A scalable approach for short-term disease forecasting in high spatial resolution areal data.

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.

Robust modeling of additive and nonadditive variation with intuitive inclusion of expert knowledge.

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.

Estimating under-five mortality in space and time in a developing world context.

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.

Bayesian bivariate meta-analysis of diagnostic test studies with interpretable priors.

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.

Projecting the future burden of cancer: Bayesian age-period-cohort analysis with integrated nested Laplace approximations.

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.

Spatial gender-age-period-cohort analysis of pancreatic cancer mortality in Spain (1990-2013).

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.

An intuitive Bayesian spatial model for disease mapping that accounts for scaling.

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.

Stomach cancer incidence in Southern Portugal 1998-2006: a spatio-temporal analysis.

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.

BayMeth: improved DNA methylation quantification for affinity capture sequencing data using a flexible Bayesian approach.

Affinity capture of DNA methylation combined with high-throughput sequencing strikes a good balance between the high cost of whole genome bisulfite sequencing and the low coverage of methylation arrays. We present BayMeth, an empirical Bayes approach that uses a fully methylated control sample to transform observed read counts into regional methylation levels. In our model, inefficient capture can readily be distinguished from low methylation levels. BayMeth improves on existing methods, allows explicit modeling of copy number variation, and offers computationally efficient analytical mean and variance estimators. BayMeth is available in the Repitools Bioconductor package.

A conditional approach for inference in multivariate age-period-cohort models.

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.

The analysis of heterogeneous time trends in multivariate age-period-cohort models.

Age-period-cohort (APC) models are frequently used to analyze mortality or morbidity rates stratified by age group and period. For the case in which rates are given in different strata, multivariate APC models have been considered only recently. Such models share a set of parameters, for example, the age effects, while the other parameters may vary across strata. We show that differences of strata-specific effects are identifiable. We then propose a Bayesian approach based on smoothing priors to estimate multivariate APC models. This provides an alternative to maximum likelihood (ML) estimates of relative risk in the case of equal intervals and gives useful results even in the case of unequal intervals, where ML estimates have severe artifacts. This is illustrated with data on female mortality in Denmark and Norway and data on chronic obstructive pulmonary disease mortality of males in England and Wales, stratified by 3 different areas: Greater London, conurbations excluding Greater London, and nonconurbation areas.

A whole genome Bayesian scan for adaptive genetic divergence in West African cattle.

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.

Bayesian variable selection for detecting adaptive genomic differences among populations.

We extend an F(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(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.