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Picinini Freitas L, Douwes-Schultz D, Schmidt AM, Ávila Monsalve B, Salazar Flórez JE, García-Balaguera C, Restrepo BN, Jaramillo-Ramirez GI, Carabali M, Zinszer K. Zika emergence, persistence, and transmission rate in Colombia: a nationwide application of a space-time Markov switching model. Sci Rep 2024; 14:10003. [PMID: 38693192 PMCID: PMC11063144 DOI: 10.1038/s41598-024-59976-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2023] [Accepted: 04/17/2024] [Indexed: 05/03/2024] Open
Abstract
Zika, a viral disease transmitted to humans by Aedes mosquitoes, emerged in the Americas in 2015, causing large-scale epidemics. Colombia alone reported over 72,000 Zika cases between 2015 and 2016. Using national surveillance data from 1121 municipalities over 70 weeks, we identified sociodemographic and environmental factors associated with Zika's emergence, re-emergence, persistence, and transmission intensity in Colombia. We fitted a zero-state Markov-switching model under the Bayesian framework, assuming Zika switched between periods of presence and absence according to spatially and temporally varying probabilities of emergence/re-emergence (from absence to presence) and persistence (from presence to presence). These probabilities were assumed to follow a series of mixed multiple logistic regressions. When Zika was present, assuming that the cases follow a negative binomial distribution, we estimated the transmission intensity rate. Our results indicate that Zika emerged/re-emerged sooner and that transmission was intensified in municipalities that were more densely populated, at lower altitudes and/or with less vegetation cover. Warmer temperatures and less weekly-accumulated rain were also associated with Zika emergence. Zika cases persisted for longer in more densely populated areas with more cases reported in the previous week. Overall, population density, elevation, and temperature were identified as the main contributors to the first Zika epidemic in Colombia. We also estimated the probability of Zika presence by municipality and week, and the results suggest that the disease circulated undetected by the surveillance system on many occasions. Our results offer insights into priority areas for public health interventions against emerging and re-emerging Aedes-borne diseases.
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Affiliation(s)
- Laís Picinini Freitas
- Université de Montréal, École de Santé Publique, Montreal, H3N 1X9, Canada.
- Centre de Recherche en Santé Publique, Montreal, H3N 1X9, Canada.
| | - Dirk Douwes-Schultz
- Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, H3A 1G1, Canada.
| | - Alexandra M Schmidt
- Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, H3A 1G1, Canada
| | - Brayan Ávila Monsalve
- Universidad Cooperativa de Colombia, Faculty of Medicine, Villavicencio, 500003, Colombia
| | - Jorge Emilio Salazar Flórez
- Instituto Colombiano de Medicina Tropical, Universidad CES, Medellín, 055450, Colombia
- Infectious and Chronic Diseases Study Group (GEINCRO), San Martín University Foundation, Medellín, 050031, Colombia
| | - César García-Balaguera
- Universidad Cooperativa de Colombia, Faculty of Medicine, Villavicencio, 500003, Colombia
| | - Berta N Restrepo
- Instituto Colombiano de Medicina Tropical, Universidad CES, Medellín, 055450, Colombia
| | | | - Mabel Carabali
- Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, H3A 1G1, Canada
| | - Kate Zinszer
- Université de Montréal, École de Santé Publique, Montreal, H3N 1X9, Canada
- Centre de Recherche en Santé Publique, Montreal, H3N 1X9, Canada
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2
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Liu M, Zhu F, Li J, Sun C. A Systematic Review of INGARCH Models for Integer-Valued Time Series. ENTROPY (BASEL, SWITZERLAND) 2023; 25:922. [PMID: 37372266 DOI: 10.3390/e25060922] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2023] [Revised: 06/05/2023] [Accepted: 06/09/2023] [Indexed: 06/29/2023]
Abstract
Count time series are widely available in fields such as epidemiology, finance, meteorology, and sports, and thus there is a growing demand for both methodological and application-oriented research on such data. This paper reviews recent developments in integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models over the past five years, focusing on data types including unbounded non-negative counts, bounded non-negative counts, Z-valued time series and multivariate counts. For each type of data, our review follows the three main lines of model innovation, methodological development, and expansion of application areas. We attempt to summarize the recent methodological developments of INGARCH models for each data type for the integration of the whole INGARCH modeling field and suggest some potential research topics.
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Affiliation(s)
- Mengya Liu
- School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
| | - Fukang Zhu
- School of Mathematics, Jilin University, Changchun 130012, China
| | - Jianfeng Li
- School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
| | - Chuning Sun
- School of Business, Zhengzhou University, Zhengzhou 450001, China
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3
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Chen CW, Liu FC, Pingal AC. Integer-valued transfer function models for counts that show zero inflation. Stat Probab Lett 2023. [DOI: 10.1016/j.spl.2022.109701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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4
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A covariate-driven beta-binomial integer-valued GARCH model for bounded counts with an application. METRIKA 2023. [DOI: 10.1007/s00184-023-00894-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
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5
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Lee S, Kim D, Kim B. Modeling and inference for multivariate time series of counts based on the INGARCH scheme. Comput Stat Data Anal 2023. [DOI: 10.1016/j.csda.2022.107579] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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6
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Lee S, Kim D. Multiple values-inflated time series of counts: modeling and inference based on INGARCH scheme. J STAT COMPUT SIM 2022. [DOI: 10.1080/00949655.2022.2134381] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Sangyeol Lee
- Department of Statistics, Seoul National University, Seoul, South Korea
| | - Dongwon Kim
- Department of Statistics, Seoul National University, Seoul, South Korea
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7
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Wang X, Wang D. Penalized empirical likelihood inference for the GINAR( p) model. STATISTICS-ABINGDON 2022. [DOI: 10.1080/02331888.2022.2107645] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Affiliation(s)
- Xinyang Wang
- School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang, People's Republic of China
| | - Dehui Wang
- School of Economics, Liaoning University, Shenyang, People's Republic of China
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8
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Li H, Wang H, Yang K, Sun J, Liu Y. A nonparametric Bayesian analysis for meningococcal disease counts based on integer-valued threshold time series models. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2022.2059683] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Han Li
- School of Science, Changchun University, Changchun, China
- School of Mathematics and Statistics, Changchun University of Technology, Changchun, China
| | - Haoyu Wang
- School of Science, Changchun University, Changchun, China
| | - Kai Yang
- School of Mathematics and Statistics, Changchun University of Technology, Changchun, China
| | - Jie Sun
- Institute of Science and Technology, Shenyang Open University, Shenyang, China
| | - Yan Liu
- School of Science, Changchun University, Changchun, China
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9
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Abstract
External events are commonly known as interventions that often affect times series of counts. This research introduces a class of transfer function models that include four different types of interventions on integer-valued time series: abrupt start and abrupt decay (additive outlier), abrupt start and gradual decay (transient shift), abrupt start and permanent effect (level shift) and gradual start and permanent effect. We propose integer-valued transfer function models incorporating a generalized Poisson, log-linear generalized Poisson or negative binomial to estimate and detect these four types of interventions in a time series of counts. Utilizing Bayesian methods, which are adaptive Markov chain Monte Carlo (MCMC) algorithms to obtain the estimation, we further employ deviance information criterion (DIC), posterior odd ratios and mean squared standardized residual for model comparisons. As an illustration, this study evaluates the effectiveness of our methods through a simulation study and application to crime data in Albury City, New South Wales (NSW) Australia. Simulation results show that the MCMC procedure is reasonably effective. The empirical outcome also reveals that the proposed models are able to successfully detect the locations and type of interventions.
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Affiliation(s)
| | - Cathy W. S. Chen
- Department of Statistics, Feng Chia University, Taichung, Taiwan
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10
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Lee S, Kim D, Seok S. Modeling and inference for counts time series based on zero-inflated exponential family INGARCH models. J STAT COMPUT SIM 2021. [DOI: 10.1080/00949655.2021.1890732] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Sangyeol Lee
- Department of Statistics, Seoul National University, Seoul, South Korea
| | - Dongwon Kim
- Department of Statistics, Seoul National University, Seoul, South Korea
| | - Seongwoo Seok
- Department of Statistics, Seoul National University, Seoul, South Korea
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11
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Recent progress in parameter change test for integer-valued time series models. J Korean Stat Soc 2021. [DOI: 10.1007/s42952-020-00102-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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12
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Lee S, Kim D. Monitoring Parameter Change for Time Series Models of Counts Based on Minimum Density Power Divergence Estimator. ENTROPY 2020; 22:e22111304. [PMID: 33287071 PMCID: PMC7711929 DOI: 10.3390/e22111304] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Revised: 11/11/2020] [Accepted: 11/14/2020] [Indexed: 11/16/2022]
Abstract
In this study, we consider an online monitoring procedure to detect a parameter change for integer-valued generalized autoregressive heteroscedastic (INGARCH) models whose conditional density of present observations over past information follows one parameter exponential family distributions. For this purpose, we use the cumulative sum (CUSUM) of score functions deduced from the objective functions, constructed for the minimum power divergence estimator (MDPDE) that includes the maximum likelihood estimator (MLE), to diminish the influence of outliers. It is well-known that compared to the MLE, the MDPDE is robust against outliers with little loss of efficiency. This robustness property is properly inherited by the proposed monitoring procedure. A simulation study and real data analysis are conducted to affirm the validity of our method.
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13
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Xu X, Chen Y, Chen CWS, Lin X. Adaptive log-linear zero-inflated generalized Poisson autoregressive model with applications to crime counts. Ann Appl Stat 2020. [DOI: 10.1214/20-aoas1360] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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14
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Chen CWS, Lee S, Khamthong K. Bayesian inference of nonlinear hysteretic integer-valued GARCH models for disease counts. Comput Stat 2020. [DOI: 10.1007/s00180-020-01018-7] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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15
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Stojanović O, Leugering J, Pipa G, Ghozzi S, Ullrich A. A Bayesian Monte Carlo approach for predicting the spread of infectious diseases. PLoS One 2019; 14:e0225838. [PMID: 31851680 PMCID: PMC6919583 DOI: 10.1371/journal.pone.0225838] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2019] [Accepted: 11/13/2019] [Indexed: 12/27/2022] Open
Abstract
In this paper, a simple yet interpretable, probabilistic model is proposed for the prediction of reported case counts of infectious diseases. A spatio-temporal kernel is derived from training data to capture the typical interaction effects of reported infections across time and space, which provides insight into the dynamics of the spread of infectious diseases. Testing the model on a one-week-ahead prediction task for campylobacteriosis and rotavirus infections across Germany, as well as Lyme borreliosis across the federal state of Bavaria, shows that the proposed model performs on-par with the state-of-the-art hhh4 model. However, it provides a full posterior distribution over parameters in addition to model predictions, which aides in the assessment of the model. The employed Bayesian Monte Carlo regression framework is easily extensible and allows for incorporating prior domain knowledge, which makes it suitable for use on limited, yet complex datasets as often encountered in epidemiology.
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Affiliation(s)
- Olivera Stojanović
- Department of Neuroinformatics, Institute of Cognitive Science, Osnabrück University, Osnabrück, Germany
| | - Johannes Leugering
- Department of Neuroinformatics, Institute of Cognitive Science, Osnabrück University, Osnabrück, Germany
| | - Gordon Pipa
- Department of Neuroinformatics, Institute of Cognitive Science, Osnabrück University, Osnabrück, Germany
| | - Stéphane Ghozzi
- Department of Infectious Diseases, Robert Koch Institute, Berlin, Germany
| | - Alexander Ullrich
- Department of Infectious Diseases, Robert Koch Institute, Berlin, Germany
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16
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Chen CWS, Khamthong K. Bayesian modelling of nonlinear negative binomial integer-valued GARCHX models. STAT MODEL 2019. [DOI: 10.1177/1471082x19845541] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This study focuses on modelling dengue cases in northeastern Thailand through two meteorological covariates: cumulative rainfall and average maximum temperature. We propose two nonlinear integer-valued GARCHX models (Markov switching and threshold specification) with a negative binomial distribution, as they take into account the stylized features of weekly dengue haemorrhagic fever cases, which contain nonlinear dynamics, lagged dependence, overdispersion, consecutive zeros and asymmetric effects of meteorological covariates. We conduct parameter estimation and one-step-ahead forecasting for two proposed models based on Bayesian Markov chain Monte Carlo (MCMC) methods. A simulation study illustrates that the adaptive MCMC sampling scheme performs well. The empirical results offer strong support for the Markov switching integer-valued GARCHX model over its competitors via Bayes factor and deviance information criterion. We also provide one-step-ahead forecasting based on the prediction interval that offers a useful early warning signal of outbreak detection.
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Affiliation(s)
- Cathy WS Chen
- Department of Statistics, Feng Chia University, Taichung, Taiwan, R.O.C
| | - K Khamthong
- Department of Statistics, Feng Chia University, Taichung, Taiwan, R.O.C
- Department of Mathematics, Mahasarakham University, Thailand
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