Farouk S. Nathoo

Assessing noninferiority in a three-arm trial using the Bayesian approach.

Non-inferiority trials, which aim to demonstrate that a test product is not worse than a competitor by more than a pre-specified small amount, are of great importance to the pharmaceutical community. As a result, methodology for designing and analyzing such trials is required, and developing new methods for such analysis is an important area of statistical research. The three-arm trial consists of a placebo, a reference and an experimental treatment, and simultaneously tests the superiority of the reference over the placebo along with comparing this reference to an experimental treatment. In this paper, we consider the analysis of non-inferiority trials using Bayesian methods which incorporate both parametric as well as semi-parametric models. The resulting testing approach is both flexible and robust. The benefit of the proposed Bayesian methods is assessed via simulation, based on a study examining home-based blood pressure interventions.

Toward a kinetic-based probabilistic time geography

Time geography represents a powerful framework for the quantitative analysis of individual movement. Time geography effectively delineates the space–time boundaries of possible individual movement by characterizing movement constraints. The goal of this paper is to synchronize two new ideas, probabilistic time geography and kinetic-based time geography, to develop a more realistic set of movement constraints that consider movement probabilities related to object kinetics. Using random-walk theory, the existing probabilistic time geography model characterizes movement probabilities for the space–time cone using a normal distribution. The normal distribution has a symmetric probability density function and is an appropriate model in the absence of skewness – which we relate to an object’s initial velocity. Moving away from a symmetric distribution for movement probabilities, we propose the use of the skew-normal distribution to model kinetic-based movement probabilities, where the degree and direction of skewness is related to movement direction and speed. Following a description of our model, we use a set of case-studies to demonstrate the skew-normal model: a random walk, a correlated random walk, wildlife data, cyclist data, and athlete movement data. Our results show that for objects characterized by random movement behavior, the existing model performs well, but for object movement with kinetic properties (e.g., athletes), the proposed model provides a substantial improvement. Future work will look to extend the proposed probabilistic framework to the space–time prism.

Predictive crime mapping

Geographic Information Systems (GIS) have emerged as a key tool in intelligence-led policing and spatial predictions of crime are being used by many police services to reduce crime. Break and entries (BNEs) are one of the most patterned and predictable crime types, and may be particularly amendable to predictive crime mapping. A pilot project was conducted to spatially predict BNEs and property crime in Vancouver, Canada. Using detailed data collected by the Vancouver Police Department on where and when observed crimes occur, the statistical model was able to predict future BNEs for residential and commercial locations. Ideally implemented within a mobile GIS, the automated model provides continually updated predictive maps and may assist patrol units in self-deployment decisions. Future research is required to overcome computational and statistical limitations, and to preform model validation.

A Hidden Markov Model for Analysis of Frontline Veterinary Data for Emerging Zoonotic Disease Surveillance

Surveillance systems tracking health patterns in animals have potential for early warning of infectious disease in humans, yet there are many challenges that remain before this can be realized. Specifically, there remains the challenge of detecting early warning signals for diseases that are not known or are not part of routine surveillance for named diseases. This paper reports on the development of a hidden Markov model for analysis of frontline veterinary sentinel surveillance data from Sri Lanka. Field veterinarians collected data on syndromes and diagnoses using mobile phones. A model for submission patterns accounts for both sentinel-related and disease-related variability. Models for commonly reported cattle diagnoses were estimated separately. Region-specific weekly average prevalence was estimated for each diagnoses and partitioned into normal and abnormal periods. Visualization of state probabilities was used to indicate areas and times of unusual disease prevalence. The analysis suggests that hidden Markov modelling is a useful approach for surveillance datasets from novel populations and/or having little historical baselines.

Recognition of Facial Expressions of Emotion in Adults with Down Syndrome

ABSTRACT Research on facial expressions in individuals with Down syndrome (DS) has been conducted using photographs. Our goal was to examine the effect of motion on perception of emotional expressions. Adults with DS, adults with typical development matched for chronological age (CA), and children with typical development matched for developmental age (DA) viewed photographs and video clips of facial expressions of: happy, sad, mad, and scared. The odds of accurate identification of facial expressions were 2.7 times greater for video clips compared with photographs. The odds of accurate identification of expressions of mad and scared were greater for video clips compared with photographs. The odds of accurate identification of expressions of mad and sad were greater for adults but did not differ between adults with DS and children. Adults with DS demonstrated the lowest accuracy for recognition of scared. These results support the importance of motion cues in evaluating the social skills of individuals with DS.

Skew-elliptical spatial random effect modeling for areal data with application to mapping health utilization rates

Mixed models incorporating spatially correlated random effects are often used for the analysis of areal data. In this setting, spatial smoothing is introduced at the second stage of a hierarchical framework, and this smoothing is often based on a latent Gaussian Markov random field. The Markov random field provides a computationally convenient framework for modeling spatial dependence; however, the Gaussian assumption underlying commonly used models can be overly restrictive in some applications. This can be a problem in the presence of outliers or discontinuities in the underlying spatial surface, and in such settings, models based on non-Gaussian spatial random effects are useful. Motivated by a study examining geographic variation in the treatment of acute coronary syndrome, we develop a robust model for smoothing small-area health service utilization rates. The model incorporates non-Gaussian spatial random effects, and we develop a formulation for skew-elliptical areal spatial models. We generalize the Gaussian conditional autoregressive model to the non-Gaussian case, allowing for asymmetric skew-elliptical marginal distributions having flexible tail behavior. The resulting new models are flexible, computationally manageable, and can be implemented in the standard Bayesian software WinBUGS. We demonstrate performance of the proposed methods and comparisons with other commonly used Gaussian and non-Gaussian spatial prior formulations through simulation and analysis in our motivating application, mapping rates of revascularization for patients diagnosed with acute coronary syndrome in Quebec, Canada.

A variational Bayes spatiotemporal model for electromagnetic brain mapping

In this article, we present a new variational Bayes approach for solving the neuroelectromagnetic inverse problem arising in studies involving electroencephalography (EEG) and magnetoencephalography (MEG). This high-dimensional spatiotemporal estimation problem involves the recovery of time-varying neural activity at a large number of locations within the brain, from electromagnetic signals recorded at a relatively small number of external locations on or near the scalp. Framing this problem within the context of spatial variable selection for an underdetermined functional linear model, we propose a spatial mixture formulation where the profile of electrical activity within the brain is represented through location-specific spike-and-slab priors based on a spatial logistic specification. The prior specification accommodates spatial clustering in brain activation, while also allowing for the inclusion of auxiliary information derived from alternative imaging modalities, such as functional magnetic resonance imaging (fMRI). We develop a variational Bayes approach for computing estimates of neural source activity, and incorporate a nonparametric bootstrap for interval estimation. The proposed methodology is compared with several alternative approaches through simulation studies, and is applied to the analysis of a multimodal neuroimaging study examining the neural response to face perception using EEG, MEG, and fMRI.

Joint Spatial Modeling of Recurrent Infection and Growth with Processes under Intermittent Observation

In this article, we present a new statistical methodology for longitudinal studies in forestry, where trees are subject to recurrent infection, and the hazard of infection depends on tree growth over time. Understanding the nature of this dependence has important implications for reforestation and breeding programs. Challenges arise for statistical analysis in this setting with sampling schemes leading to panel data, exhibiting dynamic spatial variability, and incomplete covariate histories for hazard regression. In addition, data are collected at a large number of locations, which poses computational difficulties for spatiotemporal modeling. A joint model for infection and growth is developed wherein a mixed nonhomogeneous Poisson process, governing recurring infection, is linked with a spatially dynamic nonlinear model representing the underlying height growth trajectories. These trajectories are based on the von Bertalanffy growth model and a spatially varying parameterization is employed. Spatial variability in growth parameters is modeled through a multivariate spatial process derived through kernel convolution. Inference is conducted in a Bayesian framework with implementation based on hybrid Monte Carlo. Our methodology is applied for analysis in an 11-year study of recurrent weevil infestation of white spruce in British Columbia.

A Skew-t space-varying regression model for the spectral analysis of resting state brain activity

It is known that in many neurological disorders such as Down syndrome, main brain rhythms shift their frequencies slightly, and characterizing the spatial distribution of these shifts is of interest. This article reports on the development of a Skew-t mixed model for the spatial analysis of resting state brain activity in healthy controls and individuals with Down syndrome. Time series of oscillatory brain activity are recorded using magnetoencephalography, and spectral summaries are examined at multiple sensor locations across the scalp. We focus on the mean frequency of the power spectral density, and use space-varying regression to examine associations with age, gender and Down syndrome across several scalp regions. Spatial smoothing priors are incorporated based on a multivariate Markov random field, and the markedly non-Gaussian nature of the spectral response variable is accommodated by the use of a Skew-t distribution. A range of models representing different assumptions on the association structure and response distribution are examined, and we conduct model selection using the deviance information criterion. 1 Our analysis suggests region-specific differences between healthy controls and individuals with Down syndrome, particularly in the left and right temporal regions, and produces smoothed maps indicating the scalp topography of the estimated differences.

A Bayesian space-time model for discrete spread processes on a lattice

In this article we present a Bayesian Markov model for investigating environmental spread processes. We formulate a model where the spread of a disease over a heterogeneous landscape through time is represented as a probabilistic function of two processes: local diffusion and random-jump dispersal. This formulation represents two mechanisms of spread which result in highly peaked and long-tailed distributions of dispersal distances (i.e., local and long-distance spread), commonly observed in the spread of infectious diseases and biological invasions. We demonstrate the properties of this model using a simulation experiment and an empirical case study - the spread of mountain pine beetle in western Canada. Posterior predictive checking was used to validate the number of newly inhabited regions in each time period. The model performed well in the simulation study in which a goodness-of-fit statistic measuring the number of newly inhabited regions in each time interval fell within the 95% posterior predictive credible interval in over 97% of simulations. The case study of a mountain pine beetle infestation in western Canada (1999-2009) extended the base model in two ways. First, spatial covariates thought to impact the local diffusion parameters, elevation and forest cover, were included in the model. Second, a refined definition for translocation or jump-dispersal based on mountain pine beetle ecology was incorporated improving the fit of the model. Posterior predictive checks on the mountain pine beetle model found that the observed goodness-of-fit test statistic fell within the 95% posterior predictive credible interval for 8 out of 10 years. The simulation study and case study provide evidence that the model presented here is both robust and flexible; and is therefore appropriate for a wide range of spread processes in epidemiology and ecology.