Integrated Nested Laplace Approximation Research Articles

Spatial Effects of Livestock Farming on Human Infections With Shiga Toxin-Producing Escherichia coli O157 in Small but Densely Populated Regions: The Case of the Netherlands.

The role of environmental transmission of typically foodborne pathogens like Shiga toxin‐producing Escherichia coli (STEC) O157 is increasingly recognized. To gain more insights into spatially restricted risk factors that play a role in this transmission, we assessed the spatial association between sporadic STEC O157 human infections and the exposure to livestock (i.e. small ruminants, cattle, poultry, and pigs) in a densely populated country: the Netherlands. This was done for the years 2007–2016, using a state‐of‐the‐art spatial analysis method in which hexagonal areas with different sizes (90, 50, 25 and 10 km2) were used in combination with a novel probability of exposure metric: the population‐weighted number of animals per hexagon. To identify risk factors for STEC O157 infections and their population attributable fraction (PAF), a spatial regression model was fitted using integrated nested Laplace approximation (INLA). Living in hexagonal areas of 25, 50 and 90 km2 with twice as much population‐weighted small ruminants was associated with an increase of the incidence rate of human STEC O157 infections in summer (RR of 1.09 [95%CI;1.01–1.17], RR of 1.17 [95%CI;1.07–1.28] and RR of 1.13 [95%CI;1.01–1.26]), with a PAF of 49% (95%CI;8–72%). Results suggest exposure to small ruminants to be a risk factor, although no evidence on the mode of transmission is provided. Therefore, the underlying mechanisms warrant further investigation and could offer new targets for control. The newly proposed exposure metric has potential to improve existing spatial modeling studies on infectious diseases related to livestock exposure, especially in densely populated countries like the Netherlands.

Subjective Well-Being in Early Adolescence: Observations from a Five-Year Longitudinal Study

This article aims to redress the lack of longitudinal studies on adolescents’ subjective well-being (SWB) and highlight the relevance of knowledge deriving from such research in designing public policies for improving their health and wellbeing in accordance with the stage of development they are in. To achieve this, the evolution of SWB during early adolescence (in adolescents aged between 10 and 14 in the first data collection) was explored over a five year period, considering boys and girls together and separately. This involved comparing different SWB scales and contrasting results when considering the year of data collection versus the cohort (year of birth) participants belonged to. The methodology comprised a generalized linear mixed model using the INLA (Integrated Nested Laplace Approximation) estimation within a Bayesian framework. Results support the existence of a decreasing-with-age trend, which has been previously intuited in cross-sectional studies and observed in only a few longitudinal studies and contrasts with the increasing-with-age tendency observed in late adolescence. This decrease is also found to be more pronounced for girls, with relevant differences found between instruments. The decreasing-with-age trend observed when the year of data collection is taken into account is also observed when considering the cohort, but the latter provides additional information. The results obtained suggest that there is a need to continue studying the evolution of SWB in early adolescence with samples from other cultures; this, in turn, will make it possible to establish the extent to which the observed decreasing-with-age trend among early adolescents is influenced by cultural factors.

An R package for an integrated evaluation of statistical approaches to cancer incidence projection

BackgroundProjection of future cancer incidence is an important task in cancer epidemiology. The results are of interest also for biomedical research and public health policy. Age-Period-Cohort (APC) models, usually based on long-term cancer registry data (> 20 yrs), are established for such projections. In many countries (including Germany), however, nationwide long-term data are not yet available. General guidance on statistical approaches for projections using rather short-term data is challenging and software to enable researchers to easily compare approaches is lacking.MethodsTo enable a comparative analysis of the performance of statistical approaches to cancer incidence projection, we developed an R package (incAnalysis), supporting in particular Bayesian models fitted by Integrated Nested Laplace Approximations (INLA). Its use is demonstrated by an extensive empirical evaluation of operating characteristics (bias, coverage and precision) of potentially applicable models differing by complexity. Observed long-term data from three cancer registries (SEER-9, NORDCAN, Saarland) was used for benchmarking.ResultsOverall, coverage was high (mostly > 90%) for Bayesian APC models (BAPC), whereas less complex models showed differences in coverage dependent on projection-period. Intercept-only models yielded values below 20% for coverage. Bias increased and precision decreased for longer projection periods (> 15 years) for all except intercept-only models. Precision was lowest for complex models such as BAPC models, generalized additive models with multivariate smoothers and generalized linear models with age x period interaction effects.ConclusionThe incAnalysis R package allows a straightforward comparison of cancer incidence rate projection approaches. Further detailed and targeted investigations into model performance in addition to the presented empirical results are recommended to derive guidance on appropriate statistical projection methods in a given setting.

Temperature and assault in an urban environment: An empirical study in the city of Seoul, South Korea

Although weather is expected to influence human behavior, including crime, its association with crime has been relatively understudied in an environmental context of small areal and temporal units. This study investigates the association between temperature and assaults in the city of Seoul, South Korea. It also examines how interaction between temperature and socio-economic variables relates to assaults. Monthly assault counts in small administrative units for a 36-month period are described with Bayesian Poisson models. Employing the space-time structure of the dataset, these Poisson models are specified with a set of spatial and/or temporal effects and estimated with the integrated nested Laplace approximation (INLA). Results show that a model specification accounting for spatial and temporal structure better explains the data. Also, results indicate that assault risk is higher in high temperatures, areas with low economic status, and/or highly commercialized land use areas. Moreover, significant interactions between temperature and environmental variables (specifically, economic status and commercial land use) are found.

Bayesian space-time gap filling for inference on extreme hot-spots: an application to Red Sea surface temperatures

We develop a method for probabilistic prediction of extreme value hot-spots in a spatio-temporal framework, tailored to big datasets containing important gaps. In this setting, direct calculation of summaries from data, such as the minimum over a space-time domain, is not possible. To obtain predictive distributions for such cluster summaries, we propose a two-step approach. We first model marginal distributions with a focus on accurate modeling of the right tail and then, after transforming the data to a standard Gaussian scale, we estimate a Gaussian space-time dependence model defined locally in the time domain for the space-time subregions where we want to predict. In the first step, we detrend the mean and standard deviation of the data and fit a spatially resolved generalized Pareto distribution to apply a correction of the upper tail. To ensure spatial smoothness of the estimated trends, we either pool data using nearest-neighbor techniques, or apply generalized additive regression modeling. To cope with high space-time resolution of data, the local Gaussian models use a Markov representation of the Matern correlation function based on the stochastic partial differential equations (SPDE) approach. In the second step, they are fitted in a Bayesian framework through the integrated nested Laplace approximation implemented in R-INLA. Finally, posterior samples are generated to provide statistical inferences through Monte-Carlo estimation. Motivated by the 2019 Extreme Value Analysis data challenge, we illustrate our approach to predict the distribution of local space-time minima in anomalies of Red Sea surface temperatures, using a gridded dataset (11315 days, 16703 pixels) with artificially generated gaps. In particular, we show the improved performance of our two-step approach over a purely Gaussian model without tail transformations.

Climate sensitive single tree growth modeling using a hierarchical Bayes approach and integrated nested Laplace approximations (INLA) for a distributed lag model

A novel methodological framework is presented for climate-sensitive modeling of annual radial stem increments using tree-ring width time series. The approach is based on a hierarchical Bayes model together with a distributed time lag model that take into account the effects of a series of monthly temperature and precipitation values, as well as their interactions. By using a set of random walk priors, the hierarchical Bayes model allows both the detrending of the individual time series and the regression modeling to be performed simultaneously in a single model step. The approach was applied to comprehensive tree-ring width data from Austria collected on sample plots arranged in triplets representing different mixture types. Bayesian predictions revealed that European larch (Larix decidua Mill.), Norway spruce (Picea abies (L.) H. Karst.), and Scots pine (Pinus sylvestris L.) show positive climate-related growth trends throughout higher elevation sites in Tyrol, and these trends remain unchanged under a mixed-stand scenario. At the lower Austrian sites, Norway spruce was found to show a severely negative growth trend under both the pure- and mixed-stand scenario. The increment rates of European beech (Fagus sylvatica L.) were found to have a negative climate-related trend in pure stands, and the trend diminished through an admixture of spruce or larch. The trends of European larch and sessile oak (Quercus petraea (Matt.) Liebl.) showed stationary behavior, irrespective of the mixture scenario. Scots pine data showed a positive trend at the lower elevation sites under both the pure- and mixed-stand scenario. These findings indicate that species mixing does not lower the climate-related increment fluctuations of beech, oak, pine, and spruce at lower elevation sites.

Incorporating capture heterogeneity in the estimation of autoregressive coefficients of animal population dynamics using capture-recapture data.

Population dynamic models combine density dependence and environmental effects. Ignoring sampling uncertainty might lead to biased estimation of the strength of density dependence. This is typically addressed using state‐space model approaches, which integrate sampling error and population process estimates. Such models seldom include an explicit link between the sampling procedures and the true abundance, which is common in capture–recapture settings. However, many of the models proposed to estimate abundance in the presence of capture heterogeneity lead to incomplete likelihood functions and cannot be straightforwardly included in state‐space models. We assessed the importance of estimating sampling error explicitly by taking an intermediate approach between ignoring uncertainty in abundance estimates and fully specified state‐space models for density‐dependence estimation based on autoregressive processes. First, we estimated individual capture probabilities based on a heterogeneity model for a closed population, using a conditional multinomial likelihood, followed by a Horvitz–Thompson estimate for abundance. Second, we estimated coefficients of autoregressive models for the log abundance. Inference was performed using the methodology of integrated nested Laplace approximation (INLA). We performed an extensive simulation study to compare our approach with estimates disregarding capture history information, and using R‐package VGAM, for different parameter specifications. The methods were then applied to a real data set of gray‐sided voles Myodes rufocanus from Northern Norway. We found that density‐dependence estimation was improved when explicitly modeling sampling error in scenarios with low process variances, in which differences in coverage reached up to 8% in estimating the coefficients of the autoregressive processes. In this case, the bias also increased assuming a Poisson distribution in the observational model. For high process variances, the differences between methods were small and it appeared less important to model heterogeneity.

Estimation of annual runoff by exploiting long-term spatial patterns and short records within a geostatistical framework

Abstract. In this article, we present a Bayesian geostatistical framework that is particularly suitable for interpolation of hydrological data when the available dataset is sparse and includes both long and short records of runoff. A key feature of the proposed framework is that several years of runoff are modelled simultaneously with two spatial fields: one that is common for all years under study that represents the runoff generation due to long-term (climatic) conditions and one that is year-specific. The climatic spatial field captures how short records of runoff from partially gauged catchments vary relative to longer time series from other catchments, and transfers this information across years. To make the Bayesian model computationally feasible and fast, we use integrated nested Laplace approximations (INLAs) and the stochastic partial differential equation (SPDE) approach to spatial modelling. The geostatistical framework is demonstrated by filling in missing values of annual runoff and by predicting mean annual runoff for around 200 catchments in Norway. The predictive performance is compared to top-kriging (interpolation method) and simple linear regression (record augmentation method). The results show that if the runoff is driven by processes that are repeated over time (e.g. orographic precipitation patterns), the value of including short records in the suggested model is large. For partially gauged catchments the suggested framework performs better than comparable methods, and one annual observation from the target catchment can lead to a 50 % reduction in root mean squared error (RMSE) compared to when no observations are available from the target catchment. We also find that short records safely can be included in the framework regardless of the spatial characteristics of the underlying climate, and down to record lengths of 1 year.

Space-time analysis of ovarian cancer mortality rates by age groups in spanish provinces (1989\u20132015)

BackgroundOvarian cancer is a silent and largely asymptomatic cancer, leading to late diagnosis and worse prognosis. The late-stage detection and low survival rates, makes the study of the space-time evolution of ovarian cancer particularly relevant. In addition, research of this cancer in small areas (like provinces or counties) is still scarce.MethodsThe study presented here covers all ovarian cancer deaths for women over 50 years of age in the provinces of Spain during the period 1989-2015. Spatio-temporal models have been fitted to smooth ovarian cancer mortality rates in age groups [50,60), [60,70), [70,80), and [80,+), borrowing information from spatial and temporal neighbours. Model fitting and inference has been carried out using the Integrated Nested Laplace Approximation (INLA) technique.ResultsLarge differences in ovarian cancer mortality among the age groups have been found, with higher mortality rates in the older age groups. Striking differences are observed between northern and southern Spain. The global temporal trends (by age group) reveal that the evolution of ovarian cancer over the whole of Spain has remained nearly constant since the early 2000s.ConclusionDifferences in ovarian cancer mortality exist among the Spanish provinces, years, and age groups. As the exact causes of ovarian cancer remain unknown, spatio-temporal analyses by age groups are essential to discover inequalities in ovarian cancer mortality. Women over 60 years of age should be the focus of follow-up studies as the mortality rates remain constant since 2002. High-mortality provinces should also be monitored to look for specific risk factors.

Spatial Bayesian Modeling Applied to the Surveys of Xylella fastidiosa in Alicante (Spain) and Apulia (Italy).

The plant-pathogenic bacterium Xylella fastidiosa was first reported in Europe in 2013, in the province of Lecce, Italy, where extensive areas were affected by the olive quick decline syndrome, caused by the subsp. pauca. In Alicante, Spain, almond leaf scorch, caused by X. fastidiosa subsp. multiplex, was detected in 2017. The effects of climatic and spatial factors on the geographic distribution of X. fastidiosa in these two infested regions in Europe were studied. The presence/absence data of X. fastidiosa in the official surveys were analyzed using Bayesian hierarchical models through the integrated nested Laplace approximation (INLA) methodology. Climatic covariates were obtained from the WorldClim v.2 database. A categorical variable was also included according to Purcell’s minimum winter temperature thresholds for the risk of occurrence of Pierce’s disease of grapevine, caused by X. fastidiosa subsp. fastidiosa. In Alicante, data were presented aggregated on a 1 km grid (lattice data), where the spatial effect was included in the model through a conditional autoregressive structure. In Lecce, data were observed at continuous locations occurring within a defined spatial domain (geostatistical data). Therefore, the spatial effect was included via the stochastic partial differential equation approach. In Alicante, the pathogen was detected in all four of Purcell’s categories, illustrating the environmental plasticity of the subsp. multiplex. Here, none of the climatic covariates were retained in the selected model. Only two of Purcell’s categories were represented in Lecce. The mean diurnal range (bio2) and the mean temperature of the wettest quarter (bio8) were retained in the selected model, with a negative relationship with the presence of the pathogen. However, this may be due to the heterogeneous sampling distribution having a confounding effect with the climatic covariates. In both regions, the spatial structure had a strong influence on the models, but not the climatic covariates. Therefore, pathogen distribution was largely defined by the spatial relationship between geographic locations. This substantial contribution of the spatial effect in the models might indicate that the current extent of X. fastidiosa in the study regions had arisen from a single focus or from several foci, which have been coalesced.

Predicting spatiotemporal abundance of breeding waterfowl across Canada: A Bayesian hierarchical modelling approach

AbstractAimOur aim was to develop predictive statistical models for mapping the abundance of 18 waterfowl species at a pan‐Canadian level. We refined the previous generation of national waterfowl models by (a) developing new, more interpretable statistical models that (b) explicitly account for spatiotemporal variations in waterfowl abundance, while (c) testing for associations with an updated suite of habitat covariates.LocationAll of Canada, excluding the Northern Arctic ecozone.MethodsOur response variables were annual species counts on 2,227 aerial‐survey segments over a period of 25 years (1990–2015). Combining machine‐learning and hierarchical regression modelling, we devised an innovative covariate selection strategy to select for each species the best subset of a panel of 232 candidate habitat covariates. With the selected covariates, we implemented hierarchical generalized linear models in a Bayesian framework, using the integrated nested Laplace approximation and stochastic partial differential equation approaches.ResultsOn average, our models explained 47% of the observed variance for spatiotemporal predictions and 74% for temporally averaged spatial predictions. The 18 species models included 94 significant waterfowl‐habitat associations involving 42 distinct habitat covariates, with an average of 5.3 covariates per model. Covariates for forest attributes were the most represented in our models. The proportional biomass of Populus tremuloides was the most frequently selected covariate (10/94 associations in 10/18 species). Model predictions generated spatial and spatiotemporal maps of species abundances over almost all of Canada.Main conclusionsWe showed that it is possible to efficiently combine machine‐learning, variable selection and hierarchical Bayesian methods that exploit high‐dimensional covariate spaces. Our approach yielded powerful and easily interpretable species distribution models with very few covariates, while accounting for residual autocorrelation. Possible applications of the resulting models and maps include the development of biodiversity indicators, the evaluation and execution of conservation planning strategies, and ecosystem services monitoring.

Assessing spatial confounding in cancer disease mapping using R.

Exploring spatial patterns in the context of cancer disease mapping (DM) is a decisive approach to bring evidence of geographical tendencies in assessing disease status and progression. However, this framework is not insulated from spatial confounding, a topic of significant interest in cancer epidemiology, where the latent correlation between the spatial random effects and fixed effects (such as covariates), often lead to misleading interpretation. To introduce three popular approaches (RHZ, HH and SPOCK; details in paper) often employed to tackle spatial confounding, and illustrate their implementation in cancer research via the popular statistical software R. As a solution to alleviate spatial confounding, restricted spatial regressions are constructed by either projecting the latent effect onto the orthogonal space of covariates, or by displacing the spatial locations. Popular parametric count data models, such as the Poisson, generalized Poisson and negative binomial, were considered for the areal count responses, while the spatial association is quantified via the conditional autoregressive (CAR) model. Our method of inference in Bayesian, sometimes aided by the integrated nested Laplace approximation (INLA) to accelerate computing. The methods are implemented in the R package RASCO available from the first author's GitHub page. The results reveal that all three methods perform well in alleviating the bias and variance inflation present in the spatial models. The effects of spatial confounding were also explored, which, if ignored in practice, may lead to wrong conclusions. Spatial confounding continues to remain a critical bottleneck in deriving precise inference from spatial DM models. Hence, its effects must be investigated, and mitigated. Several approaches are available in the literature, and they produce trustworthy results. The central contribution of this paper is providing the practitioners the R package RASCO, capable of fitting a large number of spatial models, as well as their restricted versions.

Effects of human-related and biotic landscape features on the occurrence and size of modern forest fires in Sweden

The influence of landscape features on the occurrence and size of forest fires in Northern Europe has not been well-studied. In this paper, we analyzed the impact of human-related landscape properties (road and human population density), biotic features (amount of firebreak area and vegetation zone) and fire weather indices (Buildup Index, BUI and Initial Spread Index, ISI) on the occurrence and size of forest fires in Sweden from 1998 to 2017. To analyze the environmental controls of fire occurrence and fire size under different levels of climatological fire hazard, we divided the data into two subsets: (1) large fire years (LFY), defined as the years with the total amount of burned area being higher than the dataset-wide average (2002, 2003, 2006, 2008 and 2014), and (2) the remaining years (nLFY). Our analytical approach was based on spatial models using Integrated Nested Laplace Approximations (INLA). Models built on both LFY and nLFY subsets suggested a strong human influence on fire occurrence: road density, the number of firebreaks, and population density, all were positively associated with fire occurrence, suggesting an important role of human-related ignitions. The southernmost vegetation zones in Sweden (boreo-nemoral and nemoral) exhibited the highest fire occurrence (LFY), a pattern potentially related to a higher population density in combination with weather more conducive for fires in this part of the country. The patterns that emerged from the fire size models pointed to the climate as the main factor controlling fire size, irrespective of the type of years analyzed. Road density, number of firebreaks and population density showed a negative association with fire size, possibly indicating higher efficiency of fire suppression in the areas with higher human presence. Vegetation zones were selected as an informative predictor, indicating that the fire activity varies across the zones, with those in mid-Sweden being the most prone to large events. The ISI correlated strongly and positively with fire size in both subsets (LFY and nLFY), pointing to the role of weather conditions favorable for fire spread, primarily that of surface fires. The BUI showed a weak negative correlation to fire size, indicating that dryness of organic horizon, specifically its deeper layers, is less relevant for predicting fire size. Contemporary fire activity in Sweden is driven by a combination of human-related ignitions, and weather conditions controlling fire spread with a moderate effect of vegetation composition and generally efficient fire suppression. Human-related landscape features (roads and population density) play a major role in shaping ignition patterns, whereas climate (ISI) and vegetation properties appear informative as predictors of fire size, even under a modern fire suppression effort.

Spatial Modelling of Under-five Mortality in Lesotho with Reference to 2014 Demographic and Health Surveillance Dataset

Background: Lesotho is the country located in the Sub-Saharan region of Africa countries where under-five mortality (U5M) is still a big issue due to some significant social and demographic risk factors. Hence, the investigation of some social and demographic factors that are associated with the U5M, is a critical problem that needs due consideration. Methods: This study used the 2014 Lesotho Demographic and Health Survey (LDHS) that had a sample of over 9000 representative households. Individually, data consisting of a nationally representative sample of 9,543 households in the 2014 Lesotho Demographic and Health Survey were analysed. The Random Walk second-order (RW2) model was adopted for analysis. Maps construction and modelling were done through the spatially structured and unstructured random effects using the Gaussian Markov Random Field and a zero-mean Gaussian process, respectively. The full Bayesian inference was adopted to produce the results using the Integrated Nested Laplace Approximation (INLA) function in R-software. Results: In this study, age at death of an under-five child was found to have a linear association with the U5M in Lesotho. The non-stationary models outperform the stationary models. The low-risk pattern was found in the north of Lesotho, and the highest risk occurs in the centre through the south, east, west, southeast, and northwest. Breastfeeding has contributed significantly to under-five mortality to most of Lesotho districts. Conclusion: This study adopted the newly developed statistical models to model and mapped the U5M in Lesotho. The full Bayesian inference was used to produce the results using R-INLA package. The findings from this study can help introduce new policies that will help reduce disparity in Lesotho.

Canine serological survey and dog culling and its relationship with human visceral leishmaniasis in an endemic urban area

BackgroundVisceral leishmaniasis is an important but neglected disease that is spreading and is highly lethal when left untreated. This study sought to measure the Leishmania infantum seroprevalence in dogs, the coverage of its control activities (identification of the canine reservoir by serological survey, dog culling and insecticide spraying) and to evaluate its relationship with the occurrence of the disease in humans in the municipalities of Araçatuba and Birigui, state of São Paulo, Brazil.MethodsInformation from 2006 to 2015 was georeferenced for each municipality and modeling was performed for the two municipalities together. To do this, latent Gaussian Bayesian models with the incorporation of a spatio-temporal structure and Poisson distribution were used. The Besag-York-Mollie models were applied for random spatial effects, as also were autoregressive models of order 1 for random temporal effects. The modeling was performed using the INLA (Integrated Nested Laplace Approximations) deterministic approach, considering both the numbers of cases as well as the coverage paired year by year and lagged at one and two years.ResultsControl activity coverage was observed to be generally low. The behavior of the temporal tendency in the human disease presented distinct patterns in the two municipalities, however, in both the tendency was to decline. The canine serological survey presented as a protective factor only in the two-year lag model.ConclusionsThe canine serological coverage, even at low intensity, carried out jointly with the culling of the positive dogs, suggested a decreasing effect on the occurrence of the disease in humans, whose effects would be seen two years after it was carried out.

Daily gridded temperature and precipitation datasets over the Black Sea catchment: 1961–1990 and climate change scenarios for 2071–2100

This dataset improves on previous products in its spatial resolution, spatial extent and time period covering the Black Sea catchment (BSC). The spatial prediction of daily datasets was performed using the integrated nested Laplace approximation (INLA) methodology. The results show that for minimum and maximum temperature, the model with the elevation and distance to shorelines predictors is the best fitted model. The best fitted model for precipitation is obtained with the elevation predictor. The downscaling of climate change scenarios is based on HIRHAM regional climate model (RCM) from the European project PRUDENCE. The downscaling was made by means of a modified delta method. The modified delta method applied in this study explicitly considers the spatial differences of the climate scenarios and the monthly variability. For each grid point, the delta method is applied according to the rank order of values in the monthly distribution of the closest RCM grid point. The results show that the delta method gives satisfying results when considering the monthly variability. Impacts on minimum temperature, maximum temperature, precipitation, number of days without precipitation, dry spell length, number and length of days above maximum temperature above 30∘C, under conditions of climate change are also examined for this region.

Bayesian Model Averaging with the Integrated Nested Laplace Approximation

The integrated nested Laplace approximation (INLA) for Bayesian inference is an efficient approach to estimate the posterior marginal distributions of the parameters and latent effects of Bayesian hierarchical models that can be expressed as latent Gaussian Markov random fields (GMRF). The representation as a GMRF allows the associated software R-INLA to estimate the posterior marginals in a fraction of the time as typical Markov chain Monte Carlo algorithms. INLA can be extended by means of Bayesian model averaging (BMA) to increase the number of models that it can fit to conditional latent GMRF. In this paper, we review the use of BMA with INLA and propose a new example on spatial econometrics models.

A tutorial on spatio-temporal disease risk modelling in R using Markov chain Monte Carlo simulation and the CARBayesST package

Population-level disease risk varies in space and time, and is typically estimated using aggregated disease count data relating to a set of non-overlapping areal units for multiple consecutive time periods. A large research base of statistical models and corresponding software has been developed for such data, with most analyses being undertaken in a Bayesian setting using either Markov chain Monte Carlo (MCMC) simulation or integrated nested Laplace approximations (INLA). This paper presents a tutorial for undertaking spatio-temporal disease modelling using MCMC simulation, utilising the CARBayesST package in the R software environment. The tutorial describes the complete modelling journey, starting with data input, wrangling and visualisation, before focusing on model fitting, model assessment and results presentation. It is illustrated by a new case study of pneumonia mortality at the local authority level in England, and answers important public health questions including the effect of covariate risk factors, spatio-temporal trends, and health inequalities.

Reassessing the observational evidence for nitrogen deposition impacts in acid grassland: spatial Bayesian linear models indicate small and ambiguous effects on species richness.

Nitrogen deposition (Ndep) is considered a significant threat to plant diversity in grassland ecosystems around the world. The evidence supporting this conclusion comes from both observational and experimental research, with “space-for-time” substitution surveys of pollutant gradients a significant portion of the former. However, estimates of regression coefficients for Ndep impacts on species richness, derived with a focus on causal inference, are hard to locate in the observational literature. Some influential observational studies have presented estimates from univariate models, overlooking the effects of omitted variable bias, and/or have used P-value-based stepwise variable selection (PSVS) to infer impacts, a strategy known to be poorly suited to the accurate estimation of regression coefficients. Broad-scale spatial autocorrelation has also generally been unaccounted for. We re-examine two UK observational datasets that have previously been used to investigate the relationship between Ndep and plant species richness in acid grasslands, a much-researched habitat in this context. One of these studies (Stevens et al., 2004, Science, 303: 1876–1879) estimated a large negative impact of Ndep on richness through the use of PSVS; the other reported smaller impacts (Maskell et al., 2010, Global Change Biology, 16: 671–679), but did not explicitly report regression coefficients or partial effects, making the actual size of the estimated Ndep impact difficult to assess. We reanalyse both datasets using a spatial Bayesian linear model estimated using integrated nested Laplace approximation (INLA). Contrary to previous results, we found similar-sized estimates of the Ndep impact on plant richness between studies, both with and without bryophytes, albeit with some disagreement over the most likely direction of this effect. Our analyses suggest that some previous estimates of Ndep impacts on richness from space-for-time substitution studies are likely to have been over-estimated, and that the evidence from observational studies could be fragile when confronted with alternative model specifications, although further work is required to investigate potentially nonlinear responses. Given the growing literature on the use of observational data to estimate the impacts of pollutants on biodiversity, we suggest that a greater focus on clearly reporting important outcomes with associated uncertainty, the use of techniques to account for spatial autocorrelation, and a clearer focus on the aims of a study, whether explanatory or predictive, are all required.

The influence of the age-period-cohort effects on the temporal trend mortality from schistosomiasis in Brazil from 1980 to 2014.

Schistosomiasis is highly debilitating and related to poverty, leading to chronic health problems. This disease is important for public health due to the high prevalence, severity of clinical forms and heterogeneous spatial and temporal patterns. In Brazil, about 1.5 million people are at risk of infection with Schistosoma mansoni, with an annual average of 500 deaths. In this study, the temporal change in mortality was evaluated in relation to the effects of age, period and birth cohort, in Brazil and regions, from 1980 to 2014. In this study, we analyzed the influence of age, period and birth cohort (APC effects) on the temporal evolution of schistosomiasis mortality in Brazil from 1980 to 2014, according to sex and geographic regions of the country. The death records were extracted from the SIM (Mortality Information System) of the DATASUS website (Department of National Health Informatics) of the Ministry of Health of Brazil. The temporal effects were estimated using Bayesian models and the INLA (Integrated Nested Laplace Approximations) method for parameter inference. More than 24 thousand deaths were registered in the analyzed period, mainly in men from the Northeast region. In Brazil, children under 14 years of age had protection against death from schistosomiasis. There was no significant effect for others ages. From 1990 to 1999, there was a protective effect for death from schistosomiasis and a null effect in the other periods. There was a decreasing trend in the risk of death among birth cohorts. The greatest risk was among people born from 1903 to 1912. There was a protective effect for death among people born after 1968. Men were at risk of death between 25 and 54 years old, while women were at risk after seventy years of age. The southern and central-western regions had a risk of death until 1989 and had a protective effect between1995 and 1999. The northern region had a risk of death between 1985 and 1994, and a protective effect after 2005. The northeast and Southeast regions had protective effects for death between the years 1990 and 1999, and after 2000, respectively. People born until 1952 and 1957 were at risk of dying in the South and North regions, respectively, and a protective effect among people born after 1968, in both regions. In the Northeast region, there was a protective effect among people born after 1963. In the other regions, there was a risk of death among people born until 1962 and a protective effect among people born after 1973. The Central-West region had the least declining trend in risk of death among birth cohorts. The birth cohorts had a great influence on the decreasing trend of schistosomiasis mortality in Brazil. This result may be due to the interaction between demographic changes and greater access to health and sanitation services, in addition to the impact of schistosomiasis control measures experienced by younger cohorts.