A Review of Spatiotemporal Models for Count Data in R Packages. A Case Study of COVID-19 Data

Spatiotemporal models for count data are required in a wide range of scientific fields, and they have become particularly crucial today because of their ability to analyze COVID-19-related data. The main objective of this paper is to present a review describing the most important approaches, and we monitor their performance under the same dataset. For this review, we focus on the three R-packages that can be used for this purpose, and the different models assessed are representative of the two most widespread methodologies used to analyze spatiotemporal count data: the classical approach and the Bayesian point of view. A COVID-19-related case study is analyzed as an illustration of these different methodologies. Because of the current urgent need for monitoring and predicting data in the COVID-19 pandemic, this case study is, in itself, of particular importance and can be considered the secondary objective of this work. Satisfactory and promising results have been obtained in this second goal. With respect to the main objective, it has been seen that, although the three models provide similar results in our case study, their different properties and flexibility allow us to choose the model depending on the application at hand.

[1]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[2]  Noel A Cressie,et al.  Spatio-Temporal Statistics with R , 2019 .

[3]  Duncan Lee,et al.  Quantifying the Spatial Inequality and Temporal Trends in Maternal Smoking Rates in Glasgow. , 2016, The annals of applied statistics.

[4]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[5]  Peter J. Diggle,et al.  Bayesian analysis of agricultural field experiments - Discussion , 1999 .

[6]  Leonhard Held,et al.  Probabilistic forecasting in infectious disease epidemiology: the 13th Armitage lecture , 2017, Statistics in medicine.

[7]  H. Rue,et al.  Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations , 2009 .

[8]  P. Diggle,et al.  COVID-19 in England: spatial patterns and regional outbreaks , 2020, medRxiv.

[9]  L. Anselin.  Local Indicators of Spatial Association—LISA , 2010 .

[10]  G. Gurtner,et al.  Statistics in medicine. , 2011, Plastic and reconstructive surgery.

[11]  Anthony N. Pettitt,et al.  Comment on the paper: ‘Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations’ by Rue, H. Martino, S. and Chopin, N. , 2009 .

[12]  Antonio López-Quílez,et al.  Spatio-Temporal model structures with shared components for semi-continuous species distribution modelling , 2017 .

[13]  Leonhard Held,et al.  Modeling seasonality in space‐time infectious disease surveillance data , 2012, Biometrical journal. Biometrische Zeitschrift.

[14]  Xin Lu,et al.  Analysis of heterogeneous dengue transmission in Guangdong in 2014 with multivariate time series model , 2016, Scientific Reports.

[15]  Andrew B. Lawson,et al.  Bayesian disease mapping , 2013 .

[16]  Forecasting COVID-19-Associated Hospitalizations under Different Levels of Social Distancing in Lombardy and Emilia-Romagna, Northern Italy: Results from an Extended SEIR Compartmental Model , 2020, Journal of clinical medicine.

[17]  S. Zeger,et al.  Longitudinal data analysis using generalized linear models , 1986 .

[18]  Maria Michela Dickson,et al.  Modelling and Predicting the Spatio-Temporal Spread of Coronavirus Disease 2019 (COVID-19) in Italy , 2020, SSRN Electronic Journal.

[19]  J. Wakefield,et al.  Stratified space–time infectious disease modelling, with an application to hand, foot and mouth disease in China , 2018 .

[20]  L. Held,et al.  Periodically stationary multivariate autoregressive models , 2017, 1707.04635.

[21]  Duncan Lee,et al.  A model to estimate the impact of changes in MMR vaccine uptake on inequalities in measles susceptibility in Scotland , 2016, Statistical methods in medical research.

[22]  Craig Anderson,et al.  A Comparison of Spatio-Temporal Disease Mapping Approaches Including an Application to Ischaemic Heart Disease in New South Wales, Australia , 2017, International journal of environmental research and public health.

[23]  K. Pearson,et al.  Biometrika , 1902, The American Naturalist.

[24]  Norman E. Breslow,et al.  Estimation of Disease Rates in Small Areas: A new Mixed Model for Spatial Dependence , 2000 .

[25]  P. Glynn,et al.  A model to forecast regional demand for COVID-19 related hospital beds , 2020, medRxiv.

[26]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[27]  María Dolores Ugarte,et al.  Spatio‐temporal modeling of mortality risks using penalized splines , 2009 .

[28]  Sebastian Meyer,et al.  hhh4 : Endemic-epidemic modeling of areal count time series , 2018 .

[29]  Alexander Klippel,et al.  Analysing spatio-temporal autocorrelation with LISTA-Viz , 2010, Int. J. Geogr. Inf. Sci..

[30]  M. Bekker-Nielsen Dunbar,et al.  Endemic-epidemic framework used in covid-19 modelling (Discussion on the paper by nunes, caetano, antunes and dias) , 2020 .

[31]  Duncan Lee,et al.  A tutorial on spatio-temporal disease risk modelling in R using Markov chain Monte Carlo simulation and the CARBayesST package. , 2020, Spatial and spatio-temporal epidemiology.

[32]  D. Clayton,et al.  Bayesian analysis of space-time variation in disease risk. , 1995, Statistics in medicine.

[33]  Jon Wakefield,et al.  Bayesian penalized spline models for the analysis of spatio‐temporal count data , 2016, Statistics in medicine.

[34]  Jane Law,et al.  Bayesian Spatio-Temporal Modeling for Analysing Local Patterns of Crime Over Time at the Small-Area Level , 2014 .

[35]  B. Martín,et al.  Citizen science for predicting spatio-temporal patterns in seabird abundance during migration , 2020, PloS one.

[36]  V. G. Rubio,et al.  Bayesian joint spatio-temporal analysis of multiple diseases , 2019 .

[37]  A. Gusev.  Temporal structure of the global sequence of volcanic eruptions: Order clustering and intermittent discharge rate , 2008 .

[38]  Wenyaw Chan,et al.  Statistical Methods in Medical Research , 2013, Model. Assist. Stat. Appl..

[39]  Jianhong Wu,et al.  Estimation of the Transmission Risk of the 2019-nCoV and Its Implication for Public Health Interventions , 2020, Journal of clinical medicine.

[40]  B. Jørgensen,et al.  Multivariate covariance generalized linear models , 2015, 1504.01551.

[41]  ScienceDirect,et al.  Spatial and spatio-temporal epidemiology , 2009 .

[42]  L Held,et al.  Predictive assessment of a non‐linear random effects model for multivariate time series of infectious disease counts , 2011, Statistics in medicine.

[43]  HighWire Press.  Proceedings of the Royal Society of London. Series A, Containing papers of a mathematical and physical character , 1934 .

[45]  J. Paul Elhorst,et al.  Dynamic spatial panels: models, methods, and inferences , 2012, J. Geogr. Syst..

[46]  Célestin C. Kokonendji,et al.  Discrete dispersion models and their Tweedie asymptotics , 2014, 1409.7482.

[47]  Duncan Lee,et al.  An adaptive spatiotemporal smoothing model for estimating trends and step changes in disease risk , 2014, 1411.0924.

[48]  Antonio Baeza,et al.  A Spatial-Temporal Model for the Evolution of the COVID-19 Pandemic in Spain Including Mobility , 2020 .

[49]  Wagner Hugo Bonat,et al.  Multiple Response Variables Regression Models in R: The mcglm Package , 2018 .

[50]  Modelling and predicting the spatio-temporal spread of cOVID-19 in Italy , 2020, BMC Infectious Diseases.

[51]  Christian P. Robert,et al.  Statistics for Spatio-Temporal Data , 2014 .

[52]  Yaqing Fang,et al.  Transmission dynamics of the COVID‐19 outbreak and effectiveness of government interventions: A data‐driven analysis , 2020, Journal of medical virology.

[53]  L. Held,et al.  Heterogeneity in vaccination coverage explains the size and occurrence of measles epidemics in German surveillance data , 2010, Epidemiology and Infection.

[54]  L. Held,et al.  Multivariate modelling of infectious disease surveillance data , 2008, Statistics in medicine.

[55]  Leonhard Held,et al.  Calibration tests for count data , 2014 .

[56]  Duncan Lee,et al.  A spatio-temporal model for estimating the long-term effects of air pollution on respiratory hospital admissions in Greater London. , 2014, Spatial and spatio-temporal epidemiology.

[57]  Bent Jørgensen,et al.  Parameter Orthogonality and Bias Adjustment for Estimating Functions , 2004 .

[58]  Yang Liu,et al.  Early dynamics of transmission and control of COVID-19: a mathematical modelling study , 2020, The Lancet Infectious Diseases.

[59]  A. Guirao.  The Covid-19 outbreak in Spain. A simple dynamics model, some lessons, and a theoretical framework for control response , 2020, Infectious Disease Modelling.

[60]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[61]  Duncan Lee,et al.  Spatio-Temporal Areal Unit Modeling in R with Conditional Autoregressive Priors Using the CARBayesST Package , 2018 .

[62]  Benjamin Hofner,et al.  Modeling spatiotemporal abundance of mobile wildlife in highly variable environments using boosted GAMLSS hurdle models , 2019, Ecology and evolution.

[63]  M. Martínez-Beneito.  A general modelling framework for multivariate disease mapping , 2013 .

[64]  Andrew Thomas,et al.  The BUGS project: Evolution, critique and future directions , 2009, Statistics in medicine.

[65]  J. Lumley.  AUSTRALIA , 1920, The Lancet.

[66]  O. William.  Journal Of The American Statistical Association V-28 , 1932 .

[67]  Leonhard Held,et al.  Handbook of Infectious Disease Data Analysis , 2019 .

[68]  Jstor.  Journal of the Royal Statistical Society. Series A (General) , 1987 .

[69]  J. Cavanaugh.  Biostatistics , 2005, Definitions.

[70]  David L. Borchers,et al.  Spatiotemporal modelling for the annual egg production method of stock assessment using generalized additive models , 1998 .

[71]  Leonhard Held,et al.  Incorporating social contact data in spatio-temporal models for infectious disease spread , 2015, Biostatistics.

[72]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[73]  Zhe Jiang,et al.  Spatial Statistics , 2013 .

[74]  Cornetto.  Test , 2020, ACM Transactions on Algorithms.

[75]  Andrew B Lawson,et al.  Evaluation of Bayesian spatiotemporal latent models in small area health data , 2011, Environmetrics.

[76]  T. Gneiting.  Making and Evaluating Point Forecasts , 2009, 0912.0902.

[77]  Jean-Francois Richard,et al.  Likelihood-Based Inference and Prediction in Spatio-Temporal Panel Count Models for Urban Crimes , 2017 .

[78]  C. M. Acosta,et al.  Bayesian Spatio-Temporal Modeling of COVID-19: Inequalities on Case-Fatality Risk , 2020, medRxiv.

[79]  D. Reid,et al.  Investigating spatio-temporal change in spawning activity by Atlantic mackerel between 1977 and 1998 using generalized additive models , 2002 .

[80]  P. Klepac,et al.  Early dynamics of transmission and control of COVID-19: a mathematical modelling study , 2020, The Lancet Infectious Diseases.

[81]  Rajen Dinesh Shah,et al.  Statistical modelling , 2015 .

[82]  COVID-19: Short-term forecast of ICU beds in times of crisis. , 2021, PloS one.