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Small area estimation using survey data can be achieved by using either a design-based or a model-based inferential approach. With respect to assumptions, design-based direct estimators are generally preferable because of their consistency and asymptotic normality. However, when data are sparse at the desired area level, as is often the case when measuring rare events for example, these direct estimators can have extremely large uncertainty, making a model-based approach preferable. A model-based approach with a random spatial effect borrows information from surrounding areas at the cost of inducing shrinkage towards the local average. As a result, estimates may be over-smoothed and inconsistent with design-based estimates at higher area levels when aggregated. We propose a unit-level Bayesian model for small area estimation of rare event prevalence which uses design-based direct estimates at a higher area level to increase accuracy, precision, and consistency in aggregation. After introducing the model and its implementation, we conduct a simulation study to compare its properties to alternative models and apply it to the estimation of the neonatal mortality rate in Zambia, using 2014 DHS data.

Accurate and precise estimates of the under-5 mortality rate (U5MR) are an important health summary for countries. However, full survival curves allow us to better understand the pattern of mortality in children under five. Modern demographic methods for estimating a full mortality schedule for children have been developed for countries with good vital registration and reliable census data, but perform poorly in many low- and middle-income countries (LMICs). In these countries, the need to utilize nationally representative surveys to estimate the U5MR requires additional care to mitigate potential biases in survey data, acknowledge the survey design, and handle the usual characteristics of survival data, for example, censoring and truncation. In this paper, we develop parametric and non-parametric pseudo-likelihood approaches to estimating child mortality across calendar time from complex survey data. We show that the parametric approach is particularly useful in scenarios where data are sparse and parsimonious models allow efficient estimation. We compare a variety of parametric models to two existing methods for obtaining a full survival curve for children under the age of 5, and argue that a parametric pseudo-likelihood approach is advantageous in LMICs. We apply our proposed approaches to survey data from four LMICs.

Prediction is a classic challenge in spatial statistics and the inclusion of spatial covariates can greatly improve predictive performance when incorporated into a model with latent spatial effects. It is desirable to develop flexible regression models that allow for nonlinearities and interactions in the covariate structure. Machine learning models have been suggested in the spatial context, allowing for spatial dependence in the residuals, but fail to provide reliable uncertainty estimates. In this paper, we investigate a novel combination of a Gaussian process spatial model and a Bayesian Additive Regression Tree (BART) model. The computational burden of the approach is reduced by combining Markov chain Monte Carlo (MCMC) with the Integrated Nested Laplace Approximation (INLA) technique. We study the performance of the method via simulations and use the model to predict anthropometric responses, collected via household cluster samples in Kenya.

When mapping subnational health and demographic indicators, direct weighted estimators of small area means based on household survey data can be unreliable when data are limited. If survey microdata are available, unit level models can relate individual survey responses to unit level auxiliary covariates and explicitly account for spatial dependence and between area variation using random effects. These models can produce estimators with improved precision, but often neglect to account for the design of the surveys used to collect data. Pseudo-Bayesian approaches incorporate sampling weights to address informative sampling when using such models to conduct population inference but credible sets based on the resulting pseudo-posterior distributions can be poorly calibrated without adjustment. We outline a pseudo-Bayesian strategy for small area estimation that addresses informative sampling and incorporates a post-processing rescaling step that produces credible sets with close to nominal empirical frequentist coverage rates. We compare our approach with existing design-based and model-based estimators using real and simulated data.

Producing subnational estimates of the under-five mortality rate (U5MR) is a vital goal for the United Nations to reduce inequalities in mortality and well-being across the globe. There is a great disparity in U5MR between high-income and Low-and-Middle Income Countries (LMICs). Current methods for modelling U5MR in LMICs use smoothing methods to reduce uncertainty in estimates caused by data sparsity. This paper includes cohort alongside age and period in a novel application of an Age-Period-Cohort model for U5MR. In this context, current methods only use age and period (and not cohort) for smoothing. With data from the Kenyan Demographic and Health Surveys (DHS) we use a Bayesian hierarchical model with terms to smooth over temporal and spatial components whilst fully accounting for the complex stratified, multi-staged cluster design of the DHS. Our results show that the use of cohort may be useful in the context of subnational estimates of U5MR. We validate our results at the subnational level by comparing our results against direct estimates., Comment: 16 pages, 6 Figures, 2 Tables

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 1985-2019, a time period which includes the Rwandan civil war and genocide., Comment: 59 pages

We consider random forests and LASSO methods for model-based small area estimation when the number of areas with sampled data is a small fraction of the total areas for which estimates are required. Abundant auxiliary information is available for the sampled areas, from the survey, and for all areas, from an exterior source, and the goal is to use auxiliary variables to predict the outcome of interest. We compare areal-level random forests and LASSO approaches to a frequentist forward variable selection approach and a Bayesian shrinkage method. Further, to measure the uncertainty of estimates obtained from random forests and the LASSO, we propose a modification of the split conformal procedure that relaxes the assumption of identically distributed data. This work is motivated by Ghanaian data available from the sixth Living Standard Survey (GLSS) and the 2010 Population and Housing Census. We estimate the areal mean household log consumption using both datasets. The outcome variable is measured only in the GLSS for 3\% of all the areas (136 out of 5019) and more than 170 potential covariates are available from both datasets. Among the four modelling methods considered, the Bayesian shrinkage performed the best in terms of bias, MSE and prediction interval coverages and scores, as assessed through a cross-validation study. We find substantial between-area variation, the log consumption areal point estimates showing a 1.3-fold variation across the GAMA region. The western areas are the poorest while the Accra Metropolitan Area district gathers the richest areas., Comment: 40 pages, 10 figures

Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioned on the realization of a random intensity function. They are flexible tools for capturing spatial heterogeneity and dependence. However, existing implementations of doubly-stochastic spatial models are computationally demanding, often have limited theoretical guarantee, and/or rely on restrictive assumptions. We propose a penalized regression method for estimating covariate effects in doubly-stochastic point processes that is computationally efficient and does not require a parametric form or stationarity of the underlying intensity. Our approach is based on an approximate (discrete and deterministic) formulation of the true (continuous and stochastic) intensity function. We show that consistency and asymptotic normality of the covariate effect estimates can be achieved despite the model misspecification, and develop a covariance estimator that leads to a valid, albeit conservative, statistical inference procedure. A simulation study shows the validity of our approach under less restrictive assumptions on the data generating mechanism, and an application to Seattle crime data demonstrates better prediction accuracy compared with existing alternatives.

In low- and middle-income countries, household surveys are the most reliable data source to examine health and demographic indicators at the subnational level, an exercise in small area estimation. Model-based unit-level models are favored in producing the subnational estimates at fine scale, such as the admin-2 level. Typically, the surveys employ stratified two-stage cluster sampling with strata consisting of an urban/rural designation crossed with administrative regions. To avoid bias and increase predictive precision, the stratification should be acknowledged in the analysis. To move from the cluster to the area requires an aggregation step in which the prevalence surface is averaged with respect to population density. This requires estimating a partition of the study area into its urban and rural components, and to do this we experiment with a variety of classification algorithms, including logistic regression, Bayesian additive regression trees and gradient boosted trees. Pixel-level covariate surfaces are used to improve prediction. We estimate spatial HIV prevalence in women of age 15-49 in Malawi using the stratification/aggregation method we propose.

Accurate estimates of subnational health and demographic indicators are critical for informing health policy decisions. Many countries collect relevant data using complex household surveys, but when data are limited, direct survey weighted estimates of small area proportions may be unreliable. Area level models treating these direct estimates as response data can improve precision but often require known sampling variances of the direct estimators for all areas. In practice, the sampling variances are typically estimated, so standard approaches do not account for a key source of uncertainty. In order to account for variability in the estimated sampling variances, we propose a hierarchical Bayesian spatial area level model that smooths both the estimated means and sampling variances to produce point and interval estimates of small area proportions. Our model explicitly targets estimation of small area proportions rather than means of continuous variables and we consider examples of both moderate and low prevalence events. We demonstrate the performance of our approach via simulation and application to vaccination coverage and HIV prevalence data from the Demographic and Health Surveys.

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., Comment: 26 pages of main text, plus 17 pages of appendix

Spatial aggregation with respect to a population distribution involves estimating aggregate quantities for a population based on an observation of individuals in a subpopulation. 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, common practice is to treat the unknown population distribution as a known population density and ignore empirical variability in outcomes. We improve common practice by introducing a `sampling frame model' that allows aggregation models to account for the three sources of aggregation error simply and transparently. We compare the proposed and the traditional approach using two simulation studies that mimic neonatal mortality rate (NMR) data from the 2014 Kenya Demographic and Health Survey (KDHS2014). For the traditional approach, undercoverage/overcoverage depends arbitrarily on the aggregation grid resolution, while the new approach exhibits low sensitivity. The differences between the two aggregation approaches increase as the population of an area decreases. The differences are substantial at the second administrative level and finer, but also at the first administrative level for some population quantities. We find differences between the proposed and traditional approach are consistent with those we observe in an application to NMR data from the KDHS2014., Comment: main manuscript: 33 pages, 5 figures, 5 tables; supplemental materials: 15 pages, 2 figures, 15 tables

Estimating the true mortality burden of COVID-19 for every country in the world is a difficult, but crucial, public health endeavor. Attributing deaths, direct or indirect, to COVID-19 is problematic. A more attainable target is the "excess deaths", the number of deaths in a particular period, relative to that expected during "normal times", and we estimate this for all countries on a monthly time scale for 2020 and 2021. The excess mortality requires two numbers, the total deaths and the expected deaths, but the former is unavailable for many countries, and so modeling is required for these countries. The expected deaths are based on historic data and we develop a model for producing expected estimates for all countries and we allow for uncertainty in the modeled expected numbers when calculating the excess. We describe the methods that were developed to produce the World Health Organization (WHO) excess death estimates. To achieve both interpretability and transparency we developed a relatively simple overdispersed Poisson count framework, within which the various data types can be modeled. We use data from countries with national monthly data to build a predictive log-linear regression model with time-varying coefficients for countries without data. For a number of countries, subnational data only are available, and we construct a multinomial model for such data, based on the assumption that the fractions of deaths in sub-regions remain approximately constant over time. Based on our modeling, the point estimate for global excess mortality, over 2020-2021, is 14.9 million, with a 95% credible interval of (13.3, 16.6) million. This leads to a point estimate of the ratio of excess deaths to reported COVID-19 deaths of 2.75, which is a huge discrepancy.

In small area estimation, it is sometimes necessary to use model-based methods to produce estimates in areas with little or no data. In official statistics, we often require that some aggregate of small area estimates agree with a national estimate for internal consistency purposes. Enforcing this agreement is referred to as benchmarking, and while methods currently exist to perform benchmarking, few are ideal for applications with non-normal outcomes and benchmarks with uncertainty. Fully Bayesian benchmarking is a theoretically appealing approach insofar as we can obtain posterior distributions conditional on a benchmarking constraint. However, existing implementations may be computationally prohibitive. In this paper, we critically review benchmarking methods in the context of small area estimation in low- and middle-income countries with binary outcomes and uncertain benchmarks, and propose a novel approach in which an unbenchmarked method that produces area-level samples can be combined with a rejection sampler or Metropolis-Hastings algorithm to produce benchmarked posterior distributions in a computationally efficient way. To illustrate the flexibility and efficiency of our approach, we provide comparisons to an existing benchmarking approach in a simulation, and applications to HIV prevalence and under-5 mortality estimation. Code implementing our methodology is available in the R package stbench.

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 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 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., Comment: 56 pages, 6 figures

Small area estimates of population are necessary for many epidemiological studies, yet their quality and accuracy are often not assessed. In the United States, small area estimates of 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 data sources, there are important contrasts in data collection and processing methodologies, such that each set of estimates 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. Resulting small area disease/mortality rates may differ depending on which data source is used for population counts (denominator data). To accurately capture annual small area population counts, and associated uncertainties, we present a Bayesian population model (B-Pop), which fuses information from all three USCB sources, accounting for data source specific methodologies and associated errors. 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 estimates for years without USCB reported data. We focus our study on the 159 counties of Georgia, and produce estimates for years 2005-2021.

Infectious disease epidemiologists routinely fit stochastic epidemic models to time series data to elucidate infectious disease dynamics, evaluate interventions, and forecast epidemic trajectories. To improve computational tractability, many approximate stochastic models have been proposed. In this paper, we focus on one class of such approximations -- time series Susceptible-Infectious-Removed (TSIR) models. Infectious disease modeling often starts with a homogeneous mixing assumption, postulating that the rate of disease transmission is proportional to a product of the numbers of susceptible and infectious individuals. One popular way to relax this assumption proceeds by raising the number of susceptible and/or infectious individuals to some positive powers. We show that when this technique is used within the TSIR models they cannot be interpreted as approximate SIR models, which has important implications for TSIR-based statistical inference. Our simulation study shows that TSIR-based estimates of infection and mixing rates are systematically biased in the presence of non-homogeneous mixing, suggesting that caution is needed when interpreting TSIR model parameter estimates when this class of models relaxes the homogeneous mixing assumption., Comment: 16 pages of the main text, 6 figures and 3 tables in the main text

The emerging need for subnational estimation of demographic and health indicators in low- and middle-income countries (LMICs) is driving a move from design-based area-level approaches to unit-level methods. The latter are model-based and overcome data sparsity by borrowing strength across covariates and space and can, in principle, be leveraged to create fine-scale pixel level maps based on household surveys. However, typical implementations of the model-based approaches do not fully acknowledge the complex survey design, and do not enjoy the theoretical consistency of design-based approaches. We describe how spatial methods are currently used for prevalence mapping in the context of LMICs, highlight the key challenges that need to be overcome, and propose a new approach, which is methodologically closer in spirit to small area estimation. The main discussion points are demonstrated through a case study of vaccination coverage in Nigeria based on 2018 Demographic and Health Surveys (DHS) data. We discuss our key findings both generally and with an emphasis on the implications for popular approaches undertaken by industrial producers of subnational prevalence estimates., Comment: An extensive revision of the previous version of the preprint. The spatial aspects have been fleshed out more, and the temporal aspects have been removed

The integrated nested Laplace approximation (INLA) is a well-known and popular technique for spatial modeling with a user-friendly interface in the R-INLA package. Unfortunately, only a certain class of latent Gaussian models are amenable to fitting with INLA. In this paper we describe Template Model Builder (TMB), an existing technique which is well-suited to fitting complex spatio-temporal models. TMB is relatively unknown to the spatial statistics community, but is a highly flexible random effects modeling tool which allows users to define complex random effects models through simple C++ templates. After contrasting the methodology behind TMB with INLA, we provide a large-scale simulation study assessing and comparing R-INLA and TMB for continuous spatial models, fitted via the Stochastic Partial Differential Equations (SPDE) approximation. The results show that the predictive fields from both methods are comparable in most situations even though TMB estimates for fixed or random effects may have slightly larger bias than R-INLA. We also present a smaller discrete spatial simulation study, in which both approaches perform well. We conclude with an analysis of breast cancer incidence and mortality data using a joint model which cannot be fit with INLA., Comment: 84 pages, 30 figures

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 which 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. Code used to produce this manuscript is available at https://github.com/aleshing/central-role-of-identifying-assumptions., Comment: 58 pages. The material presented in Appendix A previously appeared in an unpublished preprint written by the first author: arXiv:2008.09865

Globally the SARS-CoV-2 coronavirus 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 the SARS-CoV-2 coronavirus, and only two American states -- Indiana and Connecticut -- have reported probability-based sample surveys that characterize state-wide prevalence of the SARS-CoV-2 coronavirus. One of the difficulties is the fact that the tests to detect and characterize SARS-CoV-2 coronavirus antibodies are new, 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 biomarkers and information on protective behavior related to the SARS-CoV-2 coronavirus. Several features of the survey make it difficult to estimate past prevalence: 1) a low response rate, 2) 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 new 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.

BACKGROUND There is an increasing demand for high quality subnational estimates of under-five mortality. In low and middle income countries, where the burden of under-five mortality is concentrated, vital registration is often lacking and household surveys, which provide full birth history data, are often the most reliable source. Unfortunately, these data are spatially sparse and so data are pulled from other sources to increase the available information. Summary birth histories represent a large fraction of the available data, and provide numbers of births and deaths aggregated over time, along with the mother's age. OBJECTIVE Specialized methods are needed to leverage this information, and previously the Brass method, and variants, have been used. We wish to develop a model-based approach that can propagate errors, and make the most efficient use of the data. Further, we strive to provide a method that does not have large computational overhead. CONTRIBUTION We describe a computationally efficient model-based approach which allows summary birth history and full birth history data to be combined into analyses of under-five mortality in a natural way. The method is based on fertility and mortality models that allow direct smoothing over time and space, with the possibility for including relevant covariates that are associated with fertility and/or mortality. We first examine the behavior of the approach on simulated data, before applying the model to survey and census data from Malawi.

Measles is a significant source of global disease burden and child mortality. Measles vaccination through routine immunization (RI) programs in high-burden settings remains a challenge due to poor health care infrastructure and access. Supplementary immunization activities (SIA) in the form of vaccination campaigns are therefore implemented to prevent measles outbreaks by reducing the size of the susceptible population. The SIA efficacy, defined as the fraction of susceptible population immunized by an SIA, is a critical metric for assessing campaign effectiveness. We propose a discrete-time hidden Markov model for estimating SIA efficacy and forecasting future incidence trends using reported measles incidence data. Our approach extends the time-series susceptible-infected-recovered (TSIR) framework by adding a model component to capture the impact of SIAs on the susceptible population. It also accounts for under-reporting and its associated uncertainty via a two-stage estimation procedure with uncertainty propagation. The proposed model can be used to estimate the underlying susceptible population dynamics, assess how many susceptible people were immunized by past SIAs, and forecast incidence trends in the future under various hypothetical SIA scenarios. We examine model performance via simulations under various levels of under-reporting, and apply the model to analyze monthly reported measles incidence in Benin from 2012 to 2018.

Estimation of stillbirth rates globally is complicated because of the paucity of reliable data from countries where most stillbirths occur. We compiled data and developed a Bayesian hierarchical temporal sparse regression model for estimating stillbirth rates for all countries from 2000 to 2019. The model combines covariates with a temporal smoothing process so that estimates are data-driven in country-periods with high-quality data and deter-mined by covariates for country-periods with limited or no data. Horseshoepriors are used to encourage sparseness. The model adjusts observations with alternative stillbirth definitions and accounts for bias in observations that are subject to non-sampling errors. In-sample goodness of fit and out-of-sample validation results suggest that the model is reasonably well calibrated. The model is used by the UN Inter-agency Group for Child Mortality Estimation to monitor the stillbirth rate for all countries., Comment: 29 pages, 3 figures

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.

The increasing availability of complex survey data, and the continued need for estimates of demographic and health indicators at a fine spatial and temporal scale, which leads to issues of data sparsity, has led to the need for spatio-temporal smoothing methods that acknowledge the manner in which the data were collected. The open source R package SUMMER implements a variety of methods for spatial or spatio-temporal smoothing of survey data. The emphasis is on small-area estimation. We focus primarily on indicators in a low and middle-income countries context. Our methods are particularly useful for data from Demographic Health Surveys and Multiple Indicator Cluster Surveys. We build upon functions within the survey package, and use INLA for fast Bayesian computation. This paper includes a brief overview of these methods and illustrates the workflow of accessing and processing surveys, estimating subnational child mortality rates, and visualizing results with both simulated data and DHS surveys.

Despite substantial advances in global measles vaccination, measles disease burden remains high in many low- and middle-income countries. A key public health strategy for controling measles in such high-burden settings is to conduct supplementary immunization activities (SIAs) in the form of mass vaccination campaigns, in addition to delivering scheduled vaccination through routine immunization (RI) programs. To achieve balanced implementations of RI and SIAs, robust measurement of sub-national RI-specific coverage is crucial. In this paper, we develop a space-time smoothing model for estimating RI-specific coverage of the first dose of measles-containing-vaccines (MCV1) at sub-national level using complex survey data. The application that motivated this work is estimation of the RI-specific MCV1 coverage in Nigeria's 36 states and the Federal Capital Territory. Data come from four Demographic and Health Surveys, three Multiple Indicator Cluster Surveys, and two National Nutrition and Health Surveys conducted in Nigeria between 2003 and 2018. Our method incorporates information from the SIA calendar published by the World Health Organization and accounts for the impact of SIAs on the overall MCV1 coverage, as measured by cross-sectional surveys. The model can be used to analyze data from multiple surveys with different data collection schemes and construct coverage estimates with uncertainty that reflects the various sampling designs. Implementation of our method can be done efficiently using integrated nested Laplace approximation (INLA)., Comment: 19 pages, 10 figures

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., Comment: 53 pages, 27 figures

Current implementations of multiresolution methods are limited in terms of possible types of responses and approaches to inference. We provide a multiresolution approach for spatial analysis of non-Gaussian responses using latent Gaussian models and Bayesian inference via integrated nested Laplace approximation (INLA). The approach builds on `LatticeKrig', but uses a reparameterization of the model parameters that is intuitive and interpretable so that modeling and prior selection can be guided by expert knowledge about the different spatial scales at which dependence acts. The priors can be used to make inference robust and integration over model parameters allows for more accurate posterior estimates of uncertainty. The extended LatticeKrig (ELK) model is compared to a standard implementation of LatticeKrig (LK), and a standard Mat\'ern model, and we find modest improvement in spatial oversmoothing and prediction for the ELK model for counts of secondary education completion for women in Kenya collected in the 2014 Kenya demographic health survey. Through a simulation study with Gaussian responses and a realistic mix of short and long scale dependencies, we demonstrate that the differences between the three approaches for prediction increases with distance to nearest observation., Comment: main manuscript: 33 pages, 7 figures, 2 tables; supplemental materials: 9 pages, 3 figures, 5 tables

It is becoming increasingly popular to produce high-resolution maps of vaccination coverage by fitting Bayesian geostatistical models to data from household surveys. Often, 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 acknowledgment of the survey design in modeling, and the appropriate presentation of estimates and their uncertainties. Specifically, we consider the importance of accounting for survey 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 level. 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.

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., Comment: 16 pages, 4 figures, submitted to The Annals of Applied Statistics

There is an increasing focus on reducing inequalities in health outcomes in developing countries. Subnational variation is of particular interest, with geographic data 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, many others provide data that have their locations masked and instead only report the strata within which the data resides. How to harmonize these data sources for spatial analysis has seen previously considered though no method has been agreed upon and comparison of the validity of methods are lacking. In this paper, we present a new method for analyzing masked survey data alongside traditional geolocated data, using a method that is consistent with the data generating process. In addition, we critique two 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 spatial fields in a way that mimics the sampling frame implemented in the most common health surveys in low and middle income countries, the DHS and MICS. 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. Accurately increasing precision of child mortality estimates, and health estimates 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.

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., Comment: 67 pages, 22 pages of main text, the rest are appendices

The need for rigorous and timely health and demographic summaries has provided the impetus for an explosion in geographic studies, with a common approach being the production of pixel-level maps, particularly in low and middle income countries. In this context, household surveys are a major source of data, usually with a two-stage cluster design with stratification by region and urbanicity. Accurate estimates are of crucial interest for precision public health policy interventions, but many current studies take a cavalier approach to acknowledging the sampling design, while presenting results at a fine geographic scale. In this paper we investigate the extent to which accounting for sample design can affect predictions at the aggregate level, which is usually the target of inference. We describe a simulation study in which realistic sampling frames are created for Kenya, based on population and demographic information, with a survey design that mimics a Demographic Health Survey (DHS). We compare the predictive performance of various commonly-used models. We also describe a cluster level model with a discrete spatial smoothing prior that has not been previously used, but provides reliable inference. We find that including stratification and cluster level random effects can improve predictive performance. Spatially smoothed direct (weighted) estimates were robust to priors and survey design. Continuous spatial models performed well in the presence of fine scale variation; however, these models require the most "hand holding". Subsequently, we examine how the models perform on real data; specifically we model the prevalence of secondary education for women aged 20-29 using data from the 2014 Kenya DHS., Comment: Main text: 35 pages, 5 figures, 2 tables. Supplementary materials: 63 pages, 5 figures, 21 tables

The United Nations' Sustainable Development Goal 3.2 aims to reduce under-5 child mortality to 25 deaths per 1,000 live births by 2030. Child mortality tends to be concentrated in developing regions where much of the information needed to assess achievement of this goal 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 that uncertainty is reduced when incorporating SBH data over simply analyzing all available FBH data. We also apply our approach to data in the Central region of Malawi. We compare with the well-known Brass method., Comment: 50 pages, 18 figures

Accurate estimates of the under-5 mortality rate (U5MR) in a developing world context are a key barometer of the health of a nation. This paper describes new models to analyze survey data on mortality in this context. We are interested in both spatial and temporal description, that is, wishing to estimate U5MR across regions and years, and to investigate the association between the U5MR 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 demographic health surveys (DHS). We use a binomial likelihood with fixed effects for the urban/rural stratification to account for the complex survey design. We carry out smoothing 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 U5MR in the period 1980 - 2014, but large variability in estimated subnational rates remains. A priority for future research is understanding this variability. Temperature, precipitation and a measure of malaria infection prevalence were candidates for inclusion in the covariate model., Comment: 36 pages, 11 figures

In this chapter, we consider space-time analysis of surveillance count data. Such data are ubiquitous and a number of approaches have been proposed for their analysis. We first describe the aims of a surveillance endeavor, before reviewing and critiquing a number of common models. We focus on models in which time is discretized to the time scale of the latent and infectious periods of the disease under study. In particular, we focus on the time series SIR (TSIR) models originally described by Finkenstadt and Grenfell in their 2000 paper and the epidemic/endemic models first proposed by Held, Hohle, and Hofmann in their 2005 paper. We implement both of these models in the Stan software and illustrate their performance via analyses of measles data collected over a 2-year period in 17 regions in the Weser-Ems region of Lower Saxony, Germany., Comment: 31 pages, 7 figures. This is an author-created preprint of a book chapter to appear in the Handbook of Infectious Disease Data Analysis edited by Leonhard Held, Niel Hens, Philip D O'Neill and Jacco Wallinga, Chapman and Hall/CRC

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 this paper, we exploit recent theoretical and computational advances in continuous spatial modeling to carry out the reconstruction of an underlying continuous spatial surface. In particular, we focus on models based on stochastic partial differential equations (SPDEs). 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 estimate an underlying continuous risk surface for the classic Scottish lip cancer data., Comment: 39 pages, 11 figures