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The under-5 mortality rate (U5MR), a critical health indicator, is typically estimated from household surveys in lower and middle income countries. Spatio-temporal disaggregation of household survey data can lead to highly variable estimates of U5MR, necessitating the usage of smoothing models which borrow information across space and time. The assumptions of common smoothing models may be unrealistic when certain time periods or regions are expected to have shocks in mortality relative to their neighbors, which can lead to oversmoothing of U5MR estimates. In this paper, we develop a spatial and temporal smoothing approach based on Gaussian Markov random field models which incorporate knowledge of these expected shocks in mortality. We demonstrate the potential for these models to improve upon alternatives not incorporating knowledge of expected shocks in a simulation study. We apply these models to estimate U5MR in Rwanda at the national level from 1985 to 2019, a time period which includes the Rwandan civil war and genocide., (Published by Oxford University Press 2024.)

In countries where population census data are limited, generating accurate subnational estimates of health and demographic indicators is challenging. Existing model-based geostatistical methods leverage covariate information and spatial smoothing to reduce the variability of estimates but often ignore the survey design, while traditional small area estimation approaches may not incorporate both unit-level covariate information and spatial smoothing in a design consistent way. We propose a smoothed model-assisted estimator that accounts for survey design and leverages both unit-level covariates and spatial smoothing. Under certain regularity assumptions, this estimator is both design consistent and model consistent. We compare it with existing design-based and model-based estimators using real and simulated data.

Small area population counts are necessary for many epidemiological studies, yet their quality and accuracy are often not assessed. In the United States, small area population counts are published by the United States Census Bureau (USCB) in the form of the decennial census counts, intercensal population projections (PEP), and American Community Survey (ACS) estimates. Although there are significant relationships between these three data sources, there are important contrasts in data collection, data availability, and processing methodologies such that each set of reported population counts may be subject to different sources and magnitudes of error. Additionally, these data sources do not report identical small area population counts due to post-survey adjustments specific to each data source. Consequently, in public health studies, small area disease/mortality rates may differ depending on which data source is used for denominator data. To accurately estimate annual small area population counts and their associated uncertainties, we present a Bayesian population (BPop) model, which fuses information from all three USCB sources, accounting for data source specific methodologies and associated errors. We produce comprehensive small area race-stratified estimates of the true population, and associated uncertainties, given the observed trends in all three USCB population estimates. The main features of our framework are: (1) a single model integrating multiple data sources, (2) accounting for data source specific data generating mechanisms and specifically accounting for data source specific errors, and (3) prediction of population counts for years without USCB reported data. We focus our study on the Black and White only populations for 159 counties of Georgia and produce estimates for years 2006-2023. We compare BPop population estimates to decennial census counts, PEP annual counts, and ACS multi-year estimates. Additionally, we illustrate and explain the different types of data source specific errors. Lastly, we compare model performance using simulations and validation exercises. Our Bayesian population model can be extended to other applications at smaller spatial granularity and for demographic subpopulations defined further by race, age, and sex, and/or for other geographical regions.

We organize the discussants' major comments into the following categories: sensitivity analyses, zero counts, model selection, the marginal no-highest-order interaction (NHOI) assumption, and the usefulness of our proposed framework., (© The Author(s) 2024. Published by Oxford University Press on behalf of The International Biometric Society.)

The problem of estimating the size of a population based on a subset of individuals observed across multiple data sources is often referred to as capture-recapture or multiple-systems estimation. This is fundamentally a missing data problem, where the number of unobserved individuals represents the missing data. As with any missing data problem, multiple-systems estimation requires users to make an untestable identifying assumption in order to estimate the population size from the observed data. If an appropriate identifying assumption cannot be found for a data set, no estimate of the population size should be produced based on that data set, as models with different identifying assumptions can produce arbitrarily different population size estimates-even with identical observed data fits. Approaches to multiple-systems estimation often do not explicitly specify identifying assumptions. This makes it difficult to decouple the specification of the model for the observed data from the identifying assumption and to provide justification for the identifying assumption. We present a re-framing of the multiple-systems estimation problem that leads to an approach that decouples the specification of the observed-data model from the identifying assumption, and discuss how common models fit into this framing. This approach takes advantage of existing software and facilitates various sensitivity analyses. We demonstrate our approach in a case study estimating the number of civilian casualties in the Kosovo war., (© The Author(s) 2024. Published by Oxford University Press on behalf of The International Biometric Society.)

Branching process inspired models are widely used to estimate the effective reproduction number-a useful summary statistic describing an infectious disease outbreak-using counts of new cases. Case data is a real-time indicator of changes in the reproduction number, but is challenging to work with because cases fluctuate due to factors unrelated to the number of new infections. We develop a new model that incorporates the number of diagnostic tests as a surveillance model covariate. Using simulated data and data from the SARS-CoV-2 pandemic in California, we demonstrate that incorporating tests leads to improved performance over the state of the art., Competing Interests: Conflict of interest None declared., (© The Royal Statistical Society 2023. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Monitoring subnational healthcare quality is important for identifying and addressing geographic inequities. Yet, health facility surveys are rarely powered to support the generation of estimates at more local levels. With this study, we propose an analytical approach for estimating both temporal and subnational patterns of healthcare quality indicators from health facility survey data. This method uses random effects to account for differences between survey instruments; space-time processes to leverage correlations in space and time; and covariates to incorporate auxiliary information. We applied this method for three countries in which at least four health facility surveys had been conducted since 1999 - Kenya, Senegal, and Tanzania - and estimated measures of sick-child care quality per WHO Service Availability and Readiness Assessment (SARA) guidelines at programmatic subnational level, between 1999 and 2020. Model performance metrics indicated good out-of-sample predictive validity, illustrating the potential utility of geospatial statistical models for health facility data. This method offers a way to jointly estimate indicators of healthcare quality over space and time, which could then provide insights to decision-makers and health service program managers., (© 2023. The Author(s).)

This article is part of the Research Topic 'Health Systems Recovery in the Context of COVID-19 and Protracted Conflict'., Introduction: After the World Health Organization declared COVID-19 a pandemic, more than 184 million cases and 4 million deaths had been recorded worldwide by July 2021. These are likely to be underestimates and do not distinguish between direct and indirect deaths resulting from disruptions in health care services. The purpose of our research was to assess the early impact of COVID-19 in 2020 and early 2021 on maternal and child healthcare service delivery at the district level in Mozambique using routine health information system data, and estimate associated excess maternal and child deaths., Methods: Using data from Mozambique's routine health information system (SISMA, Sistema de Informação em Saúde para Monitoria e Avaliação), we conducted a time-series analysis to assess changes in nine selected indicators representing the continuum of maternal and child health care service provision in 159 districts in Mozambique. The dataset was extracted as counts of services provided from January 2017 to March 2021. Descriptive statistics were used for district comparisons, and district-specific time-series plots were produced. We used absolute differences or ratios for comparisons between observed data and modeled predictions as a measure of the magnitude of loss in service provision. Mortality estimates were performed using the Lives Saved Tool (LiST)., Results: All maternal and child health care service indicators that we assessed demonstrated service delivery disruptions (below 10% of the expected counts), with the number of new users of family planing and malaria treatment with Coartem (number of children under five treated) experiencing the largest disruptions. Immediate losses were observed in April 2020 for all indicators, with the exception of treatment of malaria with Coartem. The number of excess deaths estimated in 2020 due to loss of health service delivery were 11,337 (12.8%) children under five, 5,705 (11.3%) neonates, and 387 (7.6%) mothers., Conclusion: Findings from our study support existing research showing the negative impact of COVID-19 on maternal and child health services utilization in sub-Saharan Africa. This study offers subnational and granular estimates of service loss that can be useful for health system recovery planning. To our knowledge, it is the first study on the early impacts of COVID-19 on maternal and child health care service utilization conducted in an African Portuguese-speaking country., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Augusto, Roberton, Fernandes, Chicumbe, Manhiça, Tembe, Wagenaar, Anselmi, Wakefield and Sherr.)

The World Health Organization has a mandate to compile and disseminate statistics on mortality, and we have been tracking the progression of the COVID-19 pandemic since the beginning of 2020 1 . Reported statistics on COVID-19 mortality are problematic for many countries owing to variations in testing access, differential diagnostic capacity and inconsistent certification of COVID-19 as cause of death. Beyond what is directly attributable to it, the pandemic has caused extensive collateral damage that has led to losses of lives and livelihoods. Here we report a comprehensive and consistent measurement of the impact of the COVID-19 pandemic by estimating excess deaths, by month, for 2020 and 2021. We predict the pandemic period all-cause deaths in locations lacking complete reported data using an overdispersed Poisson count framework that applies Bayesian inference techniques to quantify uncertainty. We estimate 14.83 million excess deaths globally, 2.74 times more deaths than the 5.42 million reported as due to COVID-19 for the period. There are wide variations in the excess death estimates across the six World Health Organization regions. We describe the data and methods used to generate these estimates and highlight the need for better reporting where gaps persist. We discuss various summary measures, and the hazards of ranking countries' epidemic responses., (© 2022. The Author(s).)

Spatial aggregation with respect to a population distribution involves estimating aggregate population quantities based on observations from individuals. In this context, a geostatistical workflow must account for three major sources of aggregation error : aggregation weights, fine scale variation, and finite population variation. However, these sources of aggregation error are commonly ignored, and the population instead treated as a fixed population density surface. We improve common practice by introducing a sampling frame model allowing aggregation models to account for aggregation error simply and transparently. This preserves aggregate point estimates while increasing their uncertainties. We compare the proposed and the traditional approach using two simulation studies mimicking neonatal mortality rate (NMR) data from the 2014 Kenya Demographic and Health Survey. In the traditional approach, undercoverage/overcoverage of interval estimates depends arbitrarily on the aggregation grid resolution, while the new approach is resolution robust. Differences between the aggregation approaches increase as an area's population decreases, and are particularly large at the second administrative level and finer, but also at the first administrative level for some population quantities. These findings are consistent with those of an application to the true NMR data. We demonstrate in a sensitivity analysis that burden estimates and their uncertainties are not robust to changes in population density and census information, while prevalence estimates and uncertainties seem stable., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Stochastic epidemic models (SEMs) fit to incidence data are critical to elucidating outbreak dynamics, shaping response strategies, and preparing for future epidemics. SEMs typically represent counts of individuals in discrete infection states using Markov jump processes (MJPs), but are computationally challenging as imperfect surveillance, lack of subject-level information, and temporal coarseness of the data obscure the true epidemic. Analytic integration over the latent epidemic process is impossible, and integration via Markov chain Monte Carlo (MCMC) is cumbersome due to the dimensionality and discreteness of the latent state space. Simulation-based computational approaches can address the intractability of the MJP likelihood, but are numerically fragile and prohibitively expensive for complex models. A linear noise approximation (LNA) that approximates the MJP transition density with a Gaussian density has been explored for analyzing prevalence data in large-population settings, but requires modification for analyzing incidence counts without assuming that the data are normally distributed. We demonstrate how to reparameterize SEMs to appropriately analyze incidence data, and fold the LNA into a data augmentation MCMC framework that outperforms deterministic methods, statistically, and simulation-based methods, computationally. Our framework is computationally robust when the model dynamics are complex and applies to a broad class of SEMs. We evaluate our method in simulations that reflect Ebola, influenza, and SARS-CoV-2 dynamics, and apply our method to national surveillance counts from the 2013-2015 West Africa Ebola outbreak., (© 2021 The International Biometric Society.)

In trials of oral HIV pre-exposure prophylaxis (PrEP), multiple approaches have been used to measure adherence, including self-report, pill counts, electronic dose monitoring devices, and biological measures such as drug levels in plasma, peripheral blood mononuclear cells, hair, and/or dried blood spots. No one of these measures is ideal and each has strengths and weaknesses. However, accurate estimates of adherence to oral PrEP are important as drug efficacy is closely tied to adherence, and secondary analyses of trial data within identified adherent/non-adherent subgroups may yield important insights into real-world drug effectiveness. We develop a statistical approach to combining multiple measures of adherence and show in simulated data that the proposed method provides a more accurate measure of true adherence than self-report. We then apply the method to estimate adherence in the ADAPT study (HPTN 067) in South African women., (© 2022 John Wiley & Sons Ltd.)

In order to implement disease-specific interventions in young age groups, policy makers in low- and middle-income countries require timely and accurate estimates of age- and cause-specific child mortality. High-quality data is not available in settings where these interventions are most needed, but there is a push to create sample registration systems that collect detailed mortality information. current methods that estimate mortality from this data employ multistage frameworks without rigorous statistical justification that separately estimate all-cause and cause-specific mortality and are not sufficiently adaptable to capture important features of the data. We propose a flexible Bayesian modeling framework to estimate age- and cause-specific child mortality from sample registration data. We provide a theoretical justification for the framework, explore its properties via simulation, and use it to estimate mortality trends using data from the Maternal and Child Health Surveillance System in China.

Background: The Sustainable Development Goals (SDGs), set in 2015 by the UN General Assembly, call for all countries to reach an under-5 mortality rate (U5MR) of at least as low as 25 deaths per 1000 livebirths and a neonatal mortality rate (NMR) of at least as low as 12 deaths per 1000 livebirths by 2030. We estimated levels and trends in under-5 mortality for 195 countries from 1990 to 2019, and conducted scenario-based projections of the U5MR and NMR from 2020 to 2030 to assess country progress in, and potential for, reaching SDG targets on child survival and the potential under-5 and neonatal deaths over the next decade., Methods: Levels and trends in under-5 mortality are based on the UN Inter-agency Group for Child Mortality Estimation (UN IGME) database on under-5 mortality, which contains around 18 000 country-year datapoints for 195 countries-nearly 10 000 of those datapoints since 1990. The database includes nationally representative mortality data from vital registration systems, sample registration systems, population censuses, and household surveys. As with previous sets of national UN IGME estimates, a Bayesian B-spline bias-reduction model (B3) that considers the systematic biases associated with the different data source types was fitted to these data to generate estimates of under-5 (age 0-4 years) mortality with uncertainty intervals for 1990-2019 for all countries. Levels and trends in the neonatal mortality rate (0-27 days) are modelled separately as the log ratio of the neonatal mortality rate to the under-5 mortality rate using a Bayesian model. Estimated mortality rates are combined with livebirths data to calculate the number of under-5 and neonatal deaths. To assess the regional and global burden of under-5 deaths in the present decade and progress towards SDG targets, we constructed several scenario-based projections of under-5 mortality from 2020 to 2030 and estimated national, regional, and global under-5 mortality trends up to 2030 for each scenario., Findings: The global U5MR decreased by 59% (90% uncertainty interval [UI] 56-61) from 93·0 (91·7-94·5) deaths per 1000 livebirths in 1990 to 37·7 (36·1-40·8) in 2019, while the annual number of global under-5 deaths declined from 12·5 (12·3-12·7) million in 1990 to 5·2 (5·0-5·6) million in 2019-a 58% (55-60) reduction. The global NMR decreased by 52% (90% UI 48-55) from 36·6 (35·6-37·8) deaths per 1000 livebirths in 1990, to 17·5 (16·6-19·0) in 2019, and the annual number of global neonatal deaths declined from 5·0 (4·9-5·2) million in 1990, to 2·4 (2·3-2·7) million in 2019, a 51% (47-54) reduction. As of 2019, 122 of 195 countries have achieved the SDG U5MR target, and 20 countries are on track to achieve the target by 2030, while 53 will need to accelerate progress to meet the target by 2030. 116 countries have reached the SDG NMR target with 16 on track, leaving 63 at risk of missing the target. If current trends continue, 48·1 million under-5 deaths are projected to occur between 2020 and 2030, almost half of them projected to occur during the neonatal period. If all countries met the SDG target on under-5 mortality, 11 million under-5 deaths could be averted between 2020 and 2030., Interpretation: As a result of effective global health initiatives, millions of child deaths have been prevented since 1990. However, the task of ending all preventable child deaths is not done and millions more deaths could be averted by meeting international targets. Geographical and economic variation demonstrate the possibility of even lower mortality rates for children under age 5 years and point to the regions and countries with highest mortality rates and in greatest need of resources and action., Funding: Bill & Melinda Gates Foundation, US Agency for International Development., Competing Interests: Declaration of interests We declare no competing interests., (Copyright © 2022 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 license. Published by Elsevier Ltd.. All rights reserved.)

The United Nations' Sustainable Development Goal 3.2 aims to reduce under-five child mortality to 25 deaths per 1000 live births by 2030. Child mortality tends to be concentrated in developing regions where information needed to assess achievement of this goal often comes from surveys and censuses. In both, women are asked about their birth histories, but with varying degrees of detail. Full birth history (FBH) data contain the reported dates of births and deaths of every surveyed mother's children. In contrast, summary birth history (SBH) data contain only the total number of children born and total number of children who died for each mother. Specialized methods are needed to accommodate this type of data into analyses of child mortality trends. We develop a data augmentation scheme within a Bayesian framework where for SBH data, birth and death dates are introduced as auxiliary variables. Since we specify a full probability model for the data, many of the well-known biases that exist in this data can be accommodated, along with space-time smoothing on the underlying mortality rates. We illustrate our approach in a simulation, showing robustness to model misspecification and that uncertainty is reduced when incorporating SBH data over simply analyzing all available FBH data. We also apply our approach to data from the Central region of Malawi and compare with the well-known Brass method., (© 2020 The International Biometric Society.)

Introduction: HIV planning requires granular estimates for the number of people living with HIV (PLHIV), antiretroviral treatment (ART) coverage and unmet need, and new HIV infections by district, or equivalent subnational administrative level. We developed a Bayesian small-area estimation model, called Naomi, to estimate these quantities stratified by subnational administrative units, sex, and five-year age groups., Methods: Small-area regressions for HIV prevalence, ART coverage and HIV incidence were jointly calibrated using subnational household survey data on all three indicators, routine antenatal service delivery data on HIV prevalence and ART coverage among pregnant women, and service delivery data on the number of PLHIV receiving ART. Incidence was modelled by district-level HIV prevalence and ART coverage. Model outputs of counts and rates for each indicator were aggregated to multiple geographic and demographic stratifications of interest. The model was estimated in an empirical Bayes framework, furnishing probabilistic uncertainty ranges for all output indicators. Example results were presented using data from Malawi during 2016-2018., Results: Adult HIV prevalence in September 2018 ranged from 3.2% to 17.1% across Malawi's districts and was higher in southern districts and in metropolitan areas. ART coverage was more homogenous, ranging from 75% to 82%. The largest number of PLHIV was among ages 35 to 39 for both women and men, while the most untreated PLHIV were among ages 25 to 29 for women and 30 to 34 for men. Relative uncertainty was larger for the untreated PLHIV than the number on ART or total PLHIV. Among clients receiving ART at facilities in Lilongwe city, an estimated 71% (95% CI, 61% to 79%) resided in Lilongwe city, 20% (14% to 27%) in Lilongwe district outside the metropolis, and 9% (6% to 12%) in neighbouring Dowa district. Thirty-eight percent (26% to 50%) of Lilongwe rural residents and 39% (27% to 50%) of Dowa residents received treatment at facilities in Lilongwe city., Conclusions: The Naomi model synthesizes multiple subnational data sources to furnish estimates of key indicators for HIV programme planning, resource allocation, and target setting. Further model development to meet evolving HIV policy priorities and programme need should be accompanied by continued strengthening and understanding of routine health system data., (© 2021 The Authors. Journal of the International AIDS Society published by John Wiley & Sons Ltd on behalf of the International AIDS Society.)

Background: Stillbirths are a major public health issue and a sensitive marker of the quality of care around pregnancy and birth. The UN Global Strategy for Women's, Children's and Adolescents' Health (2016-30) and the Every Newborn Action Plan (led by UNICEF and WHO) call for an end to preventable stillbirths. A first step to prevent stillbirths is obtaining standardised measurement of stillbirth rates across countries. We estimated stillbirth rates and their trends for 195 countries from 2000 to 2019 and assessed progress over time., Methods: For a systematic assessment, we created a dataset of 2833 country-year datapoints from 171 countries relevant to stillbirth rates, including data from registration and health information systems, household-based surveys, and population-based studies. After data quality assessment and exclusions, we used 1531 datapoints to estimate country-specific stillbirth rates for 195 countries from 2000 to 2019 using a Bayesian hierarchical temporal sparse regression model, according to a definition of stillbirth of at least 28 weeks' gestational age. Our model combined covariates with a temporal smoothing process such that estimates were informed by data for country-periods with high quality data, while being based on covariates for country-periods with little or no data on stillbirth rates. Bias and additional uncertainty associated with observations based on alternative stillbirth definitions and source types, and observations that were subject to non-sampling errors, were included in the model. We compared the estimated stillbirth rates and trends to previously reported mortality estimates in children younger than 5 years., Findings: Globally in 2019, an estimated 2·0 million babies (90% uncertainty interval [UI] 1·9-2·2) were stillborn at 28 weeks or more of gestation, with a global stillbirth rate of 13·9 stillbirths (90% UI 13·5-15·4) per 1000 total births. Stillbirth rates in 2019 varied widely across regions, from 22·8 stillbirths (19·8-27·7) per 1000 total births in west and central Africa to 2·9 (2·7-3·0) in western Europe. After west and central Africa, eastern and southern Africa and south Asia had the second and third highest stillbirth rates in 2019. The global annual rate of reduction in stillbirth rate was estimated at 2·3% (90% UI 1·7-2·7) from 2000 to 2019, which was lower than the 2·9% (2·5-3·2) annual rate of reduction in neonatal mortality rate (for neonates aged <28 days) and the 4·3% (3·8-4·7) annual rate of reduction in mortality rate among children aged 1-59 months during the same period. Based on the lower bound of the 90% UIs, 114 countries had an estimated decrease in stillbirth rate since 2000, with four countries having a decrease of at least 50·0%, 28 having a decrease of 25·0-49·9%, 50 having a decrease of 10·0-24·9%, and 32 having a decrease of less than 10·0%. For the remaining 81 countries, we found no decrease in stillbirth rate since 2000. Of these countries, 34 were in sub-Saharan Africa, 16 were in east Asia and the Pacific, and 15 were in Latin America and the Caribbean., Interpretation: Progress in reducing the rate of stillbirths has been slow compared with decreases in the mortality rate of children younger than 5 years. Accelerated improvements are most needed in the regions and countries with high stillbirth rates, particularly in sub-Saharan Africa. Future prevention of stillbirths needs increased efforts to raise public awareness, improve data collection, assess progress, and understand public health priorities locally, all of which require investment., Funding: Bill & Melinda Gates Foundation and the UK Foreign, Commonwealth and Development Office., Competing Interests: Declaration of interests We declare no competing interests., (Copyright © 2021 World Health Organization; licensee Elsevier. This is an Open Access article published under the CC BY 3.0 IGO license which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In any use of this article, there should be no suggestion that WHO endorses any specific organisation, products or services. The use of the WHO logo is not permitted. This notice should be preserved along with the article's original URL.)

Globally, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has infected more than 59 million people and killed more than 1.39 million. Designing and monitoring interventions to slow and stop the spread of the virus require knowledge of how many people have been and are currently infected, where they live, and how they interact. The first step is an accurate assessment of the population prevalence of past infections. There are very few population-representative prevalence studies of SARS-CoV-2 infections, and only two states in the United States-Indiana and Connecticut-have reported probability-based sample surveys that characterize statewide prevalence of SARS-CoV-2. One of the difficulties is the fact that tests to detect and characterize SARS-CoV-2 coronavirus antibodies are new, are not well characterized, and generally function poorly. During July 2020, a survey representing all adults in the state of Ohio in the United States collected serum samples and information on protective behavior related to SARS-CoV-2 and coronavirus disease 2019 (COVID-19). Several features of the survey make it difficult to estimate past prevalence: 1) a low response rate; 2) a very low number of positive cases; and 3) the fact that multiple poor-quality serological tests were used to detect SARS-CoV-2 antibodies. We describe a Bayesian approach for analyzing the biomarker data that simultaneously addresses these challenges and characterizes the potential effect of selective response. The model does not require survey sample weights; accounts for multiple imperfect antibody test results; and characterizes uncertainty related to the sample survey and the multiple imperfect, potentially correlated tests., Competing Interests: The authors declare no competing interest., (Copyright © 2021 the Author(s). Published by PNAS.)

In low and middle income countries, household surveys are a valuable source of information for a range of health and demographic indicators. Increasingly, subnational estimates are required for targeting interventions and evaluating progress towards targets. In the majority of cases, stratified cluster sampling is used, with clusters corresponding to enumeration areas. The reported geographical information varies. A common procedure, to preserve confidentiality, is to give a jittered location with the true centroid of the cluster is displaced under a known algorithm. An alternative situation, which was used for older surveys in particular, is to report the geographical region within the cluster lies. In this paper, we describe a spatial hierarchical model in which we account for inaccuracies in the cluster locations. The computational algorithm we develop is fast and avoids the heavy computation of a pure MCMC approach. We illustrate by simulation the benefits of the model, over naive alternatives., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

There is an increasing focus on reducing inequalities in health outcomes in developing countries. Subnational variation is of particular interest, with geographically-indexed data being used to understand the spatial risk of detrimental outcomes and to identify who is at greatest risk. While some health surveys provide observations with associated geographic coordinates (point data), many others provide data that have their locations masked and instead only report the strata (polygon information) within which the data resides (masked data). How to harmonize these data sources for spatial analysis has been previously considered although only ad hoc methods and comparison of methods is lacking. In this paper, we present a new method for analyzing masked survey data, using a method that is consistent with the data-generating process. In addition, we critique two previously proposed approaches to analyzing masked data and illustrate that they are fundamentally flawed methodologically. To validate our method, we compare our approach with previously formulated solutions in several realistic simulation environments in which the underlying structure of the risk field is known. We simulate samples from spatiotemporal fields in a way that mimics the sampling frame implemented in the most common health surveys in low- and middle-income countries, the Demographic and Health Surveys and Multiple Indicator Cluster Surveys. In simulations, the newly proposed approach outperforms previously proposed approaches in terms of minimizing error while increasing the precision of estimates. The approaches are subsequently compared using child mortality data from the Dominican Republic where our findings are reinforced. The ability to accurately increase precision of child mortality estimates, and health outcomes in general, by leveraging various types of data, improves our ability to implement precision public health initiatives and better understand the landscape of geographic health inequalities.

It is becoming increasingly popular to produce high-resolution maps of vaccination coverage by fitting Bayesian geostatistical models to data from household surveys. Usually, the surveys adopt a stratified cluster sampling design. We discuss a number of crucial choices with respect to two key aspects of the map production process: the acknowledgement of the survey design in modeling, and the appropriate presentation of estimates and their uncertainties. Specifically, we consider the importance of accounting for urban/rural stratification and cluster-level non-spatial excess variation in survey outcomes, when fitting geostatistical models. We also discuss the trade-off between the geographical scale and precision of model-based estimates, and demonstrate visualization methods for mapping and ranking that emphasize the probabilistic interpretation of results. A novel approach to coverage map presentation is proposed to allow comparison and control of the overall map uncertainty. We use measles vaccination coverage in Nigeria as a motivating example and illustrate the different issues using data from the 2018 Nigeria Demographic and Health Survey., Competing Interests: Declaration of Competing Interest The authors declare no competing interests., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

The Sustainable Development Goals call for a total reduction of preventable child mortality before 2030. Further, the goals state the desirability to have subnational mortality estimates. Estimates at this level are required for health interventions at the subnational level. In a low and middle income countries context, the data on mortality typically consist of household surveys, which are carried out with a stratified, cluster design, and census microsamples. Most household surveys collect full birth history (FBH) data on birth and death dates of a mother's children, but censuses collect summary birth history (SBH) data which consist only of the number of children born and the number that died. In previous work, direct (survey-weighted) estimates with associated variances were derived from FBH data and smoothed in space and time. Unfortunately, the FBH data from household surveys are usually not sufficiently abundant to obtain yearly estimates at the Admin-2 level (at which interventions are often made). In this paper we describe four extensions to previous work: (i) combining SBH data with FBH data, (ii) modeling on a yearly scale, to combine data on a yearly scale with data at coarser time scales, (iii) adjusting direct estimates in Admin-2 areas where we do not observe any deaths due to small sample sizes, (iv) acknowledge differences in data sources by modeling potential bias arising from the various data sources. The methods are illustrated using household survey and census data from Kenya and Malawi, to produce mortality estimates from 1980 to the time of the most recent survey, and predictions to 2020., (© 2021 John Wiley & Sons, Ltd.)

Small area estimation (SAE) entails estimating characteristics of interest for domains, often geographical areas, in which there may be few or no samples available. SAE has a long history and a wide variety of methods have been suggested, from a bewildering range of philosophical standpoints. We describe design-based and model-based approaches and models that are specified at the area-level and at the unit-level, focusing on health applications and fully Bayesian spatial models. The use of auxiliary information is a key ingredient for successful inference when response data are sparse and we discuss a number of approaches that allow the inclusion of covariate data. SAE for HIV prevalence, using data collected from a Demographic Health Survey in Malawi in 2015-2016, is used to illustrate a number of techniques. The potential use of SAE techniques for outcomes related to COVID-19 is discussed.

The analysis of area-level aggregated summary data is common in many disciplines including epidemiology and the social sciences. Typically, Markov random field spatial models have been employed to acknowledge spatial dependence and allow data-driven smoothing. In the context of an irregular set of areas, these models always have an ad hoc element with respect to the definition of a neighborhood scheme. In this article, we exploit recent theoretical and computational advances to carry out modeling at the continuous spatial level, which induces a spatial model for the discrete areas. This approach also allows reconstruction of the continuous underlying surface, but the interpretation of such surfaces is delicate since it depends on the quality, extent and configuration of the observed data. We focus on models based on stochastic partial differential equations. We also consider the interesting case in which the aggregate data are supplemented with point data. We carry out Bayesian inference and, in the language of generalized linear mixed models, if the link is linear, an efficient implementation of the model is available via integrated nested Laplace approximations. For nonlinear links, we present two approaches: a fully Bayesian implementation using a Hamiltonian Monte Carlo algorithm and an empirical Bayes implementation, that is much faster and is based on Laplace approximations. We examine the properties of the approach using simulation, and then apply the model to the classic Scottish lip cancer data., (© The Author 2018. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Introduction: Race, ethnicity, and socioeconomic status are known to influence staging and survival in colorectal cancer (CRC). It is unclear how these relationships are affected by geographic factors and changes in insurance coverage for CRC screening. We examined the temporal trends in the association between sociodemographic and geographic factors and staging and survival among Medicare beneficiaries., Methods: We identified patients 65 years or older with CRC using the 1991-2010 Surveillance, Epidemiology, and End Results-Medicare database and extracted area-level sociogeographic data. We constructed multinomial logistic regression models and the Cox proportional hazards models to assess factors associated with CRC stage and survival in 4 periods with evolving reimbursement and screening practices: (i) 1991-1997, (ii) 1998-June 2001, (iii) July 2001-2005, and (iv) 2006-2010., Results: We observed 327,504 cases and 102,421 CRC deaths. Blacks were 24%-39% more likely to present with distant disease than whites. High-income areas had 7%-12% reduction in distant disease. Compared with whites, blacks had 16%-21% increased mortality, Asians had 32% lower mortality from 1991 to 1997 but only 13% lower mortality from 2006 to 2010, and Hispanics had 20% reduced mortality only from 1991 to 1997. High-education areas had 9%-12% lower mortality, and high-income areas had 5%-6% lower mortality after Medicare began coverage for screening colonoscopy. No consistent temporal trends were observed for the associations between geographic factors and CRC survival., Discussion: Disparities in CRC staging and survival persisted over time for blacks and residents from areas of low socioeconomic status. Over time, staging and survival benefits have decreased for Asians and disappeared for Hispanics.

Disease surveillance systems provide a rich source of data regarding infectious diseases, aggregated across geographical regions. The analysis of such ecological data is fraught with difficulties, and, unless care and suitable data summaries are available, will lead to biased estimates of individual-level parameters. We consider using surveillance data to study the impacts of vaccination. To catalog the problems of ecological inference, we start with an individual-level model, which contains familiar parameters, and derive an ecologically consistent model for infectious diseases in partially vaccinated populations. We compare with other popular model classes and highlight deficiencies. We explore the properties of the new model through simulation and demonstrate that, under standard assumptions, the ecological model provides less biased estimates. We then fit the new model to data collected on measles outbreaks in Germany from 2005-2007., (© 2019 John Wiley & Sons, Ltd.)

Since 2000, many countries have achieved considerable success in improving child survival, but localized progress remains unclear. To inform efforts towards United Nations Sustainable Development Goal 3.2-to end preventable child deaths by 2030-we need consistently estimated data at the subnational level regarding child mortality rates and trends. Here we quantified, for the period 2000-2017, the subnational variation in mortality rates and number of deaths of neonates, infants and children under 5 years of age within 99 low- and middle-income countries using a geostatistical survival model. We estimated that 32% of children under 5 in these countries lived in districts that had attained rates of 25 or fewer child deaths per 1,000 live births by 2017, and that 58% of child deaths between 2000 and 2017 in these countries could have been averted in the absence of geographical inequality. This study enables the identification of high-mortality clusters, patterns of progress and geographical inequalities to inform appropriate investments and implementations that will help to improve the health of all populations.

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.

The under-five mortality rate (U5MR) is a critical and widely available population health indicator. Both the MDGs and SDGs define targets for improvement in the U5MR, and the SDGs require spatial disaggregation of indicators. We estimate trends in the U5MR for Admin-1 subnational areas using 122 DHS surveys in 35 countries in Africa and assess progress toward the MDG target reductions for each subnational region and each country as a whole. In each country, direct weighted estimates of the U5MR from each survey are calculated and combined into a single estimate for each Admin-1 region across five-year periods. Our method fully accounts for the sample design of each survey. The region-time-specific estimates are smoothed using a Bayesian, space-time model that produces more precise estimates (when compared to the direct estimates) at a one-year scale that are consistent with each other in both space and time. The resulting estimated distributions of the U5MR are summarized and used to assess subnational progress toward the MDG 4 target of two-thirds reduction in the U5MR during 1990-2015. Our space-time modeling approach is tractable and can be readily applied to a large collection of sample survey data. Subnational, regional spatial heterogeneity in the levels and trends in the U5MR vary considerably across Africa. There is no generalizable pattern between spatial heterogeneity and levels or trends in the U5MR. Subnational, small-area estimates of the U5MR: (i) identify subnational regions where interventions are still necessary and those where improvement is well under way; and (ii) countries where there is very little spatial variation and others where there are important differences between subregions in both levels and trends. More work is necessary to improve both the data sources and methods necessary to adequately measure subnational progress toward the SDG child survival targets., Competing Interests: The authors have declared that no competing interests exist.

Background: Depression is an important contributor to the global burden of disease. Besides several known individual-level factors that contribute to depression, there is a growing recognition that neighbourhood environment can also profoundly affect mental health. This study assessed associations between three neighbourhood constructs-socioeconomic deprivation, residential instability and income inequality-and depression among adult twin pairs. The twin design is used to examine the association between neighbourhood constructs and depression, controlling for selection factors (ie, genetic and shared environmental factors) that have confounded purported associations., Methods: We used multilevel random-intercept Poisson regression among 3738 same-sex twin pairs from a community-based twin registry to examine the association between neighbourhood constructs and depression. The within-pair association controls for confounding by genetic and environmental factors shared between twins within a pair, and is the main parameter of interest. Models were adjusted for individual-level income, education and marital status, and further by neighbourhood-level population density., Results: When twins were analysed as individuals (phenotypic model), all neighbourhood constructs were significantly associated with depression. However, only neighbourhood socioeconomic deprivation showed a significant within-pair association with depression. A 10-unit within-pair difference in neighbourhood socioeconomic deprivation was associated with 6% greater depressive symptoms (1.06, 95% CI 1.01 to 1.11); the association did not substantially change in adjusted models., Conclusion: This study provides new evidence linking neighbourhood socioeconomic deprivation with greater depression. Future studies should employ longitudinal designs to better test social causation versus social selection., Competing Interests: Competing interests: None declared., (© Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2018. All rights reserved. No commercial use is permitted unless otherwise expressly granted.)

Social capital is associated with depression independently of individual-level risk factors. We used a sample of 1586 same-sex twin pairs to test the association between seven measures of social capital and two related measures of neighborhood characteristics with depressive symptoms accounting for uncontrolled selection factors (i.e., genetics and shared environment). All measures of cognitive social capital and neighborhood characteristics were associated with less depressive symptoms in between-twin analysis. However, only measures of cognitive social capital were significantly associated with less depressive symptoms within-pairs. These results demonstrate that cognitive social capital is associated with depressive symptoms free of confounding from genetic and environmental factors shared within twins., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

The often-noted and persistent increased incidence of Escherichia coli O157:H7 infections in rural areas is not well understood. We used a cohort of E. coli O157:H7 cases reported in Washington, USA, during 2005-2014, along with phylogenomic characterization of the infecting isolates, to identify geographic segregation of and temporal trends in specific phylogenetic lineages of E. coli O157:H7. Kernel estimation and generalized additive models demonstrated that pathogen lineages were spatially segregated during the period of analysis and identified a focus of segregation spanning multiple, predominantly rural, counties for each of the main clinical lineages, Ib, IIa, and IIb. These results suggest the existence of local reservoirs from which humans are infected. We also noted a secular increase in the proportion of lineage IIa and IIb isolates. Spatial segregation by phylogenetic lineage offers the potential to identify local reservoirs and intervene to prevent continued transmission.

Purpose: Colorectal cancer (CRC) incidence and mortality in the United States have steadily declined since the 1980s, but racial and socioeconomic disparities remain. The influence of geographic factors is poorly understood and may be affected by evolving insurance coverage and screening test uptake. We characterized temporal trends in the association between geographic and sociodemographic factors and CRC outcomes., Methods: We used the 1973-2010 SEER-Medicare files to identify patients aged ≥65 years with and without CRC. Beneficiary residential ZIP codes were used to extract local-level data. We constructed multivariable logistic regression models for CRC incidence and mortality using geographic and sociodemographic variables in 4 time periods: (1) 1973-1997; (2) 1998-2001; (3) 2002-2006; and (4) 2007-2010., Findings: We analyzed 1,093,758 records, including 336,321 CRC cases. Compared to urban residence, small rural residence was strongly associated with increased CRC incidence (OR 1.50, 95% CI: 1.43-1.57) and mortality (OR 1.35, 95% CI: 1.26-1.45) in 1973-1997, but the associations diminished by 2007-2010 (OR 1.09, 95% CI: 1.04-1.15 for incidence; OR 1.10, 95% CI: 1.01-1.20 for mortality). The disparity between blacks and whites increased over time for both incidence (OR 1.09, 95% CI: 1.05-1.13 in 1973-1997 vs OR 1.32, 95% CI: 1.27-1.37 in 2007-2010) and mortality (OR 1.22, 95% CI: 1.16-1.28 in 1973-1997 vs OR 1.34, 95% CI: 1.26-1.42 in 2007-2010). High socioeconomic status was associated with greater incidence and mortality in 1973-1997, but it became protective after 1998., Conclusions: Although disparities persist among Medicare beneficiaries, the relationship between geographic and sociodemographic factors and CRC incidence and mortality has evolved over time., (© 2016 National Rural Health Association.)

Background: The role of air pollution in increasing susceptibility to respiratory tract infections in the cystic fibrosis (CF) population has not been well described. We recently demonstrated that chronic PM 2.5 exposure is associated with an increased risk of initial Pseudomonas aeruginosa acquisition in young children with CF. The purpose of this study was to determine whether PM 2.5 exposure is a risk factor for acquisition of other respiratory pathogens in young children with CF., Methods: We conducted a retrospective study of initial acquisition of methicillin susceptible and methicillin resistant Staphylococcus aureus (MSSA and MRSA), Stenotrophomonas maltophilia and Achromobacter xylosoxidans in U.S. children <6 years of age with CF using the CF Foundation Patient Registry, 2003-2009. Multivariable Weibull regression with interval-censored outcomes was used to evaluate the association of PM 2.5 concentration in the year prior to birth and risk of acquisition of each organism., Results: During follow-up 63%, 17%, 24%, and 5% of children acquired MSSA, MRSA, S. maltophilia, and A. xylosoxidans, respectively. A 10 μg/m 3 increase in PM 2.5 exposure was associated with a 68% increased risk of MRSA acquisition (Hazard Ratio: 1.68; 95% Confidence Interval: 1.24, 2.27). PM 2.5 was not associated with acquisition of other respiratory pathogens., Conclusions: Fine particulate matter is an independent risk factor for initial MRSA acquisition in young children with CF. These results support the increasing evidence that air pollution contributes to pulmonary morbidities in the CF community.

Background: Seasonal variations are often observed for respiratory tract infections; however, limited information is available regarding seasonal patterns of acquisition of common cystic fibrosis (CF)-related respiratory pathogens. We previously reported differential seasonal acquisition of Pseudomonas aeruginosa in young children with CF and no such variation for methicillin-susceptible Staphylococcus aureus acquisition. The purpose of this study was to describe and compare the seasonal incidence of acquisition of other respiratory bacterial pathogens in young children with CF., Methods: We conducted a retrospective study to describe and compare the seasonal incidence of methicillin-resistant Staphylococcus aureus (MRSA), Stenotrophomonas maltophilia, Achromobacter xylosoxidans, and Haemophilus influenzae acquisition in young CF patients residing in the U.S. using the Cystic Fibrosis Foundation National Patient Registry, 2003-2009. Log-linear overdispersed Poisson regression was used to evaluate seasonal acquisition of each of these pathogens., Results: A total of 4552 children met inclusion criteria. During follow-up 910 (20%), 1161 (26%), 228 (5%), and 2148 (47%) children acquired MRSA, S. maltophilia, A. xylosoxidans and H. influenzae, respectively. Compared to winter season, MRSA was less frequently acquired in spring (Incidence Rate Ratio [IRR]: 0.79; 95% Confidence Interval [CI]: 0.65, 0.96) and summer (IRR: 0.69; 95% CI: 0.57, 0.84) seasons. Similarly, a lower rate of A. xylosoxidans acquisition was observed in spring (IRR: 0.59; 95% CI: 0.39, 0.89). For H. influenzae, summer (IRR: 0.88; 95% CI: 0.78, 0.99) and autumn (IRR: 0.78; 95% CI: 0.69, 0.88) seasons were associated with lower acquisition rates compared to winter. No seasonal variation was observed for S. maltophilia acquisition., Conclusion: Acquisition of CF-related respiratory pathogens displays seasonal variation in young children with CF, with the highest rate of acquisition for most pathogens occurring in the winter. Investigation of factors underlying these observed associations may contribute to our understanding of the aetiology of these infections and guide future infection control strategies.

Many diseases arise due to exposure to one of multiple possible pathogens. We consider the situation in which disease counts are available over time from a study region, along with a measure of clinical disease severity, for example, mild or severe. In addition, we suppose a subset of the cases are lab tested in order to determine the pathogen responsible for disease. In such a context, we focus interest on modeling the probabilities of disease incidence given pathogen type. The time course of these probabilities is of great interest as is the association with time-varying covariates such as meteorological variables. In this set up, a natural Bayesian approach would be based on imputation of the unsampled pathogen information using Markov Chain Monte Carlo but this is computationally challenging. We describe a practical approach to inference that is easy to implement. We use an empirical Bayes procedure in a first step to estimate summary statistics. We then treat these summary statistics as the observed data and develop a Bayesian generalized additive model. We analyze data on hand, foot, and mouth disease (HFMD) in China in which there are two pathogens of primary interest, enterovirus 71 (EV71) and Coxackie A16 (CA16). We find that both EV71 and CA16 are associated with temperature, relative humidity, and wind speed, with reasonably similar functional forms for both pathogens. The important issue of confounding by time is modeled using a penalized B-spline model with a random effects representation. The level of smoothing is addressed by a careful choice of the prior on the tuning variance., (© 2016, The International Biometric Society.)

Regulatory variation influencing gene expression is a key contributor to phenotypic diversity, both within and between species. Unfortunately, RNA degrades too rapidly to be recovered from fossil remains, limiting functional genomic insights about our extinct hominin relatives. Many Neanderthal sequences survive in modern humans due to ancient hybridization, providing an opportunity to assess their contributions to transcriptional variation and to test hypotheses about regulatory evolution. We developed a flexible Bayesian statistical approach to quantify allele-specific expression (ASE) in complex RNA-seq datasets. We identified widespread expression differences between Neanderthal and modern human alleles, indicating pervasive cis-regulatory impacts of introgression. Brain regions and testes exhibited significant downregulation of Neanderthal alleles relative to other tissues, consistent with natural selection influencing the tissue-specific regulatory landscape. Our study demonstrates that Neanderthal-inherited sequences are not silent remnants of ancient interbreeding but have measurable impacts on gene expression that contribute to variation in modern human phenotypes., (Copyright © 2017 Elsevier Inc. All rights reserved.)

Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time evolution of an epidemic gives rise to a complicated latent variable problem in which the state space size of the epidemic grows large as the population size increases. This makes analytically integrating over the missing data infeasible for populations of even moderate size. We present a data augmentation Markov chain Monte Carlo (MCMC) framework for Bayesian estimation of stochastic epidemic model parameters, in which measurements are augmented with subject-level disease histories. In our MCMC algorithm, we propose each new subject-level path, conditional on the data, using a time-inhomogeneous continuous-time Markov process with rates determined by the infection histories of other individuals. The method is general, and may be applied to a broad class of epidemic models with only minimal modifications to the model dynamics and/or emission distribution. We present our algorithm in the context of multiple stochastic epidemic models in which the data are binomially sampled prevalence counts, and apply our method to data from an outbreak of influenza in a British boarding school.

Despite seasonal cholera outbreaks in Bangladesh, little is known about the relationship between environmental conditions and cholera cases. We seek to develop a predictive model for cholera outbreaks in Bangladesh based on environmental predictors. To do this, we estimate the contribution of environmental variables, such as water depth and water temperature, to cholera outbreaks in the context of a disease transmission model. We implement a method which simultaneously accounts for disease dynamics and environmental variables in a Susceptible-Infected-Recovered-Susceptible (SIRS) model. The entire system is treated as a continuous-time hidden Markov model, where the hidden Markov states are the numbers of people who are susceptible, infected, or recovered at each time point, and the observed states are the numbers of cholera cases reported. We use a Bayesian framework to fit this hidden SIRS model, implementing particle Markov chain Monte Carlo methods to sample from the posterior distribution of the environmental and transmission parameters given the observed data. We test this method using both simulation and data from Mathbaria, Bangladesh. Parameter estimates are used to make short-term predictions that capture the formation and decline of epidemic peaks. We demonstrate that our model can successfully predict an increase in the number of infected individuals in the population weeks before the observed number of cholera cases increases, which could allow for early notification of an epidemic and timely allocation of resources.

In recent years, the availability of infectious disease counts in time and space has increased, and consequently, there has been renewed interest in model formulation for such data. In this paper, we describe a model that was motivated by the need to analyze hand, foot, and mouth disease surveillance data in China. The data are aggregated by geographical areas and by week, with the aims of the analysis being to gain insight into the space-time dynamics and to make short-term predictions, which will aid in the implementation of public health campaigns in those areas with a large predicted disease burden. The model we develop decomposes disease-risk into marginal spatial and temporal components and a space-time interaction piece. The latter is the crucial element, and we use a tensor product spline model with a Markov random field prior on the coefficients of the basis functions. The model can be formulated as a Gaussian Markov random field and so fast computation can be carried out using the integrated nested Laplace approximation approach. A simulation study shows that the model can pick up complex space-time structure and our analysis of hand, foot, and mouth disease data in the central north region of China provides new insights into the dynamics of the disease., (Copyright © 2015 John Wiley & Sons, Ltd.)

Introduction: King County, Washington, fares well overall in many health indicators. However, county-level data mask disparities among subcounty areas. For disparity-focused assessment, a demand exists for examining health data at subcounty levels such as census tracts and King County health reporting areas (HRAs)., Methods: We added a "nearest intersection" question to the Behavioral Risk Factor Surveillance System (BRFSS) and geocoded the data for subcounty geographic areas, including census tracts. To overcome small sample size at the census tract level, we used hierarchical Bayesian models to obtain smoothed estimates in cigarette smoking rates at the census tract and HRA levels. We also used multiple imputation to adjust for missing values in census tracts., Results: Direct estimation of adult smoking rates at the census tract level ranged from 0% to 56% with a median of 10%. The 90% confidence interval (CI) half-width for census tract with nonzero rates ranged from 1 percentage point to 37 percentage points with a median of 13 percentage points. The smoothed-multiple-imputation rates ranged from 5% to 28% with a median of 12%. The 90% CI half-width ranged from 4 percentage points to 13 percentage points with a median of 8 percentage points., Conclusion: The nearest intersection question in the BRFSS provided geocoded data at subcounty levels. The Bayesian model provided estimation with improved precision at the census tract and HRA levels. Multiple imputation can be used to account for missing geographic data. Small-area estimation, which has been used for King County public health programs, has increasingly become a useful tool to meet the demand of presenting data at more granular levels.

Cluster detection is an important public health endeavor, and in this article, we describe and apply a recently developed Bayesian method. Commonly used approaches are based on so-called scan statistics and suffer from a number of difficulties, which include how to choose a level of significance and how to deal with the possibility of multiple clusters. The basis of our model is to partition the study region into a set of areas that are either "null" or "non-null," the latter corresponding to clusters (excess risk) or anticlusters (reduced risk). We demonstrate the Bayesian method and compare with a popular existing approach, using data on breast, brain, lung, prostate, and colorectal cancer, in the Puget Sound region of Washington State.

Although Neandertal sequences that persist in the genomes of modern humans have been identified in Eurasians, comparable studies in people whose ancestors hybridized with both Neandertals and Denisovans are lacking. We developed an approach to identify DNA inherited from multiple archaic hominin ancestors and applied it to whole-genome sequences from 1523 geographically diverse individuals, including 35 previously unknown Island Melanesian genomes. In aggregate, we recovered 1.34 gigabases and 303 megabases of the Neandertal and Denisovan genome, respectively. We use these maps of archaic sequences to show that Neandertal admixture occurred multiple times in different non-African populations, characterize genomic regions that are significantly depleted of archaic sequences, and identify signatures of adaptive introgression., (Copyright © 2016, American Association for the Advancement of Science.)

We present a Bayesian model for area-level count data that uses Gaussian random effects with a novel type of G-Wishart prior on the inverse variance- covariance matrix. Specifically, we introduce a new distribution called the truncated G-Wishart distribution that has support over precision matrices that lead to positive associations between the random effects of neighboring regions while preserving conditional independence of non-neighboring regions. We describe Markov chain Monte Carlo sampling algorithms for the truncated G-Wishart prior in a disease mapping context and compare our results to Bayesian hierarchical models based on intrinsic autoregression priors. A simulation study illustrates that using the truncated G-Wishart prior improves over the intrinsic autoregressive priors when there are discontinuities in the disease risk surface. The new model is applied to an analysis of cancer incidence data in Washington State.

Many people living in low and middle-income countries are not covered by civil registration and vital statistics systems. Consequently, a wide variety of other types of data including many household sample surveys are used to estimate health and population indicators. In this paper we combine data from sample surveys and demographic surveillance systems to produce small area estimates of child mortality through time. Small area estimates are necessary to understand geographical heterogeneity in health indicators when full-coverage vital statistics are not available. For this endeavor spatio-temporal smoothing is beneficial to alleviate problems of data sparsity. The use of conventional hierarchical models requires careful thought since the survey weights may need to be considered to alleviate bias due to non-random sampling and non-response. The application that motivated this work is estimation of child mortality rates in five-year time intervals in regions of Tanzania. Data come from Demographic and Health Surveys conducted over the period 1991-2010 and two demographic surveillance system sites. We derive a variance estimator of under five years child mortality that accounts for the complex survey weighting. For our application, the hierarchical models we consider include random effects for area, time and survey and we compare models using a variety of measures including the conditional predictive ordinate (CPO). The method we propose is implemented via the fast and accurate integrated nested Laplace approximation (INLA).

Background: The aetiology of Africa's easterly-lying corridor of squamous cell oesophageal cancer is poorly understood. Micronutrient deficiencies have been implicated in this cancer in other areas of the world, but their role in Africa is unclear. Without prospective cohorts, timely insights can instead be gained through ecological studies., Methods: Across Africa we assessed associations between a country's oesophageal cancer incidence rate and food balance sheet-derived estimates of mean national dietary supplies of 7 nutrients: calcium (Ca), copper (Cu), iron (Fe), iodine (I), magnesium (Mg), selenium (Se) and zinc (Zn). We included 32 countries which had estimates of dietary nutrient supplies and of better-quality GLOBCAN 2012 cancer incidence rates. Bayesian hierarchical Poisson lognormal models were used to estimate incidence rate ratios for oesophageal cancer associated with each nutrient, adjusted for age, gender, energy intake, phytate, smoking and alcohol consumption, as well as their 95% posterior credible intervals (CI). Adult dietary deficiencies were quantified using an estimated average requirements (EAR) cut-point approach., Results: Adjusted incidence rate ratios for oesophageal cancer associated with a doubling of mean nutrient supply were: for Fe 0.49 (95% CI: 0.29-0.82); Mg 0.58 (0.31-1.08); Se 0.40 (0.18-0.90); and Zn 0.29 (0.11-0.74). There were no associations with Ca, Cu and I. Mean national nutrient supplies exceeded adult EARs for Mg and Fe in most countries. For Se, mean supplies were less than EARs (both sexes) in 7 of the 10 highest oesophageal cancer ranking countries, compared to 23% of remaining countries. For Zn, mean supplies were less than the male EARs in 8 of these 10 highest ranking countries compared to in 36% of other countries., Conclusions: Ecological associations are consistent with the potential role of Se and/or Zn deficiencies in squamous cell oesophageal cancer in Africa. Individual-level analytical studies are needed to elucidate their causal role in this setting.