On the application of integer-valued time series models for the analysis of disease incidence.

Statistical time series models are practical tools in public health surveillance. Their capacity to forecast future disease incidence values exemplifies their usefulness. Using these forecasts, one can develop strategies to trigger alerts to public health officials when irregular disease incidence values have occurred. Clearly, the better the forecasting performance of the model class used in the time series analysis, the more realistic are the alerts triggered. The time series analysis of disease incidence values has often entailed the Box and Jenkins model class. However, this class was designed to model real-valued variables whereas disease incidences are integer-valued variables. A new class of time series models, called integer-valued autoregressive models, has been developed and studied over the past decade. The objective of this paper is to introduce this new class of models to the application of time series analysis of infectious disease incidence, and to demonstrate its advantages over the class of real-valued Box and Jenkins models. The paper also presents a bootstrap method developed for the calculation of forecast interval limits.     

Monitoring change in spatial patterns of disease: comparing univariate and multivariate cumulative sum approaches

Prospective disease surveillance has gained increasing attention, particularly in light of recent concern for quick detection of bioterrorist events. Monitoring of health events has the potential for the detection of such events, but the benefits of surveillance extend much more broadly to the quick detection of change in public health. In this paper, univariate and multivariate cumulative sum methods for disease surveillance are compared. Although the univariate method has been previously used in the context of health surveillance, the multivariate method has not. The univariate approach consists of simultaneously and independently monitoring the disease rate in each region; the multivariate approach accounts explicitly for any covariation between regions. The univariate approaches are limited by their lack of ability to account for the spatial autocorrelation of regional data; the multivariate methods are limited by the difficulty in accurately specifying the multiregional covariance structure. The methods are illustrated using both simulated data and county-level data on breast cancer in the northeastern United States. When the degree of spatial autocorrelation is low, the univariate method is generally better at detecting changes in rates that occur in a small number of regions; the multivariate is better when change occurs in a large number of regions.     

Multivariate modelling of infectious disease surveillance data

This paper describes a model-based approach to analyse multivariate time series data on counts of infectious diseases. It extends a method previously described in the literature to deal with possible dependence between disease counts from different pathogens. In a spatio-temporal context it is proposed to include additional information on global dispersal of the pathogen in the model. Two examples are given: the first describes an analysis of weekly influenza and meningococcal disease counts from Germany. The second gives an analysis of the spatio-temporal spread of influenza in the U.S.A., 1996-2006, using air traffic information. Maximum likelihood estimates in this non-standard model class are obtained using general optimization routines, which are integrated in the R package surveillance.     

Modified models and simulations for estimating dynamic functional connectivity in resting state functional magnetic resonance imaging

As understanding the nature of brain networks through dynamic functional connectivity (dFC) estimation is of paramount significant, the introduction and revision of blood-oxygen-level dependent (BOLD) signal simulation methods in brain regions and dFC estimation methods have gained significant ground in recent years. Based on the observation of BOLD signals with multivariate nonnormal distribution in functional magnetic resonance imaging (fMRI) images, we first propose a copula-based method for the production of these signals, in which nonnormal data are generated with a selected time-varying covariance matrix. Therefore, we can compare the performance of models in the cases where brain signals have a multivariate nonnormal distribution. Then, two kendallized exponentially weighted moving average (KEWMA) and kendallized dynamic conditional correlation (KDCC) multivariate volatility models are introduced which are based on two well-known and commonly used exponentially weighted moving average (EMWA) and dynamic conditional correlation (DCC) models. The results show that KDCC model can estimate conditional correlation significantly far better than the former ones (ie, DCC, standardized dynamic conditional correlation, EWMA, and standardized exponentially weighted moving average) on both types of data (ie, multivariate normal and nonnormal). In the next step, the bivariate normal distribution in Iranian resting state fMRI data is confirmed by using statistical tests, and it is shown that the dynamic nature of FC is not optimally detected using prevalent methods. Two alternative Portmanteau and rank-based tests are proposed for the examination of conditional heteroscedasticity in data. Finally, dFC in these data is estimated by employing the KDCC model.     

珠海市学校传染病症状监测系统建立和分析

目的探讨建立本地区学校传染病症状监测系统及应用。方法以网络技术、浏览器/服务器技术(B/S)为基础,进行系统集成。定义发热等7个症状数据及聚集性事件监测标准,利用时间序列建模预警预测,Spearman相关分析进行数据源分析。结果开发建设了"珠海市学校突发卫生事件症状监测系统",温特斯法对学生就诊ILI%跟踪和拟合性好。结论学校症状监测系统运行良好,能较准确的预测、预警,对学校传染病防控及其他突发公共卫生事件有积极预防作用,适宜推广。     

Assessing correlation of clustered mixed outcomes from a multivariate generalized linear mixed model

The classic concordance correlation coefficient measures the agreement between two variables. In recent studies, concordance correlation coefficients have been generalized to deal with responses from a distribution from the exponential family using the univariate generalized linear mixed model. Multivariate data arise when responses on the same unit are measured repeatedly by several methods. The relationship among these responses is often of interest. In clustered mixed data, the correlation could be present between repeated measurements either within the same observer or between different methods on the same subjects. Indices for measuring such association are needed. This study proposes a series of indices, namely, intra‐correlation, inter‐correlation, and total correlation coefficients to measure the correlation under various circumstances in a multivariate generalized linear model, especially for joint modeling of clustered count and continuous outcomes. The proposed indices are natural extensions of the concordance correlation coefficient. We demonstrate the methodology with simulation studies. A case example of osteoarthritis study is provided to illustrate the use of these proposed indices. Copyright © 2014 John Wiley & Sons, Ltd.     

Dynamic linear model and SARIMA: a comparison of their forecasting performance in epidemiology

One goal of a public health surveillance system is to provide a reliable forecast of epidemiological time series. This paper describes a study that used data collected through a national public health surveillance system in the United States to evaluate and compare the performances of a seasonal autoregressive integrated moving average (SARIMA) and a dynamic linear model (DLM) for estimating case occurrence of two notifiable diseases. The comparison uses reported cases of malaria and hepatitis A from January 1980 to June 1995 for the United States. The residuals for both predictor models show that they were adequate tools for use in epidemiological surveillance. Qualitative aspects were considered for both models to improve the comparison of their usefulness in public health. Our comparison found that the two forecasting modelling techniques (SARIMA and DLM) are comparable when long historical data are available (at least 52 reporting periods). However, the DLM approach has some advantages, such as being more easily applied to different types of time series and not requiring a new cycle of identification and modelling when new data become available.     

监测数据统计分析模型在生态学研究中的应用

近年来，环境监测、疾病监测等各种监测网络不断健全，监测系统成为开展生态学研究的重要数据来源。监测数据类型包括了横断面数据、时间序列数据和面板数据，涉及暴露、结局和混杂3个维度。针对该数据的信息属性和结构特点，相关统计学方法逐渐发展完善，出现了一些新的方法、模型。基于数据的时空属性，本文对监测数据在生态学研究中常用模型的原理、适用条件及优劣进行了综述。     

Probabilistic forecasting in infectious disease epidemiology: the 13th Armitage lecture

Routine surveillance of notifiable infectious diseases gives rise to daily or weekly counts of reported cases stratified by region and age group. From a public health perspective, forecasts of infectious disease spread are of central importance. We argue that such forecasts need to properly incorporate the attached uncertainty, so they should be probabilistic in nature. However, forecasts also need to take into account temporal dependencies inherent to communicable diseases, spatial dynamics through human travel and social contact patterns between age groups. We describe a multivariate time series model for weekly surveillance counts on norovirus gastroenteritis from the 12 city districts of Berlin, in six age groups, from week 2011/27 to week 2015/26. The following year (2015/27 to 2016/26) is used to assess the quality of the predictions. Probabilistic forecasts of the total number of cases can be derived through Monte Carlo simulation, but first and second moments are also available analytically. Final size forecasts as well as multivariate forecasts of the total number of cases by age group, by district and by week are compared across different models of varying complexity. This leads to a more general discussion of issues regarding modelling, prediction and evaluation of public health surveillance data. Copyright © 2017 John Wiley & Sons, Ltd.     

Regression B-spline smoothing in Bayesian disease mapping: with an application to patient safety surveillance

In the context of Bayesian disease mapping, recent literature presents generalized linear mixed models that engender spatial smoothing. The methods assume spatially varying random effects as a route to partially pooling data and 'borrowing strength' in small-area estimation. When spatiotemporal disease rates are available for sequential risk mapping of several time periods, the 'smoothing' issue may be explored by considering spatial smoothing, temporal smoothing and spatiotemporal interaction. In this paper, these considerations are motivated and explored through development of a Bayesian semiparametric disease mapping model framework which facilitates temporal smoothing of rates and relative risks via regression B-splines with mixed-effect representation of coefficients. Specifically, we develop spatial priors such as multivariate Gaussian Markov random fields and non-spatial priors such as unstructured multivariate Gaussian distributions and illustrate how time trends in small-area relative risks may be explored by splines which vary in either a spatially structured or unstructured manner. In particular, we show that with suitable prior specifications for the random effects ensemble, small-area relative risk trends may be fit by 'spatially varying' or randomly varying B-splines. A recently developed Bayesian hierarchical model selection criterion, the deviance information criterion, is used to assess the trade-off between goodness-of-fit and smoothness and to select the number of knots. The methodological development aims to provide reliable information about the patterns (both over space and time) of disease risks and to quantify uncertainty. The study offers a disease and health outcome surveillance methodology for flexible and efficient exploration and assessment of emerging risk trends and clustering. The methods are motivated and illustrated through a Bayesian analysis of adverse medical events (also known as iatrogenic injuries) among hospitalized elderly patients in British Columbia, Canada.     

上海市创新传染病监测模式的实践和思考

腹泻病综合监测和急性呼吸道感染综合监测是上海市开启传染病监测模式创新的一次有益探索。本期重点号文章旨在总结现有综合监测经验，为将该模式进一步拓展到其他疾病监测领域，以实现监测系统间相互协同提供科学依据。     

Joint modeling of multiple ordinal adherence outcomes via generalized estimating equations with flexible correlation structure

Adherence to medication is critical in achieving effectiveness of many treatments. Factors that influence adherence behavior have been the subject of many clinical studies. Analyzing adherence is complicated because it is often measured on multiple drugs over a period, resulting in a multivariate longitudinal outcome. This paper is motivated by the Viral Resistance to Antiviral Therapy of Chronic Hepatitis C study, where adherence is measured on two drugs as a bivariate ordinal longitudinal outcome. To analyze such outcome, we propose a joint model assuming the multivariate ordinal outcome arose from a partitioned latent multivariate normal process. We also provide a flexible multilevel association structure covering both between and within outcome correlation. In simulation studies, we show that the joint model provides unbiased estimators for regression parameters, which are more efficient than those obtained through fitting separate model for each outcome. The joint method also yields unbiased estimators for the correlation parameters when the correlation structure is correctly specified. Finally, we analyze the Viral Resistance to Antiviral Therapy of Chronic Hepatitis C adherence data and discuss the findings.     

The mixed model for the analysis of a repeated-measurement multivariate count data

Clustered overdispersed multivariate count data are challenging to model due to the presence of correlation within and between samples. Typically, the first source of correlation needs to be addressed but its quantification is of less interest. Here, we focus on the correlation between time points. In addition, the effects of covariates on the multivariate counts distribution need to be assessed. To fulfill these requirements, a regression model based on the Dirichlet-multinomial distribution for association between covariates and the categorical counts is extended by using random effects to deal with the additional clustering. This model is the Dirichlet-multinomial mixed regression model. Alternatively, a negative binomial regression mixed model can be deployed where the corresponding likelihood is conditioned on the total count. It appears that these two approaches are equivalent when the total count is fixed and independent of the random effects. We consider both subject-specific and categorical-specific random effects. However, the latter has a larger computational burden when the number of categories increases. Our work is motivated by microbiome data sets obtained by sequencing of the amplicon of the bacterial 16S rRNA gene. These data have a compositional structure and are typically overdispersed. The microbiome data set is from an epidemiological study carried out in a helminth-endemic area in Indonesia. The conclusions are as follows: time has no statistically significant effect on microbiome composition, the correlation between subjects is statistically significant, and treatment has a significant effect on the microbiome composition only in infected subjects who remained infected.     

用自回归模型预测流感样病例数的变化趋势

目的建立合适的统计模型预测流感样病例数。方法采集广州市2002年6月至2004年12月各周的流感流行病学监测数据,应用谱分析和自回归时间序列方法模拟流感样病例数的变化趋势,用决定系数和残差分析选择最佳模型,并用相对预测误差对模型进行回顾性和前瞻性考核。结果两年的流感样病例数呈线性上升趋势(r=0.423,P<0.001),并具备一定的周期性(P<0.05),线性回归模型的残差具有显著一阶自相关(r=0.524,P<0.001),自回归模型的残差为白噪声序列,回代考核的相对预测误差为16.4%;随后16周的数据作前瞻性考核,相对误差为14.3%。结论综合流感样疾病的长期趋势和周期性的自回归能较好地模拟流感样病例的流行特征,并进行中、短期预测。该研究是流感预测方法学上的一次有益探索,为流感的监测、预防和控制措施的制定提供了一定参考依据。     

Automated detection of infectious disease outbreaks: hierarchical time series models

The purpose of infectious disease surveillance is to inform the public health policy makers on the incidence and trends of infectious diseases and to trigger appropriate actions to control infectious disease outbreaks. The enormous amount of data collected with automated laboratory-based surveillance systems require automated algorithms for detecting unexpected aberrations that may signal infectious disease outbreaks. In this paper, we explore the potential of hierarchical time series models to detect deviations from expected incidence. As these count data are extremely noisy it can be expected that these models are suitable to detect signal from noise and accommodate for possible autocorrelation. The proposed procedure consists of three steps; (1) the model parameters are estimated by empirical Bayes on a training period of, e.g. a year; (2) the expected values are updated for small time steps (e.g. daily) as new data arrive; (3) threshold levels are updated conditionally on the past expected values and an alarm is triggered when the threshold level is exceeded. To test the potential of the models we estimated sensitivity, specificity and timeliness on simulated time series and compared the results with an alternative approach of a linear regression model adjusted for trends and season. We also used two observed series for Rubella notifications and Salmonella infections and compared our findings with the expert opinions on these series. The hierarchical time series models approach shows high sensitivity and specificity and correctly identifies outbreaks at an early stage. This, in our opinion, makes the proposed model a reliable tool for adequate automated detection of infectious disease outbreaks.     

Spatiotemporal surveillance methods in the presence of spatial correlation

Health surveillance involves collecting public health data on chronic and infectious diseases to detect changes in disease incidence rates in order to improve public health. Timely detection of disease clusters is essential in prospective public health surveillance. Most existing health surveillance research is based on the assumption that observations from different regions are independent. This paper proposes a set of multivariate surveillance schemes generalized from well-known detection methods in multivariate statistical process control based on likelihood ratio tests. We use Monte Carlo simulations to compare these methods for health surveillance in the presence of spatial correlations. By taking advantage of correlations among regions,the proposed schemes are able to perform better than existing surveillance methods and provide faster and more accurate detection of outbreaks. An example of breast cancer in New Hampshire is presented to demonstrate the application of these methods when observations are spatially correlated counts.     

Conditional predictive inference for online surveillance of spatial disease incidence

This paper deals with the development of statistical methodology for timely detection of incident disease clusters in space and time. The increasing availability of data on both the time and the location of events enables the construction of multivariate surveillance techniques, which may enhance the ability to detect localized clusters of disease relative to the surveillance of the overall count of disease cases across the entire study region. We introduce the surveillance conditional predictive ordinate as a general Bayesian model-based surveillance technique that allows us to detect small areas of increased disease incidence when spatial data are available. To address the problem of multiple comparisons, we incorporate a common probability that each small area signals an alarm when no change in the risk pattern of disease takes place into the analysis. We investigate the performance of the proposed surveillance technique within the framework of Bayesian hierarchical Poisson models using a simulation study. Finally, we present a case study of salmonellosis in South Carolina.     

Multivariate meta-analysis

Meta-analysis is now a standard statistical tool for assessing the overall strength and interesting features of a relationship, on the basis of multiple independent studies. There is, however, recent acknowledgement of the fact that in many applications responses are rarely uniquely determined. Hence there has been some change of focus from a single response to the analysis of multiple outcomes. In this paper we propose and evaluate three Bayesian multivariate meta-analysis models: two multivariate analogues of the traditional univariate random effects models which make different assumptions about the relationships between studies and estimates, and a multivariate random effects model which is a Bayesian adaptation of the mixed model approach. Our preferred method is then illustrated through an analysis of a new data set on parental smoking and two health outcomes (asthma and lower respiratory disease) in children.     

Robustness of a parametric model for informatively censored bivariate longitudinal data under misspecification of its distributional assumptions: A simulation study

Repeated measurements of surrogate markers are frequently used to track disease progression, but these series are often prematurely terminated due to disease progression or death. Analysing such data through standard likelihood-based approaches can yield severely biased estimates if the censoring mechanism is non-ignorable. Motivated by this problem, we have proposed the bivariate joint multivariate random effects (JMRE) model, which has shown that when correctly specified it performs well in terms of bias reduction and precision.The bivariate JMRE model is fully parametric and belongs to the class of shared parameters joint models where a survival model for the dropouts and a mixed model for the markers' evolution are linked through a multivariate normal distribution of random effects. As in every parametric model, robustness under violations of its distributional assumptions is of great importance. In this study we generated 500 simulated data sets assuming that random effects jointly follow a heavy-tailed distribution, two skewed distributions or a mixture of two normal distributions. Moreover, we generated data where level-1 errors or residuals in the survival part of the model follow a skewed distribution. Further sensitivity analysis on the effects of reduced sample size, increased level-1 variances and altered fixed effects values was also performed.We found that fixed effects estimates are almost unaffected, but their standard errors (SEs) may be underestimated especially under heavily skewed distributions. The proposed model seems robust enough, but its performance on smaller data sets or under more extreme departures of its assumptions needs further investigation.     

Proposal of a framework for evaluating military surveillance systems for early detection of outbreaks on duty areas

Background  

In recent years a wide variety of epidemiological surveillance systems have been developed to provide early identification of outbreaks of infectious disease. Each system has had its own strengths and weaknesses. In 2002 a Working Group of the Centers for Disease Control and Prevention (CDC) produced a framework for evaluation, which proved suitable for many public health surveillance systems. However this did not easily adapt to the military setting, where by necessity a variety of different parameters are assessed, different constraints placed on the systems, and different objectives required. This paper describes a proposed framework for evaluation of military syndromic surveillance systems designed to detect outbreaks of disease on operational deployments.