Space-time mixture modelling of public health data

Bayesian spatio-temporal joint disease mapping of Covid-19 cases and deaths in local authorities of England

The overwhelming spatio-temporal nature of the spread of the ongoing Covid-19 pandemic demands urgent attention of data analysts and model developers. Modelling results obtained from analytical tool development are essential to understand the ongoing pandemic dynamics with a view to helping the public and policy makers. The pandemic has generated data on a huge number of interesting statistics such as the number of new cases, hospitalisations and deaths in many spatio-temporal resolutions for the analysts to investigate. The multivariate nature of these data sets, along with the inherent spatio-temporal dependencies, poses new challenges for modellers. This article proposes a two-stage hierarchical Bayesian model as a joint bivariate model for the number of cases and deaths observed weekly for the different local authority administrative regions in England. An adaptive model is proposed for the weekly Covid-19 death rates as part of the joint bivariate model. The adaptive model is able to detect possible step changes in death rates in neighbouring areas. The joint model is also used to evaluate the effects of several socio-economic and environmental covariates on the rates of cases and deaths. Inclusion of these covariates points to the presence of a north-south divide in both the case and death rates. Nitrogen dioxide, the only air pollution measure used in the model, is seen to be significantly positively associated with the number cases, even in the presence of the spatio-temporal random effects taking care of spatio-temporal dependencies present in the data. The proposed models provide excellent fits to the observed data and are seen to perform well for predicting the location specific number of deaths a week in advance. The structure of the models is very general and the same framework can be used for modelling other areally aggregated temporal statistics of the pandemics, e.g. the rate of hospitalisation.

Temporal and spatial distribution trends of human brucellosis in Liaoning Province, China

Brucellosis is a natural epidemic zoonotic disease. Liaoning province, north-east of China, has been among the top 10 provinces with highest brucellosis incidence. In this study, the spatial and temporal distribution of brucellosis in Liaoning Province from 2006 through 2017 was analysed using the Bayesian theory of space-time modelling. The study found that in Liaoning Province, (a) all regions of the entire study area were stable counties; (b) the risk of brucellosis declined slowly with time without an obvious trend; (c) the declining trend of disease risk in three sub-hot-spot counties was faster than the overall trend, whereas in other counties, the trend was similar to the overall trend. Furthermore, the time and spatial trends of brucellosis incidence in Liaoning Province were calculated and analysed. These results may provide a theoretical and scientific basis for the public health department to develop targeted effective prevention and control measures for the disease.

Distribution of the COVID-19 epidemic and correlation with population emigration from Wuhan, China

Background

The ongoing new coronavirus pneumonia (Corona Virus Disease 2019, COVID-19) outbreak is spreading in China, but it has not yet reached its peak. Five million people emigrated from Wuhan before lockdown, potentially representing a source of virus infection. Determining case distribution and its correlation with population emigration from Wuhan in the early stage of the epidemic is of great importance for early warning and for the prevention of future outbreaks.

Methods

The official case report on the COVID-19 epidemic was collected as of January 30, 2020. Time and location information on COVID-19 cases was extracted and analyzed using ArcGIS and WinBUGS software. Data on population migration from Wuhan city and Hubei province were extracted from Baidu Qianxi, and their correlation with the number of cases was analyzed.

Results

The COVID-19 confirmed and death cases in Hubei province accounted for 59.91% (5806/9692) and 95.77% (204/213) of the total cases in China, respectively. Hot spot provinces included Sichuan and Yunnan, which are adjacent to Hubei. The time risk of Hubei province on the following day was 1.960 times that on the previous day. The number of cases in some cities was relatively low, but the time risk appeared to be continuously rising. The correlation coefficient between the provincial number of cases and emigration from Wuhan was up to 0.943. The lockdown of 17 cities in Hubei province and the implementation of nationwide control measures efficiently prevented an exponential growth in the number of cases.

Conclusions

The population that emigrated from Wuhan was the main infection source in other cities and provinces. Some cities with a low number of cases showed a rapid increase in case load. Owing to the upcoming Spring Festival return wave, understanding the risk trends in different regions is crucial to ensure preparedness at both the individual and organization levels and to prevent new outbreaks.

Spatiotemporal trends in teen birth rates in the USA, 2003-2012

The objective of this analysis was to explore temporal and spatial variation in teen birth rates TBRs across counties in the USA, from 2003 to 2012, by using hierarchical Bayesian models. Prior examination of spatiotemporal variation in TBRs has been limited by the reliance on large-scale geographies such as states, because of the potential instability in TBRs at smaller geographical scales such as counties. We implemented hierarchical Bayesian models with space-time interaction terms and spatially structured and unstructured random effects to produce smoothed county level TBR estimates, allowing for examination of spatiotemporal patterns and trends in TBRs at a smaller geographic scale across the USA. The results may help to highlight US counties where TBRs are higher or lower and to inform efforts to reduce birth rates to adolescents in the USA further.

Spatial variation in cancer incidence and survival over time across Queensland, Australia

Interpreting changes over time in small-area variation in cancer survival, in light of changes in cancer incidence, aids understanding progress in cancer control, yet few space-time analyses have considered both measures. Bayesian space-time hierarchical models were applied to Queensland Cancer Registry data to examine geographical changes in cancer incidence and relative survival over time for the five most common cancers (colorectal, melanoma, lung, breast, prostate) diagnosed during 1997-2004 and 2005-2012 across 516 Queensland residential small-areas. Large variation in both cancer incidence and survival was observed. Survival improvements were fairly consistent across the state, although small for lung cancer. Incidence changes varied by location and cancer type, ranging from lung and colorectal cancers remaining relatively constant over time, to prostate cancer dramatically increasing across the entire state. Reducing disparities in cancer-related outcomes remains a health priority, and space-time modelling of different measures provides an important mechanism by which to monitor progress.

A Comparison of Spatio-Temporal Disease Mapping Approaches Including an Application to Ischaemic Heart Disease in New South Wales, Australia

The field of spatio-temporal modelling has witnessed a recent surge as a result of developments in computational power and increased data collection. These developments allow analysts to model the evolution of health outcomes in both space and time simultaneously. This paper models the trends in ischaemic heart disease (IHD) in New South Wales, Australia over an eight-year period between 2006 and 2013. A number of spatio-temporal models are considered, and we propose a novel method for determining the goodness-of-fit for these models by outlining a spatio-temporal extension of the Moran's I statistic. We identify an overall decrease in the rates of IHD, but note that the extent of this health improvement varies across the state. In particular, we identified a number of remote areas in the north and west of the state where the risk stayed constant or even increased slightly.

Trends of breast cancer incidence in Iran during 2004-2008: a Bayesian space-time model

BACKGROUND

Breast cancer is the most frequently diagnosed cancer in women and estimating its relative risks and trends of incidence at the area-level is helpful for health policy makers. However, traditional methods of estimation which do not take spatial heterogeneity into account suffer from drawbacks and their results may be misleading, as the estimated maps of incidence vary dramatically in neighboring areas. Spatial methods have been proposed to overcome drawbacks of traditional methods by including spatial sources of variation in the model to produce smoother maps.

MATERIALS AND METHODS

In this study we analyzed the breast cancer data in Iran during 2004-2008. We used a method proposed to cover spatial and temporal effects simultaneously and their interactions to study trends of breast cancer incidence in Iran.

RESULTS

The results agree with previous studies but provide new information about two main issues regarding the trend of breast cancer in provinces of Iran. First, this model discovered provinces with high relative risks of breast cancer during the 5 years of the study. Second, new information was provided with respect to overall trend trends o. East-Azerbaijan, Golestan, North-Khorasan, and Khorasan-Razavi had the highest increases in rates of breast cancer incidence whilst Tehran, Isfahan, and Yazd had the highest incidence rates during 2004-2008.

CONCLUSIONS

Using spatial methods can provide more accurate and detailed information about the incidence or prevalence of a disease. These models can specify provinces with different health priorities in terms of needs for therapy and drugs or demands for efficient education, screening, and preventive policy into action.

Spatiotemporal property analysis of birth defects in Wuxi, China

OBJECTIVE

To describe the temporal trends and spatial patterns of birth defects occurring in Wuxi, a developed region of China.

METHODS

Wavelet analysis was used to decompose the temporal trends of birth defect prevalence based on the birth defect rates over the past 16 years. Birth defect cases with detailed personal and family information were geo-coded and the relative risk in each village was calculated. General G statistic was used to test the spatial property with different scales.

RESULTS

Wavelet analysis showed an increasing temporal trend of birth defects in this region. Clustering analysis revealed that changes continued in the spatial patterns with different scales.

CONCLUSION

Wuxi is confronted with severe challenges to reduce birth defect prevalence. The risk factors are stable and show no change with spatial scale but an increasing temporal trend. Interventions should be focused on villages with a higher prevalence of birth defects.

Bayesian spatio-temporal modeling of Schistosoma japonicum prevalence data in the absence of a diagnostic 'gold' standard

Background

Spatial modeling is increasingly utilized to elucidate relationships between demographic, environmental, and socioeconomic factors, and infectious disease prevalence data. However, there is a paucity of studies focusing on spatio-temporal modeling that take into account the uncertainty of diagnostic techniques.

Methodology/Principal Findings

We obtained Schistosoma japonicum prevalence data, based on a standardized indirect hemagglutination assay (IHA), from annual reports from 114 schistosome-endemic villages in Dangtu County, southeastern part of the People's Republic of China, for the period 1995 to 2004. Environmental data were extracted from satellite images. Socioeconomic data were available from village registries. We used Bayesian spatio-temporal models, accounting for the sensitivity and specificity of the IHA test via an equation derived from the law of total probability, to relate the observed with the ‘true’ prevalence. The risk of S. japonicum was positively associated with the mean land surface temperature, and negatively correlated with the mean normalized difference vegetation index and distance to the nearest water body. There was no significant association between S. japonicum and socioeconomic status of the villages surveyed. The spatial correlation structures of the observed S. japonicum seroprevalence and the estimated infection prevalence differed from one year to another. Variance estimates based on a model adjusted for the diagnostic error were larger than unadjusted models. The generated prediction map for 2005 showed that most of the former and current infections occur in close proximity to the Yangtze River.

Conclusion/Significance

Bayesian spatial-temporal modeling incorporating diagnostic uncertainty is a suitable approach for risk mapping S. japonicum prevalence data. The Yangtze River and its tributaries govern schistosomiasis transmission in Dangtu County, but spatial correlation needs to be taken into consideration when making risk prediction at small scales.

Schistosomiasis is a serious public health problem in the People's Republic of China and elsewhere, and mapping of risk areas is important for guiding control interventions. Here, a 10-year surveillance database from Dangtu County in the southeastern part of the People's Republic of China was utilized for modeling the spatial and temporal distribution of infections in relation to environmental features and socioeconomic factors. Disease surveillance was done on the basis of a serological test, and we explicitly considered the imperfect sensitivity and specificity of the test when modeling the ‘true’ infection prevalence of Schistosoma japonicum. We then produced a risk map for S. japonicum transmission, which can assist decision making for local control interventions. Our work emphasizes the importance of accounting for the uncertainty in the diagnosis of schistosomiasis, and the potential of predicting the spatial and temporal distribution of the disease when using a Bayesian modeling framework. Our study can therefore serve as a template for future risk profiling of neglected tropical diseases studies, particularly when exploring spatial and temporal disease patterns in relation to environmental and socioeconomic factors, and how to account for the influence of diagnostic uncertainty.

Modeling disease incidence data with spatial and spatio temporal dirichlet process mixtures

Disease incidence or mortality data are typically available as rates or counts for specified regions, collected over time. We propose Bayesian nonparametric spatial modeling approaches to analyze such data. We develop a hierarchical specification using spatial random effects modeled with a Dirichlet process prior. The Dirichlet process is centered around a multivariate normal distribution. This latter distribution arises from a log-Gaussian process model that provides a latent incidence rate surface, followed by block averaging to the areal units determined by the regions in the study. With regard to the resulting posterior predictive inference, the modeling approach is shown to be equivalent to an approach based on block averaging of a spatial Dirichlet process to obtain a prior probability model for the finite dimensional distribution of the spatial random effects. We introduce a dynamic formulation for the spatial random effects to extend the model to spatio-temporal settings. Posterior inference is implemented through Gibbs sampling. We illustrate the methodology with simulated data as well as with a data set on lung cancer incidences for all 88 counties in the state of Ohio over an observation period of 21 years.

A comparison of the active surveillance of scrapie in the European Union

The abattoir and the fallen stock surveys constitute the active surveillance component aimed at improving the detection of scrapie across the European Union. Previous studies have suggested the occurrence of significant differences in the operation of the surveys across the EU. In the present study we assessed the standardisation of the surveys throughout time across the EU and identified clusters of countries with similar underlying characteristics allowing comparisons between them. In the absence of sufficient covariate information to explain the observed variability across countries, we modelled the unobserved heterogeneity by means of non-parametric distributions on the risk ratios of the fallen stock over the abattoir survey. More specifically, we used the profile likelihood method on 2003, 2004 and 2005 active surveillance data for 18 European countries on classical scrapie, and on 2004 and 2005 data for atypical scrapie separately. We extended our analyses to include the limited covariate information available, more specifically, the proportion of the adult sheep population sampled by the fallen stock survey every year. Our results show that the between-country heterogeneity dropped in 2004 and 2005 relative to that of 2003 for classical scrapie. As a consequence, the number of clusters in the last two years was also reduced indicating the gradual standardisation of the surveillance efforts across the EU. The crude analyses of the atypical data grouped all the countries in one cluster and showed non-significant gain in the detection of this type of scrapie by any of the two sources. The proportion of the population sampled by the fallen stock appeared significantly associated with our risk ratio for both types of scrapie, although in opposite directions: negative for classical and positive for atypical. The initial justification for the fallen stock, targeting a high-risk population to increase the likelihood of case finding, appears compromised for both types of scrapie in some countries.

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.

Minimum Hellinger distance estimation for k-component poisson mixture with random effects

The k-component Poisson regression mixture with random effects is an effective model in describing the heterogeneity for clustered count data arising from several latent subpopulations. However, the residual maximum likelihood estimation (REML) of regression coefficients and variance component parameters tend to be unstable and may result in misleading inferences in the presence of outliers or extreme contamination. In the literature, the minimum Hellinger distance (MHD) estimation has been investigated to obtain robust estimation for finite Poisson mixtures. This article aims to develop a robust MHD estimation approach for k-component Poisson mixtures with normally distributed random effects. By applying the Gaussian quadrature technique to approximate the integrals involved in the marginal distribution, the marginal probability function of the k-component Poisson mixture with random effects can be approximated by the summation of a set of finite Poisson mixtures. Simulation study shows that the MHD estimates perform satisfactorily for data without outlying observation(s), and outperform the REML estimates when data are contaminated. Application to a data set of recurrent urinary tract infections (UTI) with random institution effects demonstrates the practical use of the robust MHD estimation method.

Bayesian statistics in medicine: a 25 year review

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.

Mapping disability-adjusted life years: a Bayesian hierarchical model framework for burden of disease and injury assessment

This paper presents a Bayesian disability-adjusted life year (DALY) methodology for spatial and spatiotemporal analyses of disease and/or injury burden. A Bayesian disease mapping model framework, which blends together spatial modelling, shared-component modelling (SCM), temporal modelling, ecological modelling, and non-linear modelling, is developed for small-area DALY estimation and inference. In particular, we develop a model framework that enables SCM as well as multivariate CAR modelling of non-fatal and fatal disease or injury rates and facilitates spline smoothing for non-linear modelling of temporal rate and risk trends. Using British Columbia (Canada) hospital admission-separation data and vital statistics mortality data on non-fatal and fatal road traffic injuries to male population age 20-39 for year 1991-2000 and for 84 local health areas and 16 health service delivery areas, spatial and spatiotemporal estimation and inference on years of life lost due to premature death, years lived with disability, and DALYs are presented. Fully Bayesian estimation and inference, with Markov chain Monte Carlo implementation, are illustrated. We present a methodological framework within which the DALY and the Bayesian disease mapping methodologies interface and intersect. Its development brings the relative importance of premature mortality and disability into the assessment of community health and health needs in order to provide reliable information and evidence for community-based public health surveillance and evaluation, disease and injury prevention, and resource provision.

The misuse of count data aggregated over time for disease mapping

The ongoing spread of spatial analysis techniques for small areas has facilitated the publication of mortality and morbidity Atlases based on time periods that group information spanning several years. Although this is a widespread practice, this paper proves that the use of count data aggregated over time for disease mapping may give inappropriate area-specific relative risk. As a result, both decision-making and healthcare policies could be affected by inappropriate model specifications using aggregated information over time. The Poisson distribution properties were used in order to quantify the bias in area-specific relative risk estimation due to count data aggregated over time. A hierarchical Bayesian model with spatio-temporal random structure is proposed as an alternative to smoothing relative risk if the period of study need to span several years. Methods discussed in this paper were applied to a small-area survey on male mortality from all causes in Southern Spain for the period 1985-1999. The results suggest that particular caution should be taken when interpreting risk maps based on clustered annual data that use models with no temporal structure to smooth out the rates.

A Bayesian hierarchical model for accident and injury surveillance

This article presents a recent study which applies Bayesian hierarchical methodology to model and analyse accident and injury surveillance data. A hierarchical Poisson random effects spatio-temporal model is introduced and an analysis of inter-regional variations and regional trends in hospitalisations due to motor vehicle accident injuries to boys aged 0-24 in the province of British Columbia, Canada, is presented. The objective of this article is to illustrate how the modelling technique can be implemented as part of an accident and injury surveillance and prevention system where transportation and/or health authorities may routinely examine accidents, injuries, and hospitalisations to target high-risk regions for prevention programs, to evaluate prevention strategies, and to assist in health planning and resource allocation. The innovation of the methodology is its ability to uncover and highlight important underlying structure of the data. Between 1987 and 1996, British Columbia hospital separation registry registered 10,599 motor vehicle traffic injury related hospitalisations among boys aged 0-24 who resided in British Columbia, of which majority (89%) of the injuries occurred to boys aged 15-24. The injuries were aggregated by three age groups (0-4, 5-14, and 15-24), 20 health regions (based of place-of-residence), and 10 calendar years (1987 to 1996) and the corresponding mid-year population estimates were used as 'at risk' population. An empirical Bayes inference technique using penalised quasi-likelihood estimation was implemented to model both rates and counts, with spline smoothing accommodating non-linear temporal effects. The results show that (a) crude rates and ratios at health region level are unstable, (b) the models with spline smoothing enable us to explore possible shapes of injury trends at both the provincial level and the regional level, and (c) the fitted models provide a wealth of information about the patterns (both over space and time) of the injury counts, rates and ratios. During the 10-year period, high injury risk ratios evolved from northwest to central-interior and the southeast [corrected].