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Short‐term disease forecasting at specific discrete spatial resolutions has become a high‐impact decision‐support tool in health planning. However, when the number of areas is very large obtaining predictions can be computationally intensive or even unfeasible using standard spatiotemporal models. The purpose of this paper is to provide a method for short‐term predictions in high‐dimensional areal data based on a newly proposed "divide‐and‐conquer" approach. We assess the predictive performance of this method and other classical spatiotemporal models in a validation study that uses cancer mortality data for the 7907 municipalities of continental Spain. The new proposal outperforms traditional models in terms of mean absolute error, root mean square error, and interval score when forecasting cancer mortality 1, 2, and 3 years ahead. Models are implemented in a fully Bayesian framework using the well‐known integrated nested Laplace estimation technique. [ABSTRACT FROM AUTHOR]

Cancer incidence numbers are routinely recorded by national or regional population-based cancer registries (PBCRs). However, in most southern European countries, the local PBCRs cover only a fraction of the country. Therefore, national cancer incidence can be only obtained through estimation methods. In this paper, we predict incidence rates in areas without cancer registry using multivariate spatial models modelling jointly cancer incidence and mortality. To evaluate the proposal, we use cancer incidence and mortality data from all the German states. We also conduct a simulation study by mimicking the real case of Spain considering different scenarios depending on the similarity of spatial patterns between incidence and mortality, the levels of lethality, and varying the amount of incidence data available. The new proposal provides good interval estimates in regions without PBCRs and reduces the relative error in estimating national incidence compared to one of the most widely used methodologies. [ABSTRACT FROM AUTHOR]

We extend an [F.sub.st]-based Bayesian hierarchical model, implemented via Markov chain Monte Carlo, for the detection of loci that might be subject to positive selection. This model divides the [F.sub.st]-influencing factors into locus-specific effects, population-specific effects, and effects that are specific for the locus in combination with the population. We introduce a Bayesian auxiliary variable for each locus effect to automatically select nonneutral locus effects. As a by-product, the efficiency of the original approach is improved by using a reparameterization of the model. The statistical power of the extended algorithm is assessed with simulated data sets from a Wright-Fisher model with migration. We find that the inclusion of model selection suggests a clear improvement in discrimination as measured by the area under the receiver operating characteristic (ROC) curve. Additionally, we illustrate and discuss the quality of the newly developed method on the basis of an allozyme data set of the fruit fly Drosophila melanogaster and a sequence data set of the wild tomato Solanum chilense. For data sets with small sample sizes, high mutation rates, and/or long sequences, however, methods based on nucleotide statistics should be preferred.

The need for rigorous and timely health and demographic summaries has provided the impetus for an explosion in geographic studies in low- and middle-income countries. Many of these studies present fine-scale pixel-level maps in an attempt to answer the needs of the current era of precision public health. However, even though household surveys with a two-stage cluster design stratified by region and urbanicity are a major source of data, cavalier approaches are taken to acknowledging the survey design. We investigate the extent to which accounting for the sample design affects the predictive performance at the aggregate level of interest for health policy decisions. We consider various commonly used models and introduce a new Bayesian cluster-level model with a discrete spatial smoothing prior. The investigation is performed through a simulation study in which realistic sampling frames are created for Kenya, based on the population and demographic information, with a survey design that mimics a Demographic Health Survey (DHS). We find that including stratification and cluster-level random effects can improve predictive performance. Spatially smoothed direct (weighted) estimates and area-level models accounting for stratification were robust to the underlying population and survey design. Continuous spatial models showed some promise in the presence of fine-scale variation; however, these models require the most "hand holding." Subsequently, we examine how the models perform on real data, estimating the prevalence of secondary education for women aged 20–29 and neonatal mortality rates, using data from the 2014 Kenya DHS. [ABSTRACT FROM AUTHOR]

Abstract Background The recent settlement of cattle in West Africa after several waves of migration from remote centres of domestication has imposed dramatic changes in their environmental conditions, in particular through exposure to new pathogens. West African cattle populations thus represent an appealing model to unravel the genome response to adaptation to tropical conditions. The purpose of this study was to identify footprints of adaptive selection at the whole genome level in a newly collected data set comprising 36,320 SNPs genotyped in 9 West African cattle populations. Results After a detailed analysis of population structure, we performed a scan for SNP differentiation via a previously proposed Bayesian procedure including extensions to improve the detection of loci under selection. Based on these results we identified 53 genomic regions and 42 strong candidate genes. Their physiological functions were mainly related to immune response (MHC region which was found under strong balancing selection, CD79A, CXCR4, DLK1, RFX3, SEMA4A, TICAM1 and TRIM21), nervous system (NEUROD6, OLFM2, MAGI1, SEMA4A and HTR4) and skin and hair properties (EDNRB, TRSP1 and KRTAP8-1). Conclusion The main possible underlying selective pressures may be related to climatic conditions but also to the host response to pathogens such as Trypanosoma(sp). Overall, these results might open the way towards the identification of important variants involved in adaptation to tropical conditions and in particular to resistance to tropical infectious diseases.

Variance parameters in additive models are typically assigned independent priors that do not account for model structure. We present a new framework for prior selection based on a hierarchical decomposition of the total variance along a tree structure to the individual model components. For each split in the tree, an analyst may be ignorant or have a sound intuition on how to attribute variance to the branches. In the former case a Dirichlet prior is appropriate to use, while in the latter case a penalised complexity (PC) prior provides robust shrinkage. A bottom-up combination of the conditional priors results in a proper joint prior. We suggest default values for the hyperparameters and offer intuitive statements for eliciting the hyperparameters based on expert knowledge. The prior framework is applicable for R packages for Bayesian inference such as INLA and RStan. Three simulation studies show that, in terms of the application-specific measures of interest, PC priors improve inference over Dirichlet priors when used to penalise different levels of complexity in splits. However, when expressing ignorance in a split, Dirichlet priors perform equally well and are preferred for their simplicity. We find that assigning current state-of-the-art default priors for each variance parameter individually is less transparent and does not perform better than using the proposed joint priors. We demonstrate practical use of the new framework by analysing spatial heterogeneity in neonatal mortality in Kenya in 2010-2014 based on complex survey data. [ABSTRACT FROM AUTHOR]

Accurate estimates of the under-five mortality rate in a developing world context are a key barometer of the health of a nation. This paper describes a new model to analyze survey data on mortality in this context. We are interested in both spatial and temporal description, that is wishing to estimate under-five mortality rate across regions and years and to investigate the association between the under-five mortality rate and spatially varying covariate surfaces. We illustrate the methodology by producing yearly estimates for subnational areas in Kenya over the period 1980-2014 using data from the Demographic and Health Surveys, which use stratified cluster sampling. We use a binomial likelihood with fixed effects for the urban/rural strata and random effects for the clustering to account for the complex survey design. Smoothing is carried out using Bayesian hierarchical models with continuous spatial and temporally discrete components. A key component of the model is an offset to adjust for bias due to the effects of HIV epidemics. Substantively, there has been a sharp decline in Kenya in the under-five mortality rate in the period 1980-2014, but large variability in estimated subnational rates remains. A priority for future research is understanding this variability. In exploratory work, we examine whether a variety of spatial covariate surfaces can explain the variability in under-five mortality rate. Temperature, precipitation, a measure of malaria infection prevalence, and a measure of nearness to cities were candidates for inclusion in the covariate model, but the interplay between space, time, and covariates is complex. [ABSTRACT FROM AUTHOR]

In a bivariate meta-analysis, the number of diagnostic studies involved is often very low so that frequentist methods may result in problems. Using Bayesian inference is particularly attractive as informative priors that add a small amount of information can stabilise the analysis without overwhelming the data. However, Bayesian analysis is often computationally demanding and the selection of the prior for the covariance matrix of the bivariate structure is crucial with little data. The integrated nested Laplace approximations method provides an efficient solution to the computational issues by avoiding any sampling, but the important question of priors remain. We explore the penalised complexity (PC) prior framework for specifying informative priors for the variance parameters and the correlation parameter. PC priors facilitate model interpretation and hyperparameter specification as expert knowledge can be incorporated intuitively. We conduct a simulation study to compare the properties and behaviour of differently defined PC priors to currently used priors in the field. The simulation study shows that the PC prior seems beneficial for the variance parameters. The use of PC priors for the correlation parameter results in more precise estimates when specified in a sensible neighbourhood around the truth. To investigate the usage of PC priors in practice, we reanalyse a meta-analysis using the telomerase marker for the diagnosis of bladder cancer and compare the results with those obtained by other commonly used modelling approaches. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The projection of age-stratified cancer incidence and mortality rates is of great interest due to demographic changes, but also therapeutical and diagnostic developments. Bayesian age-period-cohort (APC) models are well suited for the analysis of such data, but are not yet used in routine practice of epidemiologists. Reasons may include that Bayesian APC models have been criticized to produce too wide prediction intervals. Furthermore, the fitting of Bayesian APC models is usually done using Markov chain Monte Carlo (MCMC), which introduces complex convergence concerns and may be subject to additional technical problems. In this paper we address both concerns, developing efficient MCMC-free software for routine use in epidemiological applications. We apply Bayesian APC models to annual lung cancer data for females in five different countries, previously analyzed in the literature. To assess the predictive quality, we omit the observations from the last 10 years and compare the projections with the actual observed data based on the absolute error and the continuous ranked probability score. Further, we assess calibration of the one-step-ahead predictive distributions. In our application, the probabilistic forecasts obtained by the Bayesian APC model are well calibrated and not too wide. A comparison to projections obtained by a generalized Lee-Carter model is also given. The methodology is implemented in the user-friendly R-package BAPC using integrated nested Laplace approximations. [ABSTRACT FROM AUTHOR]

Recently, the interest in studying pancreatic cancer mortality has increased due to its high lethality. In this work a detailed analysis of pancreatic cancer mortality in Spanish provinces was performed using recent data. A set of multivariate spatial gender-age-period-cohort models was considered to look for potential candidates to analyze pancreatic cancer mortality rates. The selected model combines features of APC (age-period-cohort) models with disease mapping approaches. To ensure model identifiability sum-to-zero constraints were applied. A fully Bayesian approach based on integrated nested Laplace approximations (INLA) was considered for model fitting and inference. Sensitivity analyses were also conducted. In general, estimated average rates by age, cohort, and period are higher in males than in females. The higher differences according to age between males and females correspond to the age groups [65, 70), [70, 75), and [75, 80). Regarding the cohort, the greatest difference between men and women is observed for those born between the forties and the sixties. From there on, the younger the birth cohort is, the smaller the difference becomes. Some cohort differences are also identified by regions and age-groups. The spatial pattern indicates a North-South gradient of pancreatic cancer mortality in Spain, the provinces in the North being the ones with the highest effects on mortality during the studied period. Finally, the space-time evolution shows that the space pattern has changed little over time. [ABSTRACT FROM AUTHOR]

In recent years, disease mapping studies have become a routine application within geographical epidemiology and are typically analysed within a Bayesian hierarchical model formulation. A variety of model formulations for the latent level have been proposed but all come with inherent issues. In the classical BYM (Besag, York and Mollié) model, the spatially structured component cannot be seen independently from the unstructured component. This makes prior definitions for the hyperparameters of the two random effects challenging. There are alternative model formulations that address this confounding; however, the issue on how to choose interpretable hyperpriors is still unsolved. Here, we discuss a recently proposed parameterisation of the BYM model that leads to improved parameter control as the hyperparameters can be seen independently from each other. Furthermore, the need for a scaled spatial component is addressed, which facilitates assignment of interpretable hyperpriors and make these transferable between spatial applications with different graph structures. The hyperparameters themselves are used to define flexible extensions of simple base models. Consequently, penalised complexity priors for these parameters can be derived based on the information-theoretic distance from the flexible model to the base model, giving priors with clear interpretation. We provide implementation details for the new model formulation which preserve sparsity properties, and we investigate systematically the model performance and compare it to existing parameterisations. Through a simulation study, we show that the new model performs well, both showing good learning abilities and good shrinkage behaviour. In terms of model choice criteria, the proposed model performs at least equally well as existing parameterisations, but only the new formulation offers parameters that are interpretable and hyperpriors that have a clear meaning. [ABSTRACT FROM AUTHOR]

Stomach cancer belongs to the most common malignant tumors in Portugal. Main causal factors are age, dietary habits, smoking, and Helicobacter pylori infections. As these factors do not only operate on different time dimensions, such as age, period, or birth cohort, but may also vary along space, it is of utmost interest to model temporal and spatial trends jointly. In this paper, we analyze incidence of stomach cancer in Southern Portugal between 1998 and 2006 for females and males jointly using a spatial multivariate age-period-cohort model. Thus, we avoid age aggregation and allow the exploration of heterogeneous time trends between males and females across age, period, birth cohort, and space. Model estimation is performed within a Bayesian setting assuming (gender specific) smoothing priors. Our results show that the posterior expected rate of stomach cancer is decreasing for all counties in Southern Portugal and that males around 70 have a two times higher risk of getting stomach cancer compared with their female counterparts. We further found that, except for some few counties, the spatial influence is almost constant over time and negligible in the southern counties of Southern Portugal. [ABSTRACT FROM AUTHOR]

Age-period-cohort (APC) models are used to analyse data from disease registers given by age and time. When data are stratified by one further variable, for example geographical location, multivariate APC (MAPC) models can be applied to identify and estimate heterogeneous time trends across the different strata. In such models, outcomes share a set of parameters, typically the age effects, while the remaining parameters may differ across strata. In this article, we propose a conditional approach for inference to directly model relative time trends. We show that in certain situations the conditional approach can handle unmeasured confounding so that relative risks might be estimated with higher precision. Furthermore, we propose an extension for data with more stratification levels. Maximum likelihood estimation is performed using software for multinomial logistic regression. The usage of smoothing splines is suggested to stabilise estimates of relative time trends, if necessary. We apply the methodology to chronic obstructive pulmonary disease mortality data in England & Wales, stratified by three different areas and gender. [ABSTRACT FROM PUBLISHER]

Background: The recent settlement of cattle in West Africa after several waves of migration from remote centres of domestication has imposed dramatic changes in their environmental conditions, in particular through exposure to new pathogens. West African cattle populations thus represent an appealing model to unravel the genome response to adaptation to tropical conditions. The purpose of this study was to identify footprints of adaptive selection at the whole genome level in a newly collected data set comprising 36,320 SNPs genotyped in 9 West African cattle populations. Results: After a detailed analysis of population structure, we performed a scan for SNP differentiation via a previously proposed Bayesian procedure including extensions to improve the detection of loci under selection. Based on these results we identified 53 genomic regions and 42 strong candidate genes. Their physiological functions were mainly related to immune response (MHC region which was found under strong balancing selection, CD79A, CXCR4, DLK1, RFX3, SEMA4A, TICAM1 and TRIM21), nervous system (NEUROD6, OLFM2, MAGI1, SEMA4A and HTR4) and skin and hair properties (EDNRB, TRSP1 and KRTAP8-1). Conclusion: The main possible underlying selective pressures may be related to climatic conditions but also to the host response to pathogens such as Trypanosoma(sp). Overall, these results might open the way towards the identification of important variants involved in adaptation to tropical conditions and in particular to resistance to tropical infectious diseases. [ABSTRACT FROM AUTHOR]

Coming up with Bayesian models for spatial data is easy, but performing inference with them can be challenging. Writing fast inference code for a complex spatial model with realistically‐sized datasets from scratch is time‐consuming, and if changes are made to the model, there is little guarantee that the code performs well. The key advantages of R‐INLA are the ease with which complex models can be created and modified, without the need to write complex code, and the speed at which inference can be done even for spatial problems with hundreds of thousands of observations. R‐INLA handles latent Gaussian models, where fixed effects, structured and unstructured Gaussian random effects are combined linearly in a linear predictor, and the elements of the linear predictor are observed through one or more likelihoods. The structured random effects can be both standard areal model such as the Besag and the BYM models, and geostatistical models from a subset of the Matérn Gaussian random fields. In this review, we discuss the large success of spatial modeling with R‐INLA and the types of spatial models that can be fitted, we give an overview of recent developments for areal models, and we give an overview of the stochastic partial differential equation (SPDE) approach and some of the ways it can be extended beyond the assumptions of isotropy and separability. In particular, we describe how slight changes to the SPDE approach leads to straight‐forward approaches for nonstationary spatial models and nonseparable space–time models. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and TheoryStatistical Models > Bayesian ModelsData: Types and Structure > Massive Data In spatial statistics, an important problem is how to represent spatial models in a way that is computationally efficient, accurate, and convenient to use. Models in R‐INLA focus on sparse precision (inverse covariance) matrices to compute inference quickly. Hence, our implementations of spatial models focus on how to represent the spatial field in such a way that the precision matrix for the "representation" is very sparse. This graphic shows a representation of a Norwegian fjord with a mesh, from which basis functions are built in the finite element method. We use sums of these basis functions to represent the spatial field. This representation has many advantages, but requires some mathematical effort to understand and to set up. [ABSTRACT FROM AUTHOR]

Fine-scale covariate rasters are routinely used in geostatistical models for mapping demographic and health indicators based on household surveys from the Demographic and Health Surveys (DHS) program. However, the geostatistical analyses ignore the fact that GPS coordinates in DHS surveys are jittered for privacy purposes. We demonstrate the need to account for this jittering, and we propose a computationally efficient approach that can be routinely applied. We use the new method to analyse the prevalence of completion of secondary education for 20-49 year old women in Nigeria in 2018 based on the 2018 DHS survey. The analysis demonstrates substantial changes in the estimates of spatial range and fixed effects compared to when we ignore jittering. Through a simulation study that mimics the dataset, we demonstrate that accounting for jittering reduces attenuation in the estimated coefficients for covariates and improves predictions. The results also show that the common approach of averaging covariate values in windows around the observed locations does not lead to the same improvements as accounting for jittering. [ABSTRACT FROM AUTHOR]

We propose a novel Bayesian approach that robustifies genomic modeling by leveraging expert knowledge (EK) through prior distributions. The central component is the hierarchical decomposition of phenotypic variation into additive and nonadditive genetic variation, which leads to an intuitive model parameterization that can be visualized as a tree. The edges of the tree represent ratios of variances, for example broad-sense heritability, which are quantities for which EK is natural to exist. Penalized complexity priors are defined for all edges of the tree in a bottom-up procedure that respects the model structure and incorporates EK through all levels. We investigate models with different sources of variation and compare the performance of different priors implementing varying amounts of EK in the context of plant breeding. A simulation study shows that the proposed priors implementing EK improve the robustness of genomic modeling and the selection of the genetically best individuals in a breeding program. We observe this improvement in both variety selection on genetic values and parent selection on additive values; the variety selection benefited the most. In a real case study, EK increases phenotype prediction accuracy for cases in which the standard maximum likelihood approach did not find optimal estimates for the variance components. Finally, we discuss the importance of EK priors for genomic modeling and breeding, and point to future research areas of easy-to-use and parsimonious priors in genomic modeling. [ABSTRACT FROM AUTHOR]