Bayesian computing with INLA: New features

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.

Mapping geographical inequalities in oral rehydration therapy coverage in low-income and middle-income countries, 2000-17

BACKGROUND

Oral rehydration solution (ORS) is a form of oral rehydration therapy (ORT) for diarrhoea that has the potential to drastically reduce child mortality; yet, according to UNICEF estimates, less than half of children younger than 5 years with diarrhoea in low-income and middle-income countries (LMICs) received ORS in 2016. A variety of recommended home fluids (RHF) exist as alternative forms of ORT; however, it is unclear whether RHF prevent child mortality. Previous studies have shown considerable variation between countries in ORS and RHF use, but subnational variation is unknown. This study aims to produce high-resolution geospatial estimates of relative and absolute coverage of ORS, RHF, and ORT (use of either ORS or RHF) in LMICs.

METHODS

We used a Bayesian geostatistical model including 15 spatial covariates and data from 385 household surveys across 94 LMICs to estimate annual proportions of children younger than 5 years of age with diarrhoea who received ORS or RHF (or both) on continuous continent-wide surfaces in 2000-17, and aggregated results to policy-relevant administrative units. Additionally, we analysed geographical inequality in coverage across administrative units and estimated the number of diarrhoeal deaths averted by increased coverage over the study period. Uncertainty in the mean coverage estimates was calculated by taking 250 draws from the posterior joint distribution of the model and creating uncertainty intervals (UIs) with the 2·5th and 97·5th percentiles of those 250 draws.

FINDINGS

While ORS use among children with diarrhoea increased in some countries from 2000 to 2017, coverage remained below 50% in the majority (62·6%; 12 417 of 19 823) of second administrative-level units and an estimated 6 519 000 children (95% UI 5 254 000-7 733 000) with diarrhoea were not treated with any form of ORT in 2017. Increases in ORS use corresponded with declines in RHF in many locations, resulting in relatively constant overall ORT coverage from 2000 to 2017. Although ORS was uniformly distributed subnationally in some countries, within-country geographical inequalities persisted in others; 11 countries had at least a 50% difference in one of their units compared with the country mean. Increases in ORS use over time were correlated with declines in RHF use and in diarrhoeal mortality in many locations, and an estimated 52 230 diarrhoeal deaths (36 910-68 860) were averted by scaling up of ORS coverage between 2000 and 2017. Finally, we identified key subnational areas in Colombia, Nigeria, and Sudan as examples of where diarrhoeal mortality remains higher than average, while ORS coverage remains lower than average.

INTERPRETATION

To our knowledge, this study is the first to produce and map subnational estimates of ORS, RHF, and ORT coverage and attributable child diarrhoeal deaths across LMICs from 2000 to 2017, allowing for tracking progress over time. Our novel results, combined with detailed subnational estimates of diarrhoeal morbidity and mortality, can support subnational needs assessments aimed at furthering policy makers' understanding of within-country disparities. Over 50 years after the discovery that led to this simple, cheap, and life-saving therapy, large gains in reducing mortality could still be made by reducing geographical inequalities in ORS coverage.

FUNDING

Bill & Melinda Gates Foundation.

Bayesian hierarchical modeling of joint spatiotemporal risk patterns for Human Immunodeficiency Virus (HIV) and Tuberculosis (TB) in Kenya

The simultaneous spatiotemporal modeling of multiple related diseases strengthens inferences by borrowing information between related diseases. Numerous research contributions to spatiotemporal modeling approaches exhibit their strengths differently with increasing complexity. However, contributions that combine spatiotemporal approaches to modeling of multiple diseases simultaneously are not so common. We present a full Bayesian hierarchical spatio-temporal approach to the joint modeling of Human Immunodeficiency Virus and Tuberculosis incidences in Kenya. Using case notification data for the period 2012–2017, we estimated the model parameters and determined the joint spatial patterns and temporal variations. Our model included specific and shared spatial and temporal effects. The specific random effects allowed for departures from the shared patterns for the different diseases. The space-time interaction term characterized the underlying spatial patterns with every temporal fluctuation. We assumed the shared random effects to be the structured effects and the disease-specific random effects to be unstructured effects. We detected the spatial similarity in the distribution of Tuberculosis and Human Immunodeficiency Virus in approximately 29 counties around the western, central and southern regions of Kenya. The distribution of the shared relative risks had minimal difference with the Human Immunodeficiency Virus disease-specific relative risk whereas that of Tuberculosis presented many more counties as high-risk areas. The flexibility and informative outputs of Bayesian Hierarchical Models enabled us to identify the similarities and differences in the distribution of the relative risks associated with each disease. Estimating the Human Immunodeficiency Virus and Tuberculosis shared relative risks provide additional insights towards collaborative monitoring of the diseases and control efforts.

Mapping geographical inequalities in childhood diarrhoeal morbidity and mortality in low-income and middle-income countries, 2000-17: analysis for the Global Burden of Disease Study 2017

BACKGROUND

Across low-income and middle-income countries (LMICs), one in ten deaths in children younger than 5 years is attributable to diarrhoea. The substantial between-country variation in both diarrhoea incidence and mortality is attributable to interventions that protect children, prevent infection, and treat disease. Identifying subnational regions with the highest burden and mapping associated risk factors can aid in reducing preventable childhood diarrhoea.

METHODS

We used Bayesian model-based geostatistics and a geolocated dataset comprising 15 072 746 children younger than 5 years from 466 surveys in 94 LMICs, in combination with findings of the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2017, to estimate posterior distributions of diarrhoea prevalence, incidence, and mortality from 2000 to 2017. From these data, we estimated the burden of diarrhoea at varying subnational levels (termed units) by spatially aggregating draws, and we investigated the drivers of subnational patterns by creating aggregated risk factor estimates.

FINDINGS

The greatest declines in diarrhoeal mortality were seen in south and southeast Asia and South America, where 54·0% (95% uncertainty interval [UI] 38·1-65·8), 17·4% (7·7-28·4), and 59·5% (34·2-86·9) of units, respectively, recorded decreases in deaths from diarrhoea greater than 10%. Although children in much of Africa remain at high risk of death due to diarrhoea, regions with the most deaths were outside Africa, with the highest mortality units located in Pakistan. Indonesia showed the greatest within-country geographical inequality; some regions had mortality rates nearly four times the average country rate. Reductions in mortality were correlated to improvements in water, sanitation, and hygiene (WASH) or reductions in child growth failure (CGF). Similarly, most high-risk areas had poor WASH, high CGF, or low oral rehydration therapy coverage.

INTERPRETATION

By co-analysing geospatial trends in diarrhoeal burden and its key risk factors, we could assess candidate drivers of subnational death reduction. Further, by doing a counterfactual analysis of the remaining disease burden using key risk factors, we identified potential intervention strategies for vulnerable populations. In view of the demands for limited resources in LMICs, accurately quantifying the burden of diarrhoea and its drivers is important for precision public health.

FUNDING

Bill & Melinda Gates Foundation.

Pain rates in general population for the period 1991-2015 and 10-years prediction: results from a multi-continent age-period-cohort analysis

Background

Pain is a common symptom, often associated with neurological and musculoskeletal conditions, and experienced especially by females and by older people. The aims of this study are to evaluate the temporal variations of pain rates among general populations for the period 1991–2015 and to project 10-year pain rates.

Methods

We used the harmonized dataset of ATHLOS project, which included 660,028 valid observations in the period 1990–2015 and we applied Bayesian age–period–cohort modeling to perform projections up to 2025. The harmonized Pain variable covers the content “self-reported pain experienced at the time of the interview”, with a dichotomous (yes or no) modality.

Results

Pain rates were higher among females, older subjects, in recent periods, and among observations referred to cohorts of subjects born between the 20s and the 60s. The 10-year projections indicate a noteworthy increase in pain rates in both genders and particularly among subjects aged 66 or over, for whom a 10–20% increase in pain rate is foreseen; among females only, a 10–15% increase in pain rates is foreseen for those aged 36–50.

Conclusions

Projected increase in pain rates will require specific interventions by health and welfare systems, as pain is responsible for limited quality of subjective well-being, reduced employment rates and hampered work performance. Worksite and lifestyle interventions will therefore be needed to limit the impact of projected higher pain rates.

Spatiophylogenetic modelling of extinction risk reveals evolutionary distinctiveness and brief flowering period as threats in a hotspot plant genus

Comparative models used to predict species threat status can help identify the diagnostic features of species at risk. Such models often combine variables measured at the species level with spatial variables, causing multiple statistical challenges, including phylogenetic and spatial non-independence. We present a novel Bayesian approach for modelling threat status that simultaneously deals with both forms of non-independence and estimates their relative contribution, and we apply the approach to modelling threat status in the Australian plant genus Hakea. We find that after phylogenetic and spatial effects are accounted for, species with greater evolutionary distinctiveness and a shorter annual flowering period are more likely to be threatened. The model allows us to combine information on evolutionary history, species biology and spatial data, calculate latent extinction risk (potential for non-threatened species to become threatened), estimate the most important drivers of risk for individual species and map spatial patterns in the effects of different predictors on extinction risk. This could be of value for proactive conservation decision-making based on the early identification of species and regions of potential conservation concern.

Hearing Aid Amplification Reduces Communication Effort of People With Hearing Impairment and Their Conversation Partners

Objectives This study investigates the hypothesis that hearing aid amplification reduces effort within conversation for both hearing aid wearers and their communication partners. Levels of effort, in the form of speech production modifications, required to maintain successful spoken communication in a range of acoustic environments are compared to earlier reported results measured in unaided conversation conditions. Design Fifteen young adult normal-hearing participants and 15 older adult hearing-impaired participants were tested in pairs. Each pair consisted of one young normal-hearing participant and one older hearing-impaired participant. Hearing-impaired participants received directional hearing aid amplification, according to their audiogram, via a master hearing aid with gain provided according to the NAL-NL2 fitting formula. Pairs of participants were required to take part in naturalistic conversations through the use of a referential communication task. Each pair took part in five conversations, each of 5-min duration. During each conversation, participants were exposed to one of five different realistic acoustic environments presented through highly open headphones. The ordering of acoustic environments across experimental blocks was pseudorandomized. Resulting recordings of conversational speech were analyzed to determine the magnitude of speech modifications, in terms of vocal level and spectrum, produced by normal-hearing talkers as a function of both acoustic environment and the degree of high-frequency average hearing impairment of their conversation partner. Results The magnitude of spectral modifications of speech produced by normal-hearing talkers during conversations with aided hearing-impaired interlocutors was smaller than the speech modifications observed during conversations between the same pairs of participants in the absence of hearing aid amplification. Conclusions The provision of hearing aid amplification reduces the effort required to maintain communication in adverse conditions. This reduction in effort provides benefit to hearing-impaired individuals and also to the conversation partners of hearing-impaired individuals. By considering the impact of amplification on both sides of dyadic conversations, this approach contributes to an increased understanding of the likely impact of hearing impairment on everyday communication.

Inference and computation with generalized additive models and their extensions

Regression models in which a response variable is related to smooth functions of some predictor variables are popular as a result of their appealing balance between flexibility and interpretability. Since the original generalized additive models of Hastie and Tibshirani (Generalized additive models. Chapman & Hall, Boca Raton, 1990) numerous model extensions have been proposed, and a variety of practically useful computational strategies have emerged. This paper provides an overview of some widely applicable frameworks for this type of modelling, emphasizing the similarities between the different approaches, and the equivalence of smoothing, Gaussian latent process models and Gaussian random effects. The focus is particularly on Bayes empirical smoother theory, fully Bayesian inference via stochastic simulation or integrated nested Laplace approximation and boosting.

Mapping local patterns of childhood overweight and wasting in low- and middle-income countries between 2000 and 2017

A double burden of malnutrition occurs when individuals, household members or communities experience both undernutrition and overweight. Here, we show geospatial estimates of overweight and wasting prevalence among children under 5 years of age in 105 low- and middle-income countries (LMICs) from 2000 to 2017 and aggregate these to policy-relevant administrative units. Wasting decreased overall across LMICs between 2000 and 2017, from 8.4% (62.3 (55.1–70.8) million) to 6.4% (58.3 (47.6–70.7) million), but is predicted to remain above the World Health Organization’s Global Nutrition Target of <5% in over half of LMICs by 2025. Prevalence of overweight increased from 5.2% (30 (22.8–38.5) million) in 2000 to 6.0% (55.5 (44.8–67.9) million) children aged under 5 years in 2017. Areas most affected by double burden of malnutrition were located in Indonesia, Thailand, southeastern China, Botswana, Cameroon and central Nigeria. Our estimates provide a new perspective to researchers, policy makers and public health agencies in their efforts to address this global childhood syndemic.

Fine-scale geospatial mapping of overweight and wasting (two components of the double burden of malnutrition) in 105 LMICs shows that overweight has increased from 5.2% in 2000 to 6.0% in children under 5 in 2017. Although overall wasting decreased over the same period, most countries are not on track to meet the World Health Organization’s Global Nutrition Target of <5% in over half of LMICs by 2025.

The Fine-Scale Landscape of Immunity and Parasitism in a Wild Ungulate Population

Spatial heterogeneity in susceptibility and exposure to parasites is a common source of confounding variation in disease ecology studies. However, it is not known whether spatial autocorrelation acts on immunity at small scales, within wild animal populations, and whether this predicts spatial patterns in infection. Here we used a well-mixed wild population of individually recognized red deer (Cervus elaphus) inhabiting a heterogeneous landscape to investigate fine-scale spatial patterns of immunity and parasitism. We noninvasively collected 842 fecal samples from 141 females with known ranging behavior over 2 years. We quantified total and helminth-specific mucosal antibodies and counted propagules of three gastrointestinal helminth taxa. These data were analyzed with linear mixed models using the Integrated Nested Laplace Approximation, using a Stochastic Partial Differentiation Equation approach to control for and quantify spatial autocorrelation. We also investigated whether spatial patterns of immunity and parasitism changed seasonally. We discovered substantial spatial heterogeneity in general and helminth-specific antibody levels and parasitism with two helminth taxa, all of which exhibited contrasting seasonal variation in their spatial patterns. Notably, Fasciola hepatica intensity appeared to be strongly influenced by the presence of wet grazing areas, and antibody hotspots did not correlate with distributions of any parasites. Our results suggest that spatial heterogeneity may be an important factor affecting immunity and parasitism in a wide range of study systems. We discuss these findings with regards to the design of sampling regimes and public health interventions, and suggest that disease ecology studies investigate spatial heterogeneity more regularly to enhance their results, even when examining small geographic areas.

Bayesian and Frequentist Analytical Approaches Using Log-Normal and Gamma Frailty Parametric Models for Breast Cancer Mortality

One of the major causes of death among females in Saudi Arabia is breast cancer. Newly diagnosed cases of breast cancer among the female population in Saudi Arabia is 19.5%. With this high incidence, it is crucial that we explore the determinants associated with breast cancer among the Saudi Arabia populace—the focus of this current study. The total sample size for this study is 8312 (8172 females and about 140 representing 1.68% males) patients that were diagnosed with advanced breast cancer. These are facility-based cross-sectional data collected over a 9-year period (2004 to 2013) from a routine health information system database. The data were obtained from the Saudi Cancer Registry (SCR). Both descriptive and inferential (Cox with log-normal and gamma frailties) statistics were conducted. The deviance information criterion (DIC), Watanabe–Akaike information criterion (WAIC), Bayesian information criterion (BIC), and Akaike information criterion were used to evaluate or discriminate between models. For all the six models fitted, the models which combined the fixed and random effects performed better than those with only the fixed effects. This is so because those models had smaller AIC and BIC values. The analyses were done using R and the INLA statistical software. There are evident disparities by regions with Riyadh, Makkah, and Eastern Province having the highest number of cancer patients at 28%, 26%, and 20% respectively. Grade II (46%) and Grade III (45%) are the most common cancer grades. Left paired site laterality (51%) and regional extent (52%) were also most common characteristics. Overall marital status, grade, and cancer extent increased the risk of a cancer patient dying. Those that were married had a hazard ratio of 1.36 (95% CI: 1.03–1.80) while widowed had a hazard ratio of 1.57 (95% CI: 1.14–2.18). Both the married and widowed were at higher risk of dying with cancer relative to respondents who had divorced. For grade, the risk was higher for all the levels, that is, Grade I (Well diff) (HR = 7.11, 95% CI: 3.32–15.23), Grade II (Mod diff) (HR = 7.89, 95% CI: 3.88–16.06), Grade III (Poor diff) (HR = 5.90, 95% CI (2.91–11.96), and Grade IV (Undiff) (HR = 5.44, 95% (2.48–11.9), relative to B-cell. These findings provide empirical evidence that information about individual patients and their region of residence is an important contributor in understanding the inequalities in cancer mortalities and that the application of robust statistical methodologies is also needed to better understand these issues well.

Mapping malaria seasonality in Madagascar using health facility data

BACKGROUND

Many malaria-endemic areas experience seasonal fluctuations in case incidence as Anopheles mosquito and Plasmodium parasite life cycles respond to changing environmental conditions. Identifying location-specific seasonality characteristics is useful for planning interventions. While most existing maps of malaria seasonality use fixed thresholds of rainfall, temperature, and/or vegetation indices to identify suitable transmission months, we construct a statistical modelling framework for characterising the seasonal patterns derived directly from monthly health facility data.

METHODS

With data from 2669 of the 3247 health facilities in Madagascar, a spatiotemporal regression model was used to estimate seasonal patterns across the island. In the absence of catchment population estimates or the ability to aggregate to the district level, this focused on the monthly proportions of total annual cases by health facility level. The model was informed by dynamic environmental covariates known to directly influence seasonal malaria trends. To identify operationally relevant characteristics such as the transmission start months and associated uncertainty measures, an algorithm was developed and applied to model realisations. A seasonality index was used to incorporate burden information from household prevalence surveys and summarise 'how seasonal' locations are relative to their surroundings.

RESULTS

Positive associations were detected between monthly case proportions and temporally lagged covariates of rainfall and temperature suitability. Consistent with the existing literature, model estimates indicate that while most parts of Madagascar experience peaks in malaria transmission near March-April, the eastern coast experiences an earlier peak around February. Transmission was estimated to start in southeast districts before southwest districts, suggesting that indoor residual spraying should be completed in the same order. In regions where the data suggested conflicting seasonal signals or two transmission seasons, estimates of seasonal features had larger deviations and therefore less certainty.

CONCLUSIONS

Monthly health facility data can be used to establish seasonal patterns in malaria burden and augment the information provided by household prevalence surveys. The proposed modelling framework allows for evidence-based and cohesive inferences on location-specific seasonal characteristics. As health surveillance systems continue to improve, it is hoped that more of such data will be available to improve our understanding and planning of intervention strategies.

Investigating the spatial variation and risk factors of childhood anaemia in four sub-Saharan African countries

Background

The causes of childhood anaemia are multifactorial, interrelated and complex. Such causes vary from country to country, and within a country. Thus, strategies for anaemia control should be tailored to local conditions and take into account the specific etiology and prevalence of anaemia in a given setting and sub-population. In addition, policies and programmes for anaemia control that do not account for the spatial heterogeneity of anaemia in children may result in certain sub-populations being excluded, limiting the effectiveness of the programmes. This study investigated the demographic and socio-economic determinants as well as the spatial variation of anaemia in children aged 6 to 59 months in Kenya, Malawi, Tanzania and Uganda.

Methods

The study made use of data collected from nationally representative Malaria Indicator Surveys (MIS) and Demographic and Health Surveys (DHS) conducted in all four countries between 2015 and 2017. During these surveys, all children under the age of five years old in the sampled households were tested for malaria and anaemia. A child’s anaemia status was based on the World Health Organization’s cut-off points where a child was considered anaemic if their altitude adjusted haemoglobin (Hb) level was less than 11 g/dL. The explanatory variables considered comprised of individual, household and cluster level factors, including the child’s malaria status. A multivariable hierarchical Bayesian geoadditive model was used which included a spatial effect for district of child’s residence.

Results

Prevalence of childhood anaemia ranged from 36.4% to 61.9% across the four countries. Children with a positive malaria result had a significantly higher odds of anaemia [AOR = 4.401; 95% CrI: (3.979, 4.871)]. After adjusting for a child’s malaria status and other demographic, socio-economic and environmental factors, the study revealed distinct spatial variation in childhood anaemia within and between Malawi, Uganda and Tanzania. The spatial variation appeared predominantly due to unmeasured district-specific factors that do not transcend boundaries.

Conclusions

Anaemia control measures in Malawi, Tanzania and Uganda need to account for internal spatial heterogeneity evident in these countries. Efforts in assessing the local district-specific causes of childhood anaemia within each country should be focused on.

Hearing Impairment Increases Communication Effort During Conversations in Noise

Purpose This article describes patterns of speech modifications produced by talkers as a function of the degree of hearing impairment of communication partners during naturalistic conversations in noise. An explanation of observed speech modifications is proposed in terms of a generalization of the concept of effort. This account complements existing theories of listening effort by extending the concept of effort to the domain of interactive communication. Method Twenty young adult normal hearing participants and 20 older adult hearing-impaired participants were tested in pairs. Each pair consisted of 1 young normal hearing participant and 1 older hearing-impaired participant. Pairs of participants took part in naturalistic conversations through the use of a referential communication task. Each pair completed a 5-min conversation in each of 5 different realistic acoustic environments. Results Talkers modified their speech, in terms of level and spectrum, in a gradient manner reflecting both the acoustic environment and the degree of hearing impairment of their conversation partner. All pairs of participants were able to maintain communication across all acoustic environments regardless of degree of hearing impairment and the level of environmental noise. Contrasting effects of noise and hearing impairment on speech production revealed distinct patterns of speech modifications produced by normal hearing and hearing-impaired talkers during conversation. This may reflect the fact that only the speech modifications produced by normal hearing talkers functioned to compensate for the hearing impairment of a conversation partner. Conclusions The data presented support the concept of communication effort as a dynamic feedback system between conversation participants. Additionally, these results provide insight into the nature of realistic speech signals, which are encountered by people with hearing impairment in everyday communication scenarios.

Mapping child growth failure across low- and middle-income countries

Childhood malnutrition is associated with high morbidity and mortality globally1. Undernourished children are more likely to experience cognitive, physical, and metabolic developmental impairments that can lead to later cardiovascular disease, reduced intellectual ability and school attainment, and reduced economic productivity in adulthood2. Child growth failure (CGF), expressed as stunting, wasting, and underweight in children under five years of age (0-59 months), is a specific subset of undernutrition characterized by insufficient height or weight against age-specific growth reference standards3-5. The prevalence of stunting, wasting, or underweight in children under five is the proportion of children with a height-for-age, weight-for-height, or weight-for-age z-score, respectively, that is more than two standard deviations below the World Health Organization's median growth reference standards for a healthy population6. Subnational estimates of CGF report substantial heterogeneity within countries, but are available primarily at the first administrative level (for example, states or provinces)7; the uneven geographical distribution of CGF has motivated further calls for assessments that can match the local scale of many public health programmes8. Building from our previous work mapping CGF in Africa9, here we provide the first, to our knowledge, mapped high-spatial-resolution estimates of CGF indicators from 2000 to 2017 across 105 low- and middle-income countries (LMICs), where 99% of affected children live1, aggregated to policy-relevant first and second (for example, districts or counties) administrative-level units and national levels. Despite remarkable declines over the study period, many LMICs remain far from the ambitious World Health Organization Global Nutrition Targets to reduce stunting by 40% and wasting to less than 5% by 2025. Large disparities in prevalence and progress exist across and within countries; our maps identify high-prevalence areas even within nations otherwise succeeding in reducing overall CGF prevalence. By highlighting where the highest-need populations reside, these geospatial estimates can support policy-makers in planning interventions that are adapted locally and in efficiently directing resources towards reducing CGF and its health implications.

Identifying residual hotspots and mapping lower respiratory infection morbidity and mortality in African children from 2000 to 2017

Lower respiratory infections (LRIs) are the leading cause of death in children under the age of 5, despite the existence of vaccines against many of their aetiologies. Furthermore, more than half of these deaths occur in Africa. Geospatial models can provide highly detailed estimates of trends subnationally, at the level where implementation of health policies has the greatest impact. We used Bayesian geostatistical modelling to estimate LRI incidence, prevalence and mortality in children under 5 subnationally in Africa for 2000-2017, using surveys covering 1.46 million children and 9,215,000 cases of LRI. Our model reveals large within-country variation in both health burden and its change over time. While reductions in childhood morbidity and mortality due to LRI were estimated for almost every country, we expose a cluster of residual high risk across seven countries, which averages 5.5 LRI deaths per 1,000 children per year. The preventable nature of the vast majority of LRI deaths mandates focused health system efforts in specific locations with the highest burden.

Flexible modelling of spatial variation in agricultural field trials with the R package INLA

KEY MESSAGE

Established spatial models improve the analysis of agricultural field trials with or without genomic data and can be fitted with the open-source R package INLA. The objective of this paper was to fit different established spatial models for analysing agricultural field trials using the open-source R package INLA. Spatial variation is common in field trials, and accounting for it increases the accuracy of estimated genetic effects. However, this is still hindered by the lack of available software implementations. We compare some established spatial models and show possibilities for flexible modelling with respect to field trial design and joint modelling over multiple years and locations. We use a Bayesian framework and for statistical inference the integrated nested Laplace approximations (INLA) implemented in the R package INLA. The spatial models we use are the well-known independent row and column effects, separable first-order autoregressive ([Formula: see text]) models and a Gaussian random field (Matérn) model that is approximated via the stochastic partial differential equation approach. The Matérn model can accommodate flexible field trial designs and yields interpretable parameters. We test the models in a simulation study imitating a wheat breeding programme with different levels of spatial variation, with and without genome-wide markers and with combining data over two locations, modelling spatial and genetic effects jointly. The results show comparable predictive performance for both the [Formula: see text] and the Matérn models. We also present an example of fitting the models to a real wheat breeding data and simulated tree breeding data with the Nelder wheel design to show the flexibility of the Matérn model and the R package INLA.

Integrating anthropogenic factors into regional-scale species distribution models-A novel application in the imperiled sagebrush biome

Species distribution models (SDMs) that rely on regional-scale environmental variables will play a key role in forecasting species occurrence in the face of climate change. However, in the Anthropocene, a number of local-scale anthropogenic variables, including wildfire history, land-use change, invasive species, and ecological restoration practices can override regional-scale variables to drive patterns of species distribution. Incorporating these human-induced factors into SDMs remains a major research challenge, in part because spatial variability in these factors occurs at fine scales, rendering prediction over regional extents problematic. Here, we used big sagebrush (Artemisia tridentata Nutt.) as a model species to explore whether including human-induced factors improves the fit of the SDM. We applied a Bayesian hurdle spatial approach using 21,753 data points of field-sampled vegetation obtained from the LANDFIRE program to model sagebrush occurrence and cover by incorporating fire history metrics and restoration treatments from 1980 to 2015 throughout the Great Basin of North America. Models including fire attributes and restoration treatments performed better than those including only climate and topographic variables. Number of fires and fire occurrence had the strongest relative effects on big sagebrush occurrence and cover, respectively. The models predicted that the probability of big sagebrush occurrence decreases by 1.2% (95% CI: -6.9%, 0.6%) when one fire occurs and cover decreases by 44.7% (95% CI: -47.9%, -41.3%) if at least one fire occurred over the 36 year period of record. Restoration practices increased the probability of big sagebrush occurrence but had minimal effect on cover. Our results demonstrate the potential value of including disturbance and land management along with climate in models to predict species distributions. As an increasing number of datasets representing land-use history become available, we anticipate that our modeling framework will have broad relevance across a range of biomes and species.

Investigation of the consequences of the modifiable areal unit problem in macroscopic traffic safety analysis: A case study accounting for scale and zoning

Traffic safety analysis at the macroscopic level usually relies on previously defined areal traffic analysis zones (TAZs) that are used as the units of investigation. Hence, statistical inference is made on the basis of such units, implying that the consideration of a certain TAZ configuration may influence the results and conclusions achieved. Regarding this, the modifiable areal unit problem (MAUP) is a well-known issue in the field of spatial statistics, which refers to the effects that arise in statistical properties and estimations when there is a change in areal units of analysis. In this paper, the consequences of MAUP have been investigated through a dataset of traffic crashes that occurred in Valencia within the years 2014 and 2015 and two common statistical models: a conditional autoregressive model and a geographically weighted regression. In the absence of an established TAZ scheme for the city, four classes of basic spatial units (BSUs) were considered: census tracts, hexagonal units and two types with construction based on the structure of main roads and intersections of the city. Each of these BSU types was specified at different levels of spatial aggregation. The main research objective was to investigate the final effects that changes in BSU type and scale have on model parameter estimations, but also the specific alterations that MAUP causes to data in terms of the distributional characteristics of the response, multicollinearity among the covariates and covariates' spatial autocorrelation. The results showed the presence and severity of MAUP for the dataset and area that were analysed. Although effects from scale variations were more moderate, changing the BSU type affected the results severely. The joint use of hexagonal units and a conditional autoregressive model achieved the best performance among all the possibilities explored, but the choice of a proper BSU unit should rely on more factors. Despite MAUP effects, educational centres showed a consistent (and negative) association with traffic crashes, a fact possibly related to their distribution across the whole city. Other covariates revealed a positive correlation with crash counts, but these findings were more uncertain given the discrepancies found at different scales and zonings.

Estimating the occurrence of traffic accidents near school locations: A case study from Valencia (Spain) including several approaches

Traffic safety around school locations is a topic of particular interest given the large number of vulnerable users, such as pedestrians or cyclists, that commute to them at certain times of the day. A dataset of traffic accidents recorded in Valencia (Spain) during 2014 and 2015 is analyzed in order to estimate the effects that school locations produce on traffic risk within their surroundings. The four typologies of school in this city according to the academic levels they offer (All-level, Preschool, Primary, Secondary) are distinguished and taken into consideration for the analysis. Two time windows comprising the starting time in the morning and the evening time once day school has ended are analyzed independently. Several statistical methods are used, including observed vs expected ratios, macroscopic conditional autoregressive modelling, logistic regression in the context of a case-control study design and risk modelling in relation to several school locations. The distances to each type of school and a set of environmental, traffic-related, demographic and socioeconomic covariates are employed for the analysis. The macroscopic modelling of accident counts and the modelling of risk as a function of the distance to each type of school serves to confirm that proximity to a school has an effect on the incidence of traffic accidents in particular time windows. Specifically, school types coexisting in Valencia show differential behaviour in this regard. In addition, several covariates have displayed a positive (bus stop density, complex intersections, main road length) and negative (land use entropy) association with accident counts in the time windows investigated. Finally, the definition of a case-control study design enabled us to observe some differences undetected by the macroscopic approaches that would require further research.

Data Integration for Large-Scale Models of Species Distributions

With the expansion in the quantity and types of biodiversity data being collected, there is a need to find ways to combine these different sources to provide cohesive summaries of species' potential and realized distributions in space and time. Recently, model-based data integration has emerged as a means to achieve this by combining datasets in ways that retain the strengths of each. We describe a flexible approach to data integration using point process models, which provide a convenient way to translate across ecological currencies. We highlight recent examples of large-scale ecological models based on data integration and outline the conceptual and technical challenges and opportunities that arise.

Anthropogenic modifications to fire regimes in the wider Serengeti-Mara ecosystem

Fire is a key driver in savannah systems and widely used as a land management tool. Intensifying human land uses are leading to rapid changes in the fire regimes, with consequences for ecosystem functioning and composition. We undertake a novel analysis describing spatial patterns in the fire regime of the Serengeti-Mara ecosystem, document multidecadal temporal changes and investigate the factors underlying these patterns. We used MODIS active fire and burned area products from 2001 to 2014 to identify individual fires; summarizing four characteristics for each detected fire: size, ignition date, time since last fire and radiative power. Using satellite imagery, we estimated the rate of change in the density of livestock bomas as a proxy for livestock density. We used these metrics to model drivers of variation in the four fire characteristics, as well as total number of fires and total area burned. Fires in the Serengeti-Mara show high spatial variability-with number of fires and ignition date mirroring mean annual precipitation. The short-term effect of rainfall decreases fire size and intensity but cumulative rainfall over several years leads to increased standing grass biomass and fuel loads, and, therefore, in larger and hotter fires. Our study reveals dramatic changes over time, with a reduction in total number of fires and total area burned, to the point where some areas now experience virtually no fire. We suggest that increasing livestock numbers are driving this decline, presumably by inhibiting fire spread. These temporal patterns are part of a global decline in total area burned, especially in savannahs, and we caution that ecosystem functioning may have been compromised. Land managers and policy formulators need to factor in rapid fire regime modifications to achieve management objectives and maintain the ecological function of savannah ecosystems.

The total dispersal kernel: a review and future directions

The distribution and abundance of plants across the world depends in part on their ability to move, which is commonly characterized by a dispersal kernel. For seeds, the total dispersal kernel (TDK) describes the combined influence of all primary, secondary and higher-order dispersal vectors on the overall dispersal kernel for a plant individual, population, species or community. Understanding the role of each vector within the TDK, and their combined influence on the TDK, is critically important for being able to predict plant responses to a changing biotic or abiotic environment. In addition, fully characterizing the TDK by including all vectors may affect predictions of population spread. Here, we review existing research on the TDK and discuss advances in empirical, conceptual modelling and statistical approaches that will facilitate broader application. The concept is simple, but few examples of well-characterized TDKs exist. We find that significant empirical challenges exist, as many studies do not account for all dispersal vectors (e.g. gravity, higher-order dispersal vectors), inadequately measure or estimate long-distance dispersal resulting from multiple vectors and/or neglect spatial heterogeneity and context dependence. Existing mathematical and conceptual modelling approaches and statistical methods allow fitting individual dispersal kernels and combining them to form a TDK; these will perform best if robust prior information is available. We recommend a modelling cycle to parameterize TDKs, where empirical data inform models, which in turn inform additional data collection. Finally, we recommend that the TDK concept be extended to account for not only where seeds land, but also how that location affects the likelihood of establishing and producing a reproductive adult, i.e. the total effective dispersal kernel.

Simplified integrated nested Laplace approximation

Integrated nested Laplace approximation provides accurate and efficient approximations for marginal distributions in latent Gaussian random field models. Computational feasibility of the original Rue et al. (2009) methods relies on efficient approximation of Laplace approximations for the marginal distributions of the coefficients of the latent field, conditional on the data and hyperparameters. The computational efficiency of these approximations depends on the Gaussian field having a Markov structure. This note provides equivalent efficiency without requiring the Markov property, which allows for straightforward use of latent Gaussian fields without a sparse structure, such as reduced rank multi-dimensional smoothing splines. The method avoids the approximation for conditional modes used in Rue et al. (2009), and uses a log determinant approximation based on a simple quasi-Newton update. The latter has a desirable property not shared by the most commonly used variant of the original method.

Bias in the detection of negative density dependence in plant communities

Regression dilution is a statistical inference bias that causes underestimation of the strength of dependency between two variables when the predictors are error-prone proxies (EPPs). EPPs are widely used in plant community studies focused on negative density-dependence (NDD) to quantify competitive interactions. Because of the nature of the bias, conspecific NDD is often overestimated in recruitment analyses, and in some cases, can be erroneously detected when absent. In contrast, for survival analyses, EPPs typically cause NDD to be underestimated, but underestimation is more severe for abundant species and for heterospecific effects, thereby generating spurious negative relationships between the strength of NDD and the abundances of con- and heterospecifics. This can explain why many studies observed rare species to suffer more severely from conspecific NDD, and heterospecific effects to be disproportionally smaller than conspecific effects. In general, such species-dependent bias is often related to traits associated with likely mechanisms of NDD, which creates false patterns and complicates the ecological interpretation of the analyses. Classic examples taken from literature and simulations demonstrate that this bias has been pervasive, which calls into question the emerging paradigm that intraspecific competition has been demonstrated by direct field measurements to be generally stronger than interspecific competition.

Compatibility between agendas for improving human development and wildlife conservation outside protected areas: Insights from 20 years of data

The UN Sustainable Development Goals (SDGs) include economic, social and environmental dimensions of human development and make explicit commitments to all of life on Earth. Evidence of continuing global biodiversity loss has, at the same time, led to a succession of internationally agreed conservation targets.With multiple targets (even within one policy realm, e.g. the CBD Aichi Targets for biodiversity), it is possible for different indicators to respond in the same direction, in opposite directions or to show no particular relationship. When considering the different sectors of the SDGs, there are many possible relationships among indicators that have been widely discussed, but rarely analysed in detail.Here, we present a comparative cross-national analysis exploring temporally integrated linkages between human development indicators and wildlife conservation trends.The results suggest that in lower income countries there are negative relationships between measures of human population growth and bird and mammal population abundance trends outside protected areas.The results also suggest a positive relationship between economic growth and wildlife population trends in lower income countries. We stress, however, the need for future research to further explore the relationships between economic growth and natural resource-based imports.Our results highlight a clear potential for compatibility of the conservation and development agendas and support the need for further integration among sustainable development strategies. A free Plain Language Summary can be found within the Supporting Information of this article.

Bayesian spatial modelling for quasi-experimental designs: An interrupted time series study of the opening of Municipal Waste Incinerators in relation to infant mortality and sex ratio

BACKGROUND

There is limited evidence on potential health risks from Municipal Waste Incinerators (MWIs), and previous studies on birth outcomes show inconsistent results. Here, we evaluate whether the opening of MWIs is associated with infant mortality and sex ratio in the surrounding areas, extending the Interrupted Time Series (ITS) methodological approach to account for spatial dependencies at the small area level.

METHODS

We specified a Bayesian hierarchical model to investigate the annual risks of infant mortality and sex-ratio (female relative to male) within 10 km of eight MWIs in England and Wales, during the period 1996-2012. We included comparative areas matched one-to-one of similar size and area characteristics.

RESULTS

During the study period, infant mortality rates decreased overall by 2.5% per year in England. The opening of an incinerator in the MWI area was associated with -8 deaths per 100,000 infants (95% CI -62, 40) and with a difference in sex ratio of -0.004 (95% CI -0.02, 0.01), comparing the period after opening with that before, corrected for before-after trends in the comparator areas.

CONCLUSION

Our method is suitable for the analysis of quasi-experimental time series studies in the presence of spatial structure and when there are global time trends in the outcome variable. Based on our approach, we do not find evidence of an association of MWI opening with changes in risks of infant mortality or sex ratio in comparison with control areas.

Analysis of multisite intervention studies using generalized linear mixed models

Multisite intervention studies have become increasingly common in infection control, for example, looking for a change in hospital infection rates after a regional policy change. The design of these studies can take various forms, from pre–post observational studies to randomized trials, in which sites are randomly assigned to the intervention or in which the intervention is sequentially introduced to different sites over time. Data collected under these settings are clustered by hospital and/or ward, consist of repeated measurements and, in some cases, exhibit temporal and/or seasonal patterns. Failure to account for these features in data analysis could well result in biased estimates of intervention effectiveness and impact on the generalizability of model results.

A Bayesian General Linear Modeling Approach to Cortical Surface fMRI Data Analysis

Cortical surface fMRI (cs-fMRI) has recently grown in popularity versus traditional volumetric fMRI. In addition to offering better whole-brain visualization, dimension reduction, removal of extraneous tissue types, and improved alignment of cortical areas across subjects, it is also more compatible with common assumptions of Bayesian spatial models. However, as no spatial Bayesian model has been proposed for cs-fMRI data, most analyses continue to employ the classical general linear model (GLM), a "massive univariate" approach. Here, we propose a spatial Bayesian GLM for cs-fMRI, which employs a class of sophisticated spatial processes to model latent activation fields. We make several advances compared with existing spatial Bayesian models for volumetric fMRI. First, we use integrated nested Laplacian approximations (INLA), a highly accurate and efficient Bayesian computation technique, rather than variational Bayes (VB). To identify regions of activation, we utilize an excursions set method based on the joint posterior distribution of the latent fields, rather than the marginal distribution at each location. Finally, we propose the first multi-subject spatial Bayesian modeling approach, which addresses a major gap in the existing literature. The methods are very computationally advantageous and are validated through simulation studies and two task fMRI studies from the Human Connectome Project.

Quantifying geographic regions of excess stillbirth risk in the presence of spatial and spatio-temporal heterogeneity

Motivated by population-based geocoded data for Iowa stillbirths and live births delivered during 2005-2011, we sought to identify spatio-temporal variation of stillbirth risk. Our high-quality data consisting of point locations of these delivery events allows use of a Bayesian Poisson point process approach to evaluate the spatial pattern of events. With this large epidemiologic dataset, we implemented the integrated nested Laplace approximation (INLA) to fit the conditional formulation of the point process via a Bayesian hierarchical model and empirically showed that INLA, compared to Markov chain Monte Carlo (MCMC) sampling, is an attractive approach. Furthermore, we modeled the temporal variability in stillbirth to better understand how stillbirths are geographically linked over the seven-year study period and demonstrate the similarity between the conditional formulation of the spatio-temporal model and a log Gaussian Cox process governed by discrete space-time random fields. After controlling for important features of the data, the Bayesian temporal relative risk maps identified areas of increasing and decreasing stillbirth risk over the birth period, which may warrant further public health investigation in the regions identified.

Mapping diphtheria-pertussis-tetanus vaccine coverage in Africa, 2000-2016: a spatial and temporal modelling study

BACKGROUND

Routine childhood vaccination is among the most cost-effective, successful public health interventions available. Amid substantial investments to expand vaccine delivery throughout Africa and strengthen administrative reporting systems, most countries still require robust measures of local routine vaccine coverage and changes in geographical inequalities over time.

METHODS

This analysis drew from 183 surveys done between 2000 and 2016, including data from 881 268 children in 49 African countries. We used a Bayesian geostatistical model calibrated to results from the Global Burden of Diseases, Injuries, and Risk Factors Study 2017, to produce annual estimates with high-spatial resolution (5 ×    5 km) of diphtheria-pertussis-tetanus (DPT) vaccine coverage and dropout for children aged 12-23 months in 52 African countries from 2000 to 2016.

FINDINGS

Estimated third-dose (DPT3) coverage increased in 72·3% (95% uncertainty interval [UI] 64·6-80·3) of second-level administrative units in Africa from 2000 to 2016, but substantial geographical inequalities in DPT coverage remained across and within African countries. In 2016, DPT3 coverage at the second administrative (ie, district) level varied by more than 25% in 29 of 52 countries, with only two (Morocco and Rwanda) of 52 countries meeting the Global Vaccine Action Plan target of 80% DPT3 coverage or higher in all second-level administrative units with high confidence (posterior probability ≥95%). Large areas of low DPT3 coverage (≤50%) were identified in the Sahel, Somalia, eastern Ethiopia, and in Angola. Low first-dose (DPT1) coverage (≤50%) and high relative dropout (≥30%) together drove low DPT3 coverage across the Sahel, Somalia, eastern Ethiopia, Guinea, and Angola.

INTERPRETATION

Despite substantial progress in Africa, marked national and subnational inequalities in DPT coverage persist throughout the continent. These results can help identify areas of low coverage and vaccine delivery system vulnerabilities and can ultimately support more precise targeting of resources to improve vaccine coverage and health outcomes for African children.

FUNDING

Bill & Melinda Gates Foundation.

A Bayesian spatio-temporal analysis on racial disparities in hypertensive disorders of pregnancy in Florida, 2005-2014

Disparities in hypertensive disorders of pregnancy (HDP) exist among racial and ethnic groups in the US. However, little is known about spatio-temporal variations in HDP disparities. We used a Bayesian hierarchical regression approach to investigate spatio-temporal variations in HDP disparities from 2005 to 2014. County-level variation was firstly examined, followed by census tract-level variation assessment in counties where high HDP disparities were observed. A significant disadvantage in HDP was revealed for African Americans in Florida overall (Odds Ratio: 1.27, 95% Confidence Interval: 1.25, 1.29), with significant spatial variations. The greatest HDP disparities between African Americans and non-African Americans occurred in North Central Florida counties (the Big Bend region of Florida), with consistent patterns from 2005 to 2014. Analyses at census tract-level further revealed significant neighborhood disparities within these counties. Findings from this study provide important information for public health agencies and policymakers to reduce HDP disparities at the population level.

Determinants of bed net use conditional on access in population surveys in Ghana

Background

Insecticide-treated nets (ITNs) are one of the most effective and widely available methods for preventing malaria, and there is interest in understanding the complexities of behavioural drivers of non-use among those with access. This analysis evaluated net use behaviour in Ghana by exploring how several household and environmental variables relate to use among Ghanaians with access to a net.

Methods

Survey data from the Ghana 2014 Demographic and Health Survey and the 2016 Malaria Indicator Survey were used to calculate household members’ access to space under a net as well as the proportion of net use conditional on access (NUCA). Geospatial information on cluster location was obtained, as well as average humidex, a measure of how hot it feels, for the month each cluster was surveyed. The relationship between independent variables and net use was assessed via beta-binomial regression models that controlled for spatially correlated random effects using non-Gaussian kriging.

Results

In both surveys, increasing wealth was associated with decreased net use among those with access in households when compared to the poorest category. In 2014, exposure to messages about bed net use for malaria prevention was associated with increased net use (OR 2.5, 95% CrI 1.5–4.2), as was living in a rural area in both 2014 (OR 2.5, 95% CrI 1.5–4.3) and 2016 (OR 1.6, 95% CrI 1.1–2.3). The number of nets per person was not associated with net use in either survey. Model fit was improved for both surveys by including a spatial random effect for cluster, demonstrating some spatial autocorrelation in the proportion of people using a net. Humidex, electricity in the household and IRS were not associated with NUCA.

Conclusion

Net use conditional on access is affected by household characteristics and is also spatially-dependent in Ghana. Setting (whether the household was urban or rural) plays a role, with wealthier and more urban households less likely to use nets when they are available. It will likely be necessary in the future to focus on rural settings, urban settings, and wealth status independently, both to better understand predictors of household net use in these areas and to design more targeted interventions to ensure consistent use of vector control interventions that meet specific needs of the population.

Electronic supplementary material

The online version of this article (10.1186/s12936-019-2700-7) contains supplementary material, which is available to authorized users.

Spatial and Social Distance at the Onset of the Fertility Transition: Sweden, 1880-1900

Most studies on the fertility transition have focused either on macro-level trends or on micro-level patterns with limited geographic scope. Much less attention has been given to the interplay between individual characteristics and contextual conditions, including geographic location. Here we investigate the relevance of geography and socioeconomic status for understanding fertility variation in the initial phase of the Swedish fertility transition. We conduct spatially sensitive multilevel analyses on full-count individual-level census data. Our results show that the elite constituted the vanguard group in the fertility decline and that the shift in fertility behavior occurred quickly among them in virtually all parts of Sweden. Other socioeconomic status groups experienced the decline with some delay, and their decline patterns were more clustered around early centers of the decline. Long-distance migrants initially had higher fertility than people living close to their birthplace. However, as the fertility decline unfolded, this advantage was either reduced or reversed. This supports the view that migration and fertility are linked in this process. Our results confirm that socioeconomic status differences were of considerable relevance in structuring the fertility transition. The degree to which spatial distance fostered spatial variation in the fertility decline seems to have been negatively correlated with socioeconomic status, with the pattern of decline among the elite showing the lowest degree of spatial variation.

Warming seas increase cold-stunning events for Kemp's ridley sea turtles in the northwest Atlantic

Since the 1970s, the magnitude of turtle cold-stun strandings have increased dramatically within the northwestern Atlantic. Here, we examine oceanic, atmospheric, and biological factors that may affect the increasing trend of cold-stunned Kemp's ridleys in Cape Cod Bay, Massachusetts, United States of America. Using machine learning and Bayesian inference modeling techniques, we demonstrate higher cold-stunning years occur when the Gulf of Maine has warmer sea surface temperatures in late October through early November. Surprisingly, hatchling numbers in Mexico, a proxy for population abundance, was not identified as an important factor. Further, using our Bayesian count model and forecasted sea surface temperature projections, we predict more than 2,300 Kemp's ridley turtles may cold-stun annually by 2031 as sea surface temperatures continue to increase within the Gulf of Maine. We suggest warmer sea surface temperatures may have modified the northerly distribution of Kemp's ridleys and act as an ecological bridge between the Gulf Stream and nearshore waters. While cold-stunning may currently account for a minor proportion of juvenile mortality, we recommend continuing efforts to rehabilitate cold-stunned individuals to maintain population resiliency for this critically endangered species in the face of a changing climate and continuing anthropogenic threats.

Poisson-Gamma Mixture Spatially Varying Coefficient Modeling of Small-Area Intestinal Parasites Infection

Understanding the spatially varying effects of demographic factors on the spatio-temporal variation of intestinal parasites infections is important for public health intervention and monitoring. This paper presents a hierarchical Bayesian spatially varying coefficient model to evaluate the effects demographic factors on intestinal parasites morbidities in Ghana. The modeling relied on morbidity data collected by the District Health Information Management Systems. We developed Poisson and Poisson-gamma spatially varying coefficient models. We used the demographic factors, unsafe drinking water, unsafe toilet, and unsafe liquid waste disposal as model covariates. The models were fitted using the integrated nested Laplace approximations (INLA). The overall risk of intestinal parasites infection was estimated to be 10.9 per 100 people with a wide spatial variation in the district-specific posterior risk estimates. Substantial spatial variation of increasing multiplicative effects of unsafe drinking water, unsafe toilet, and unsafe liquid waste disposal occurs on the variation of intestinal parasites risk. The structured residual spatial variation widely dominates the unstructured component, suggesting that the unaccounted-for risk factors are spatially continuous in nature. The study concludes that both the spatial distribution of the posterior risk and the associated exceedance probability maps are essential for monitoring and control of intestinal parasites.

Understanding heterogeneities in mosquito-bite exposure and infection distributions for the elimination of lymphatic filariasis

It is well known that individuals in the same community can be exposed to a highly variable number of mosquito bites. This heterogeneity in bite exposure has consequences for the control of vector-borne diseases because a few people may be contributing significantly to transmission. However, very few studies measure sources of heterogeneity in a way which is relevant to decision-making. We investigate the relationship between two classic measures of heterogeneity, spatial and individual, within the context of lymphatic filariasis, a parasitic mosquito-borne disease. Using infection and mosquito-bite data for five villages in Papua New Guinea, we measure biting characteristics to model what impact bed-nets have had on control of the disease. We combine this analysis with geospatial modelling to understand the spatial relationship between disease indicators and nightly mosquito bites. We found a weak association between biting and infection heterogeneity within villages. The introduction of bed-nets increased biting heterogeneity, but the reduction in mean biting more than compensated for this, by reducing prevalence closer to elimination thresholds. Nightly biting was explained by a spatial heterogeneity model, while parasite load was better explained by an individual heterogeneity model. Spatial and individual heterogeneity are qualitatively different with profoundly different policy implications.

Assessing the sensitivity of the polio environmental surveillance system

BACKGROUND

The polio environmental surveillance (ES) system has been an incredible tool for advancing polio eradication efforts because of its ability to highlight the spatial and temporal extent of poliovirus circulation. While ES often outperforms, or is more sensitive than AFP surveillance, the sensitivity of the ES system has not been well characterized. Fundamental uncertainty of ES site sensitivity makes it difficult to interpret results from ES, particularly negative results.

METHODS AND FINDINGS

To study ES sensitivity, we used data from Afghanistan and Pakistan to examine the probability that each ES site detected the Sabin 1, 2, or 3 components of the oral polio vaccine (OPV) as a function of virus prevalence within the same district (estimated from AFP data). Accounting for virus prevalence is essential for estimating site sensitivity because Sabin detection rates should vary with prevalence-high immediately after supplemental immunization activities (SIAs), but low in subsequent months. We found that most ES sites in Pakistan and Afghanistan are highly sensitive for detecting poliovirus relative to AFP surveillance in the same districts. For example, even when Sabin poliovirus is at low prevalence of ~0.5-3% in AFP surveillance, most ES sites have ~34-50% probability of detecting Sabin. However, there was considerable variation in ES site sensitivity and we flagged several sites for re-evaluation based on low sensitivity rankings and low wild polio virus detection rates. In these areas, adding new sites or modifying collection methods in current sites could improve sensitivity of environmental surveillance.

CONCLUSIONS

Relating ES detections to virus prevalence significantly improved our ability to evaluate site sensitivity compared to evaluations based solely on ES detection rates. To extend our approach to new sites and regions, we provide a preliminary framework for relating ES and AFP detection rates, and descriptions of how detection rates might relate to SIAs and natural seasonality.

Decline of coastal apex shark populations over the past half century

Overexploitation of large apex marine predators is widespread in the world's oceans, yet the timing and extent of declines are poorly understood. Here we reconstruct a unique fisheries-independent dataset from a shark control programme spanning 1760 km of the Australian coastline over the past 55 years. We report substantial declines (74-92%) of catch per unit effort of hammerhead (Sphyrnidae), whaler (Carcharhinidae), tiger shark (Galeocerdo cuvier) and white sharks (Carcharodon carcharias). Following onset of the program in the 1960s, catch rates in new installations in subsequent decades occurred at a substantially lower rate, indicating regional depletion of shark populations over the past half a century. Concurrent declines in body size and the probability of encountering mature individuals suggests that apex shark populations are more vulnerable to exploitation than previously thought. Ongoing declines and lack of recovery of vulnerable and protected shark species are a cause for concern.