Statistical methods for anomalous discrete time series based on minimum cell count

Temporal incidence patterns of point epidemics often contain periods of unusually low or high frequencies. Identifying variations in incidence frequencies, which may be caused by changes in exposure to infectious or environmental agents, may provide important insights into the pathogenesis or etiology of a disease. We propose and formulate new statistical tests for temporal and space-time anomalies that are based on the minimum frequency in a unit of time and that are meaningful for the characteristic incidence patterns of the cases studied. Among the most widely applied methods are the Ederer-Myers-Mantel test, the Maxima test, and the scan test, which are all sensitive to the maximum frequency within a short period of time. We elucidate the importance and utility of our new tests and the existing tests and suggest a systematic statistical analysis of reported disease anomalies using these tests combined. Data on a temporal series of adolescent suicide from the US National Center for Health Statistics were analyzed using these methods.     

Are Obesity and Physical Activity Clustered? A Spatial Analysis Linked to Residential Density

The aim of this study was to examine spatial clustering of obesity and/or moderate physical activity and their relationship to a neighborhood's built environment. Data on levels of obesity and moderate physical activity were derived from the results of a telephone survey conducted in 2006, with 1,863 survey respondents in the study sample. This sample was spread across eight suburban neighborhoods in Metro Vancouver. These areas were selected to contrast residential density and income and do not constitute a random sample, but within each area, respondents were selected randomly. Obesity and moderate physical activity were mapped to determine levels of global and local spatial autocorrelation within the neighborhoods. Clustering was measured using Moran's I at the global level, Anselin's Local Moran's I at the local level, and geographically weighted regression (GWR). The global‐level spatial analysis reveals no significant clustering for the attributes of obesity or moderate physical activity. Within individual neighborhoods, there is moderate clustering of obesity and/or physical activity but these clusters do not achieve statistical significance. In some neighborhoods, local clustering is restricted to a single pair of respondents with moderate physical activity. In other neighborhoods, any moderate local clustering is offset by negative local spatial autocorrelation. Importantly, there is no evidence of significant clustering for the attribute of obesity at either the global or local level of analysis. The GWR analysis fails to improve significantly upon the global model—thus reinforcing the negative results. Overall, the study indicates that the relationship between the urban environment and obesity is not direct.     

Measuring the severity of disease clustering using Tango's index.

Tango [Biometrics 40:15 (1984)] proposed an index for detecting disease clustering in time applicable to grouped data obtained from a population that remains fairly stable over the study period. This index has received considerable attention in the literature including the suggestion that it be used to detect the space-time clustering of diseases and the suggestion to use similar test statistics to detect disease clustering in space and/or time while accounting for a changing population size over the study period. This paper concerns the related question of measuring the severity of the disease clustering once it has been determined that cases are not randomly distributed over space and/or time. A family of alternatives to randomness is proposed in which space and/or time versions of Tango's index are sufficient statistics for the parameters measuring the severity of the clustering. For the special case of temporal clustering, an unbiased estimator of the clustering parameter and its sampling variance is derived, and a particularly simple interpretation of this estimator is suggested. These latter results are based on some asymptotic approximations due to Tango [Biometrics 46:351 (1990)]. An application to the trisomy data given by Wallenstein [Am. J. Epidemiol. 111:367 (1980)] is discussed.     

Autologistic network model on binary data for disease progression study

This paper focuses on analysis of spatiotemporal binary data with absorbing states. The research was motivated by a clinical study on amyotrophic lateral sclerosis (ALS), a neurological disease marked by gradual loss of muscle strength over time in multiple body regions. We propose an autologistic regression model to capture complex spatial and temporal dependencies in muscle strength among different muscles. As it is not clear how the disease spreads from one muscle to another, it may not be reasonable to define a neighborhood structure based on spatial proximity. Relaxing the requirement for prespecification of spatial neighborhoods as in existing models, our method identifies an underlying network structure empirically to describe the pattern of spreading disease. The model also allows the network autoregressive effects to vary depending on the muscles’ previous status. Based on the joint distribution derived from this autologistic model, the joint transition probabilities of responses among locations can be estimated and the disease status can be predicted in the next time interval. Model parameters are estimated through maximization of penalized pseudo‐likelihood. Postmodel selection inference was conducted via a bias‐correction method, for which the asymptotic distributions were derived. Simulation studies were conducted to evaluate the performance of the proposed method. The method was applied to the analysis of muscle strength loss from the ALS clinical study.     

Early warning of hand,foot, and mouth disease transmission: A modeling study in mainland,China

BackgroundHand, foot, and mouth disease (HFMD) is a global infectious disease; particularly, it has a high disease burden in China. This study was aimed to explore the temporal and spatial distribution of the disease by analyzing its epidemiological characteristics, and to calculate the early warning signals of HFMD by using a logistic differential equation (LDE) model.MethodsThis study included datasets of HFMD cases reported in seven regions in Mainland China. The early warning time (week) was calculated using the LDE model with the key parameters estimated by fitting with the data. Two key time points, “epidemic acceleration week (EAW)” and “recommended warning week (RWW)”, were calculated to show the early warning time.ResultsThe mean annual incidence of HFMD cases per 100,000 per year was 218, 360, 223, 124, and 359 in Hunan Province, Shenzhen City, Xiamen City, Chuxiong Prefecture, Yunxiao County across the southern regions, respectively and 60 and 34 in Jilin Province and Longde County across the northern regions, respectively. The LDE model fitted well with the reported data (R² > 0.65, P < 0.001). Distinct temporal patterns were found across geographical regions: two early warning signals emerged in spring and autumn every year across southern regions while one early warning signals in summer every year across northern regions.ConclusionsThe disease burden of HFMD in China is still high, with more cases occurring in the southern regions. The early warning of HFMD across the seven regions is heterogeneous. In the northern regions, it has a high incidence during summer and peaks in June every year; in the southern regions, it has two waves every year with the first wave during spring spreading faster than the second wave during autumn. Our findings can help predict and prepare for active periods of HFMD.     

Spatial Aspects of Foot-Pad Dermatitis in Swedish Broilers

This study aimed at analysing spatial and spatio-temporal aspects of foot-pad dermatitis in Swedish broilers. The information on disease prevalence and severity was based on a two-year foot-health surveillance programme where information on producer, breed, feed manufacturer, region, abattoir, date of slaughter and several other variables was recorded. The level of clustering in space was analysed on 2-digit zipcode level using Moran's I test which measures similarity of location. The level of clustering in space was also analysed using the Ipop test, which takes the population at risk into consideration. The examination of time-space interaction was carried out using the Barton method and the Knox method. We found a significant (p<0.001) clustering of regions with respect to foot-pad dermatitis score using Moran's I test, and a significant (p<0.0001) clustering in space also when related to the number of flocks delivered from each region. The flocks with very high prevalence of foot-pad dermatitis were significantly (p<0.05) clustered in both time and space, i.e. the flocks with high prevalence of lesions came from the same geographic area during the same time periods. This information will permit us to focus the control efforts within the foot-health surveillance programme on specific regions in specific time periods, thus making the programme more effective.     

Novel technique for preprocessing high dimensional time-course data from DNA microarray: mathematical model-based clustering

MOTIVATION: Classifying genes into clusters depending on their expression profiles is one of the most important analysis techniques for microarray data. Because temporal gene expression profiles are indicative of the dynamic functional properties of genes, the application of clustering analysis to time-course data allows the more precise division of genes into functional classes. Conventional clustering methods treat the sampling data at each time point as data obtained under different experimental conditions without considering the continuity of time-course data between time periods t and t+1. Here, we propose a method designated mathematical model-based clustering (MMBC). RESULTS: The proposed method, designated MMBC, was applied to artificial data and time-course data obtained using Saccharomyces cerevisiae. Our method is able to divide data into clusters more accurately and coherently than conventional clustering methods. Furthermore, MMBC is more tolerant to noise than conventional clustering methods. AVAILABILITY: Software is available upon request. CONTACT: taizo@brs.kyushu-u.ac.jp.     

Spatial clustering of average risks and risk trends in Bayesian disease mapping

Spatiotemporal disease mapping focuses on estimating the spatial pattern in disease risk across a set of nonoverlapping areal units over a fixed period of time. The key aim of such research is to identify areas that have a high average level of disease risk or where disease risk is increasing over time, thus allowing public health interventions to be focused on these areas. Such aims are well suited to the statistical approach of clustering, and while much research has been done in this area in a purely spatial setting, only a handful of approaches have focused on spatiotemporal clustering of disease risk. Therefore, this paper outlines a new modeling approach for clustering spatiotemporal disease risk data, by clustering areas based on both their mean risk levels and the behavior of their temporal trends. The efficacy of the methodology is established by a simulation study, and is illustrated by a study of respiratory disease risk in Glasgow, Scotland.     

Finding Evidence for Local Transmission of Contagious Disease in Molecular Epidemiological Datasets

Surveillance systems of contagious diseases record information on cases to monitor incidence of disease and to evaluate effectiveness of interventions. These systems focus on a well-defined population; a key question is whether observed cases are infected through local transmission within the population or whether cases are the result of importation of infection into the population. Local spread of infection calls for different intervention measures than importation of infection. Besides standardized information on time of symptom onset and location of cases, pathogen genotyping or sequencing offers essential information to address this question. Here we introduce a method that takes full advantage of both the genetic and epidemiological data to distinguish local transmission from importation of infection, by comparing inter-case distances in temporal, spatial and genetic data. Cases that are part of a local transmission chain will have shorter distances between their geographical locations, shorter durations between their times of symptom onset and shorter genetic distances between their pathogen sequences as compared to cases that are due to importation. In contrast to generic clustering algorithms, the proposed method explicitly accounts for the fact that during local transmission of a contagious disease the cases are caused by other cases. No pathogen-specific assumptions are needed due to the use of ordinal distances, which allow for direct comparison between the disparate data types. Using simulations, we test the performance of the method in identifying local transmission of disease in large datasets, and assess how sensitivity and specificity change with varying size of local transmission chains and varying overall disease incidence.     

Distribution of dengue vectors in neighborhoods with different urbanization types of Manaus, state of Amazonas, Brazil

Aedes aegypti and Ae. albopictus are vectors of dengue viruses, which cause endemic disease in the city of Manaus, capital of the state of Amazonas, Brazil. More than 53 thousand cases have been registered in this city since the first epidemic in 1998. We evaluated the hypothesis that different ecological conditions result in different patterns of vector infestation in Manaus, by measuring the infestation level in four neighborhoods with different urbanization patterns, during the rainy (April), dry (August), and transitional (November) seasons. Ae. aegypti predominated throughout the study areas and sampling periods, representing 86% of all specimens collected in oviposition traps. High frequencies of houses positive for both species were observed in all studied sites, with Ae. aegypti present in more than 84% of the houses in all seasons. Ae. albopictus, on the other hand, showed more spatial and temporal variation in abundance. We found no association between infestation level and house traits. This study highlights the homogeneity of dengue vector distribution in Manaus.     

How Do Childhood Diagnoses of Type 1 Diabetes Cluster in Time?

Background

Previous studies have indicated that type 1 diabetes may have an infectious origin. The presence of temporal clustering—an irregular temporal distribution of cases—would provide additional evidence that occurrence may be linked with an agent that displays epidemicity. We tested for the presence and form of temporal clustering using population-based data from northeast England.

Materials and Methods

The study analysed data on children aged 0–14 years diagnosed with type 1 diabetes during the period 1990–2007 and resident in a defined geographical region of northeast England (Northumberland, Newcastle upon Tyne, and North Tyneside). Tests for temporal clustering by time of diagnosis were applied using a modified version of the Potthoff-Whittinghill method.

Results

The study analysed 468 cases of children diagnosed with type 1 diabetes. There was highly statistically significant evidence of temporal clustering over periods of a few months and over longer time intervals (p<0.001). The clustering within years did not show a consistent seasonal pattern.

Conclusions

The study adds to the growing body of literature that supports the involvement of infectious agents in the aetiology of type 1 diabetes in children. Specifically it suggests that the precipitating agent or agents involved might be an infection that occurs in “mini-epidemics”.     

Fluctuation Scaling,Taylor’s Law,and Crime

Fluctuation scaling relationships have been observed in a wide range of processes ranging from internet router traffic to measles cases. Taylor’s law is one such scaling relationship and has been widely applied in ecology to understand communities including trees, birds, human populations, and insects. We show that monthly crime reports in the UK show complex fluctuation scaling which can be approximated by Taylor’s law relationships corresponding to local policing neighborhoods and larger regional and countrywide scales. Regression models applied to local scale data from Derbyshire and Nottinghamshire found that different categories of crime exhibited different scaling exponents with no significant difference between the two regions. On this scale, violence reports were close to a Poisson distribution (α = 1.057±0.026) while burglary exhibited a greater exponent (α = 1.292±0.029) indicative of temporal clustering. These two regions exhibited significantly different pre-exponential factors for the categories of anti-social behavior and burglary indicating that local variations in crime reports can be assessed using fluctuation scaling methods. At regional and countrywide scales, all categories exhibited scaling behavior indicative of temporal clustering evidenced by Taylor’s law exponents from 1.43±0.12 (Drugs) to 2.094±0081 (Other Crimes). Investigating crime behavior via fluctuation scaling gives insight beyond that of raw numbers and is unique in reporting on all processes contributing to the observed variance and is either robust to or exhibits signs of many types of data manipulation.     

Epidemiology and genetics of neural tube defects: an application of the Utah Genealogical Data Base

The distribution and prevalence of births with neural tube defects in Utah from 1940 to 1979 are analyzed with regard to prevalence rates, secondary sex ratios, seasonality, yearly rates, and time-space clustering. The overall prevalence rate of 1.00 per thousand live births is comparable to that of other populations in the western United States. Analysis of sex ratios indicates a substantially higher proportion of females than males. No significant secular trends or time-space clustering are observed. No seasonality is seen for spina bifida; however, the anencephaly cases are delivered more frequently in the early spring and fall months. Following linkage of the neural tube defect cases to the Utah Genealogical Data Base, application of the genealogical index method shows substantial familial clustering of the disease. The average inbreeding coefficient of the neural tube defect cases is not elevated over that of matched controls. The empirical recurrence risk for the disease is calculated to be 3%, and the heritability estimate is 70%. Likelihood analysis of pedigrees containing spina bifida occulta and spina bifida cystica indicates that they may segregate as an autosomal dominant trait with a penetrance of 75%.     

基于时间聚类分析和独立成分分析的癫痫fMRI盲分析方法

提出了一种基于时间聚类分析和独立成分分析的癫痫fMRI数据盲分析方法,并将两种方法有效联合,提取发作间期的癫痫fMRI激活时空信息.该方法首先由时间聚类分析得到与激活相关的时间峰度特征曲线,以此特征作为时间参考信息;再由空间独立成分分析分解fMRI信号得到空间独立成分;最后将每个独立成分所对应的时间曲线与参考曲线做相关分析提取相应脑激活图.提出的方法无需任何关于癫痫fMRI的先验假设信息,有效解决了独立成分的排序问题,实现了对数据的盲分析.仿真试验结果阐明了这一方法的有效性及可靠性,对癫痫数据的试验结果显示空间定位准确性优于统计参数图方法.     

Object-oriented satellite image time series analysis using a graph-based representation

Nowadays, remote sensing technologies produce huge amounts of satellite images that can be helpful to monitor geographical areas over time. A satellite image time series (SITS) usually contains spatio-temporal phenomena that are complex and difficult to understand. Conceiving new data mining tools for SITS analysis is challenging since we need to simultaneously manage the spatial and the temporal dimensions at the same time. In this work, we propose a new clustering framework specifically designed for SITS data. Our method firstly detects spatio-temporal entities, then it characterizes their evolutions by mean of a graph-based representation, and finally it produces clusters of spatio-temporal entities sharing similar temporal behaviors. Unlike previous approaches, which mainly work at pixel-level, our framework exploits a purely object-based representation to perform the clustering task. Object-based analysis involves a segmentation step where segments (objects) are extracted from an image and constitute the element of analysis. We experimentally validate our method on two real world SITS datasets by comparing it with standard techniques employed in remote sensing analysis. We also use a qualitative analysis to highlight the interpretability of the results obtained.     

The temporal program of chromosome replication: genomewide replication in clb5{Delta} Saccharomyces cerevisiae

Temporal regulation of origin activation is widely thought to explain the pattern of early- and late-replicating domains in the Saccharomyces cerevisiae genome. Recently, single-molecule analysis of replication suggested that stochastic processes acting on origins with different probabilities of activation could generate the observed kinetics of replication without requiring an underlying temporal order. To distinguish between these possibilities, we examined a clb5Delta strain, where origin firing is largely limited to the first half of S phase, to ask whether all origins nonspecifically show decreased firing (as expected for disordered firing) or if only some origins ("late" origins) are affected. Approximately half the origins in the mutant genome show delayed replication while the remainder replicate largely on time. The delayed regions can encompass hundreds of kilobases and generally correspond to regions that replicate late in wild-type cells. Kinetic analysis of replication in wild-type cells reveals broad windows of origin firing for both early and late origins. Our results are consistent with a temporal model in which origins can show some heterogeneity in both time and probability of origin firing, but clustering of temporally like origins nevertheless yields a genome that is organized into blocks showing different replication times.     

Random Walk Models for Bayesian Clustering of Gene Expression Profiles

The analysis of gene expression temporal profiles is a topic of increasing interest in functional genomics. Model-based clustering methods are particularly interesting because they are able to capture the dynamic nature of these data and to identify the optimal number of clusters. We have defined a new Bayesian method that allows us to cope with some important issues that remain unsolved in the currently available approaches: the presence of time dislocations in gene expression, the non-stationarity of the processes generating the data, and the presence of data collected on an irregular temporal grid. Our method, which is based on random walk models, requires only mild a priori assumptions about the nature of the processes generating the data and explicitly models inter-gene variability within each cluster. It has first been validated on simulated datasets and then employed for the analysis of a dataset relative to serum-stimulated fibroblasts. In all cases, the results have been promising, showing that the method can be helpful in functional genomics research.     

Error-pooling-based statistical methods for identifying novel temporal replication profiles of human chromosomes observed by DNA tiling arrays

Statistical analysis on tiling array data is extremely challenging due to the astronomically large number of sequence probes, high noise levels of individual probes and limited number of replicates in these data. To overcome these difficulties, we first developed statistical error estimation and weighted ANOVA modeling approaches to high-density tiling array data, especially the former based on an advanced error-pooling method to accurately obtain heterogeneous technical error of small-sample tiling array data. Based on these approaches, we analyzed the high-density tiling array data of the temporal replication patterns during cell-cycle S phase of synchronized HeLa cells on human chromosomes 21 and 22. We found many novel temporal replication patterns, identifying about 26% of over 1 million tiling array sequence probes with significant differential replication during the four 2-h time periods of S phase. Among these differentially replicated probes, 126941 sequence probes were matched to 417 known genes. The majority of these genes were found to be replicated within one or two consecutive time periods, while the others were replicated at two non-consecutive time periods. Also, coding regions found to be more differentially replicated in particular time periods than noncoding regions in the gene-poor chromosome 21 (25% differentially replicated among genic probes versus 18.6% among intergenic probes), while such a phenomenon was less prominent in gene-rich chromosome 22. A rigorous statistical testing for local proximity of differentially replicated genic and intergenic probes was performed to identify significant stretches of differentially replicated sequence regions. From this analysis, we found that adjacent genes were frequently replicated at different time periods, potentially implying the existence of quite dense replication origins. Evaluating the conditional probability significance of identified gene ontology terms on chromosomes 21 and 22, we detected some over-represented molecular functions and biological processes among these differentially replicated genes, such as the ones relevant to hydrolase, transferase and receptor-binding activities. Some of these results were confirmed showing >70% consistency with cDNA microarray data that were independently generated in parallel with the tiling arrays. Thus, our improved analysis approaches specifically designed for high-density tiling array data enabled us to reliably and sensitively identify many novel temporal replication patterns on human chromosomes.