, such as supplementary feeding, might be considered as field experiments for further testing density-dependence hypotheses in long-lived study models. We expect these opportunities, together with the most adequate statistical tools now available, will help to better our understanding of density-dependent effects in wild populations.