Fitting spatio-temporal models for areal data is crucial in many fields such as cancer epidemiology. However, when data sets are very large, many issues arise. The main objective of this paper is to propose a general procedure to analyze high-dimensional spatio-temporal count data, with special emphasis on mortality/incidence relative risk estimation. We present a pragmatic and simple idea that permits to fit hierarchical spatio-temporal models when the number of small areas is very large. Model fitting is carried out using integrated nested Laplace approximations over a partition of the spatial domain. We also use parallel and distributed strategies to speed up computations in a setting where Bayesian model fitting is generally prohibitively time-consuming and even unfeasible. Using simulated and real data, we show that our method outperforms classical global models. We implement the methods and algorithms that we develop in the open-source R package bigDM where specific vignettes have been included to facilitate the use of the methodology for non-expert users. Our scalable methodology proposal provides reliable risk estimates when fitting Bayesian hierarchical spatio-temporal models for high-dimensional data.
Bayesian disease mapping, yet if undeniably useful to describe variation in risk over time and space, comes with the hurdle of prior elicitation on hard-to-interpret random effect precision parameters. We introduce a reparametrized version of the popular spatio-temporal interaction models, based on Kronecker product intrinsic Gaussian Markov Random Fields, that we name the variance partitioning (VP) model. The VP model includes a mixing parameter that balances the contribution of the main and interaction effects to the total (generalized) variance and enhances interpretability. The use of a pe…
In this paper we set out general principles and develop geostatistical methods for the analysis of data from spatio-temporally referenced prevalence surveys. Our objective is to provide a tutorial guide that can be used in order to identify parsimonious geostatistical models for prevalence mapping. A general variogram-based Monte Carlo procedure is proposed to check the validity of the modelling assumptions. We describe and contrast likelihood-based and Bayesian methods of inference, showing how to account for parameter uncertainty under each of the two paradigms. We also describe extensions o…
In epidemiological disease mapping one aims to estimate the spatio-temporal pattern in disease risk and identify high-risk clusters, allowing health interventions to be appropriately targeted. Bayesian spatio-temporal models are used to estimate smoothed risk surfaces, but this is contrary to the aim of identifying groups of areal units that exhibit elevated risks compared with their neighbours. Therefore, in this paper we propose a new Bayesian hierarchical modelling approach for simultaneously estimating disease risk and identifying high-risk clusters in space and time. Inference for this mo…
Routine public health surveillance of notifiable infectious diseases gives rise to weekly counts of reported cases -- possibly stratified by region and/or age group. We investigate how an age-structured social contact matrix can be incorporated into a spatio-temporal endemic-epidemic model for infectious disease counts. To illustrate the approach, we analyze the spread of norovirus gastroenteritis over 6 age groups within the 12 districts of Berlin, 2011-2015, using contact data from the POLYMOD study. The proposed age-structured model outperforms alternative scenarios with homogeneous or no m…
We propose a new centered autologistic spatio-temporal model for binary data on a lattice. The centering allows the interpretation of the autoregression coefficients in separating the large scale structure of the model corresponding to an expected mean and the small-scale structure corresponding to the auto-correlation. We discuss the existence of the joint law of the process and show by simulation the interest of this kind of centering. We propose and show the efficiency of the maximum pseudo-likelihood estimator and also a method to choose the best structure of neighborhood. Method is applie…
Spatio-temporal counts of infectious disease cases often contain an excess of zeros. With existing zero inflated count models applied to such data it is difficult to quantify space-time heterogeneity in the effects of disease spread between areas. Also, existing methods do not allow for separate dynamics to affect the reemergence and persistence of the disease. As an alternative, we develop a new zero-state coupled Markov switching negative binomial model, under which the disease switches between periods of presence and absence in each area through a series of partially hidden nonhomogeneous M…
Non-Gaussian spatial and spatio-temporal data are becoming increasingly prevalent, and their analysis is needed in a variety of disciplines. FRK is an R package for spatial/spatio-temporal modelling and prediction with very large data sets that, to date, has only supported linear process models and Gaussian data models. In this paper, we describe a major upgrade to FRK that allows for non-Gaussian data to be analysed in a generalised linear mixed model framework. These vastly more general spatial and spatio-temporal models are fitted using the Laplace approximation via the software TMB. The ex…
We introduce a Bayesian approach for analyzing high-dimensional multinomial data that are referenced over space and time. In particular, the proportions associated with multinomial data are assumed to have a logit link to a latent spatio-temporal mixed effects model. This strategy allows for covariances that are nonstationarity in both space and time, asymmetric, and parsimonious. We also introduce the use of the conditional multivariate logit-beta distribution into the dependent multinomial data setting, which leads to conjugate full-conditional distributions for use in a collapsed Gibbs samp…
The scan statistic sets the benchmark for spatio-temporal surveillance methods with its popularity. In its simplest form it scans the target area and time to find regions with disease count higher than expected. If the shape and size of the disease outbreaks are known, then to detect it sufficiently early the scan statistic can design its search area to be efficient for this shape and size. A plan that is efficient at detecting a range of disease outbreak shapes and sizes is important because these vary from one outbreak to the next and are generally never known in advance. This paper offers a…
Statistical models used to estimate the spatio-temporal pattern in disease risk from areal unit data represent the risk surface for each time period with known covariates and a set of spatially smooth random effects. The latter act as a proxy for unmeasured spatial confounding, whose spatial structure is often characterised by a spatially smooth evolution between some pairs of adjacent areal units while other pairs exhibit large step changes. This spatial heterogeneity is not consistent with existing global smoothing models, in which partial correlation exists between all pairs of adjacent spa…
Probabilistic models for infectious disease dynamics are useful for understanding the mechanism underlying the spread of infection. When the likelihood function for these models is expensive to evaluate, traditional likelihood-based inference may be computationally intractable. Furthermore, traditional inference may lead to poor parameter estimates and the fitted model may not capture important biological characteristics of the observed data. We propose a novel approach for resolving these issues that is inspired by recent work in emulation and calibration for complex computer models. Our moti…
The outbreaks of Coronavirus Disease 2019 (COVID-19) have impacted the world significantly. Modeling the trend of infection and real-time forecasting of cases can help decision making and control of the disease spread. However, data-driven methods such as recurrent neural networks (RNN) can perform poorly due to limited daily samples in time. In this work, we develop an integrated spatiotemporal model based on the epidemic differential equations (SIR) and RNN. The former after simplification and discretization is a compact model of temporal infection trend of a region while the latter models t…
The emergence of Covid-19 requires new effective tools for epidemiological surveillance. Spatio-temporal disease mapping models, which allow dealing with highly disaggregated spatial and temporal units of analysis, are a priority in this sense. Spatio-temporal models provide a geographically detailed and temporally updated overview of the current state of the pandemics, making public health interventions to be more effective. Moreover, the use of spatio-temporal disease mapping models in the new Covid-19 epidemic context, facilitates estimating newly demanded epidemiological indicators, such a…
Among the proposals for joint disease mapping, the shared component model has become more popular. Another recent advance to strengthen inference of disease data has been the extension of purely spatial models to include time and space-time interaction. Such analyses have additional benefits over purely spatial models. However, only a few proposed spatio-temporal models could address analysing multiple diseases jointly. In the proposed model, each component is shared by different subsets of diseases, spatial and temporal trends are considered for each component, and the relative weight of thes…
Understanding the spread of any disease is a highly complex and interdisciplinary exercise as biological, social, geographic, economic, and medical factors may shape the way a disease moves through a population and options for its eventual control or eradication. Disease spread poses a serious threat in animal and plant health and has implications for ecosystem functioning and species extinctions as well as implications in society through food security and potential disease spread in humans. Space-time epidemiology is based on the concept that various characteristics of the pathogenic agents a…
To study the impact of climate variables on morbidity of some diseases in Mexico, we propose a spatio-temporal varying coefficients regression model. For that we introduce a new spatio-temporal dependent process prior, in a Bayesian context, with identically distributed normal marginal distributions and joint multivariate normal distribution. We study its properties and characterise the dependence induced. Our results show that the effect of climate variables, on the incidence of specific diseases, is not constant across space and time and our proposed model is able to capture and quantify tho…
Malaria is an infectious disease affecting a large population across the world, and interventions need to be efficiently applied to reduce the burden of malaria. We develop a framework to help policy-makers decide how to allocate limited resources in realtime for malaria control. We formalize a policy for the resource allocation as a sequence of decisions, one per intervention decision, that map up-to-date disease related information to a resource allocation. An optimal policy must control the spread of the disease while being interpretable and viewed as equitable to stakeholders. We construct…
Official freely available data about the number of infected at the finest possible level of spatial areal aggregation (Italian provinces) are used to model the spatio-temporal distribution of COVID-19 infections at local level. Data time horizon ranges from 26 February 20020, which is the date when the first case not directly connected with China has been discovered in northern Italy, to 18 March 2020. An endemic-epidemic multivariate time-series mixed-effects generalized linear model for areal disease counts has been implemented to understand and predict spatio-temporal diffusion of the pheno…
This paper develops a large-scale Bayesian spatio-temporal binomial regression model for the purpose of investigating regional trends in antibody prevalence to Borrelia burgdorferi, the causative agent of Lyme disease. The proposed model uses Gaussian predictive processes to estimate the spatially varying trends and a conditional autoregressive model to account for spatio-temporal dependence. Careful consideration is made to develop a novel framework that is scalable to large spatio-temporal data. The proposed model is used to analyze approximately 16 million Borrelia burgdorferi test results …
Integrating Temporal Disaggregation and Distributed Lag Nonlinear Models for Bayesian Spatio-Temporal Disease Mapping with High-Resolution Environmental Exposures
KU Leuven（荷语鲁汶大学）；Hasselt University（哈瑟尔特大学）；Clinton Health Access Initiative（克林顿健康准入倡议）；National Malaria Control Program, Ministry of Health（卫生部国家疟疾控制项目）；University of Birmingham（伯明翰大学）
With COVID-19 affecting every country globally and changing everyday life, the ability to forecast the spread of the disease is more important than any previous epidemic. The conventional methods of disease-spread modeling, compartmental models, are based on the assumption of spatiotemporal homogeneity of the spread of the virus, which may cause forecasting to underperform, especially at high spatial resolutions. In this paper we approach the forecasting task with an alternative technique - spatiotemporal machine learning. We present COVID-LSTM, a data-driven model based on a Long Short-term M…
Recently, the Centers for Disease Control and Prevention (CDC) has worked with other federal agencies to identify counties with increasing coronavirus disease 2019 (COVID-19) incidence (hotspots) and offers support to local health departments to limit the spread of the disease. Understanding the spatio-temporal dynamics of hotspot events is of great importance to support policy decisions and prevent large-scale outbreaks. This paper presents a spatio-temporal Bayesian framework for early detection of COVID-19 hotspots (at the county level) in the United States. We assume both the observed numb…
Self-exciting spatio-temporal point process models predict the rate of events as a function of space, time, and the previous history of events. These models naturally capture triggering and clustering behavior, and have been widely used in fields where spatio-temporal clustering of events is observed, such as earthquake modeling, infectious disease, and crime. In the past several decades, advances have been made in estimation, inference, simulation, and diagnostic tools for self-exciting point process models. In this review, I describe the basic theory, survey related estimation and inference …
Unifying Physics- and Data-Driven Modeling via Novel Causal Spatiotemporal Graph Neural Network for Interpretable Epidemic Forecasting
Frankfurt Institute for Advanced Studies（法兰克福高等研究院）；Goethe Universität Frankfurt（法兰克福大学）；Xidian-FIAS International Joint Research Center（西电-法兰克福高等研究院国际联合研究中心）；School of Science and Engineering, The Chinese University of Hong Kong（香港中文大学（深圳）理工学院）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI亥姆霍兹重离子研究中心）
Ludwig Maximilian Universität（路德维希-马克西米利安大学）；Helmholtz Zentrum München – German Research Center for Environmental Health（亥姆霍兹慕尼黑中心——德国环境健康研究中心）
During 2020, the infection rate of COVID-19 has been investigated by many scholars from different research fields. In this context, reliable and interpretable forecasts of disease incidents are a vital tool for policymakers to manage healthcare resources. Several experts have called for the necessity to account for human mobility to explain the spread of COVID-19. Existing approaches are often applying standard models of the respective research field. This habit, however, often comes along with certain restrictions. For instance, most statistical or epidemiological models cannot directly incor…
Epidemic modeling is an essential tool to understand the spread of the novel coronavirus and ultimately assist in disease prevention, policymaking, and resource allocation. In this article, we establish a state of the art interface between classic mathematical and statistical models and propose a novel space-time epidemic modeling framework to study the spatial-temporal pattern in the spread of infectious disease. We propose a quasi-likelihood approach via the penalized spline approximation and alternatively reweighted least-squares technique to estimate the model. Furthermore, we provide a sh…
Epidemic data often possess certain characteristics, such as the presence of many zeros, the spatial nature of the disease spread mechanism or environmental noise. This paper addresses these issues via suitable Bayesian modelling. In doing so we utilise stochastic regression models appropriate for spatio-temporal count data with an excess number of zeros. The developed regression framework can incorporate serial correlation and time varying covariates through an Ornstein Uhlenbeck process formulation. In addition, we explore the effect of different priors, including default options and techniq…
Understanding and predicting environmental phenomena often requires the construction of spatio-temporal statistical models, which are typically Gaussian processes. A common assumption made on Gaussian processes is that of covariance stationarity, which is unrealistic in many geophysical applications. In this article, we introduce a deep-learning-inspired approach to construct descriptive nonstationary spatio-temporal models by modeling stationary processes on warped spatio-temporal domains. The warping functions we use are constructed using several simple injective warping units which, when co…
A cornerstone of the smart grid is the advanced monitorability on its assets and operations. Increasingly pervasive installation of the phasor measurement units (PMUs) allows the so-called synchrophasor measurements to be taken roughly 100 times faster than the legacy supervisory control and data acquisition (SCADA) measurements, time-stamped using the global positioning system (GPS) signals to capture the grid dynamics. On the other hand, the availability of low-latency two-way communication networks will pave the way to high-precision real-time grid state estimation and detection, remedial a…
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Microsoft Research, China（微软亚洲研究院）
Since the first coronavirus case was identified in the U.S. on Jan. 21, more than 1 million people in the U.S. have confirmed cases of COVID-19. This infectious respiratory disease has spread rapidly across more than 3000 counties and 50 states in the U.S. and have exhibited evolutionary clustering and complex triggering patterns. It is essential to understand the complex spacetime intertwined propagation of this disease so that accurate prediction or smart external intervention can be carried out. In this paper, we model the propagation of the COVID-19 as spatio-temporal point processes and p…
University College London（伦敦大学学院）；Inria（法国国家信息与自动化研究所）；Université Côte d'Azur（蔚蓝海岸大学）
Here we present DIVE: Data-driven Inference of Vertexwise Evolution. DIVE is an image-based disease progression model with single-vertex resolution, designed to reconstruct long-term patterns of brain pathology from short-term longitudinal data sets. DIVE clusters vertex-wise biomarker measurements on the cortical surface that have similar temporal dynamics across a patient population, and concurrently estimates an average trajectory of vertex measurements in each cluster. DIVE uniquely outputs a parcellation of the cortex into areas with common progression patterns, leading to a new signature…
Modern disease mapping draws upon a wealth of high resolution spatial data products reflecting environmental and/or socioeconomic factors as covariates, or `features', within a geostatistical framework to improve predictions of disease risk. Feature selection is an important step in building these models, helping to reduce overfitting and computational complexity, and to improve model interpretability. Selecting only features that have a causal relationship with the response variable could potentially improve predictions and generalisability, but identifying these causal features from non-inte…
Hotspot detection aims at identifying subgroups in the observations that are unexpected, with respect to the some baseline information. For instance, in disease surveillance, the purpose is to detect sub-regions in spatiotemporal space, where the count of reported diseases (e.g. Cancer) is higher than expected, with respect to the population. The state-of-the-art method for this kind of problem is the Space-Time Scan Statistics (STScan), which exhaustively search the whole space through a sliding window looking for significant spatiotemporal clusters. STScan makes some restrictive assumptions …
Our research focuses on analysing human activities according to a known behaviorist scenario, in case of noisy and high dimensional collected data. The data come from the monitoring of patients with dementia diseases by wearable cameras. We define a structural model of video recordings based on a Hidden Markov Model. New spatio-temporal features, color features and localization features are proposed as observations. First results in recognition of activities are promising.
As countries look towards re-opening of economic activities amidst the ongoing COVID-19 pandemic, ensuring public health has been challenging. While contact tracing only aims to track past activities of infected users, one path to safe reopening is to develop reliable spatiotemporal risk scores to indicate the propensity of the disease. Existing works which aim to develop risk scores either rely on compartmental model-based reproduction numbers (which assume uniform population mixing) or develop coarse-grain spatial scores based on reproduction number (R0) and macro-level density-based mobilit…
Introduction The tau statistic is a recent second-order correlation function that can assess the magnitude and range of global spatiotemporal clustering from epidemiological data containing geolocations of individual cases and, usually, disease onset times. This is the first review of its use, and the aspects of its computation and presentation that could affect inferences drawn and bias estimates of the statistic. Methods Using Google Scholar we searched papers or preprints that cited the papers that first defined/reformed the statistic. We tabulated their key characteristics to understand th…
Forest fires are the outcome of a complex interaction between environmental factors, topography and socioeconomic factors (Bedia et al, 2014). Therefore, understand causality and early prediction are crucial elements for controlling such phenomenon and saving lives.The aim of this study is to build spatio-temporal model to understand causality of forest fires in Europe, at NUTS2 level between 2012 and 2016, using environmental and socioeconomic variables.We have considered a disease mapping approach, commonly used in small area studies to assess thespatial pattern and to identify areas charact…
Confronted by a rapidly evolving health threat, such as an infectious disease outbreak, it is essential that decision-makers are able to comprehend the complex dynamics not just in space but also in the 4th dimension, time. In this paper this is addressed by a novel visualisation tool, referred to as the Dynamic Health Atlas web app, which is designed specifically for displaying the spatial evolution of data over time while simultaneously acknowledging its uncertainty. It is an interactive and open-source web app, coded predominantly in JavaScript, in which the geospatial and temporal data are…
Most COVID-19 studies commonly report figures of the overall infection at a state- or county-level. This aggregation tends to miss out on fine details of virus propagation. In this paper, we analyze a high-resolution COVID-19 dataset in Cali, Colombia, that records the precise time and location of every confirmed case. We develop a non-stationary spatio-temporal point process equipped with a neural network-based kernel to capture the heterogeneous correlations among COVID-19 cases. The kernel is carefully crafted to enhance expressiveness while maintaining model interpretability. We also incor…
Reliable estimation of spatio-temporal trends in population-level HIV incidence is becoming an increasingly critical component of HIV prevention policy-making. However, direct measurement is nearly impossible. Current, widely used models infer incidence from survey and surveillance seroprevalence data, but they require unrealistic assumptions about spatial independence across spatial units. In this study, we present an epidemic model of HIV that explicitly simulates the spatial dynamics of HIV over many small, interacting areal units. By integrating all available population-level data, we are …
