arXiv subjects

Jon Wakefield

Publications and source records attributed to Jon Wakefield.

At least 37 records · Page 2Linked to original sources

arXiv2023

Estimating Subnational Under-Five Mortality Rates Using a Spatio-Temporal Age-Period-Cohort Model

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.

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arXiv2023

Adaptive Gaussian Markov Random Fields for Child Mortality Estimation

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.

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arXiv2023

Small Area Estimation with Random Forests and the LASSO

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.

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arXiv2023

A Computationally Efficient Approach to Fully Bayesian Benchmarking

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.

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arXiv2022

Modeling Urban/Rural Fractions in Low- and Middle-Income Countries

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.

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arXiv2022

A spatial variance-smoothing area level model for small area estimation of demographic rates

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.

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arXiv2022

Smoothed Model-Assisted Small Area Estimation

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.

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arXiv2022

Spatial Aggregation with Respect to a Population Distribution

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.

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arXiv2022

The Central Role of the Identifying Assumption in Population Size Estimation

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.

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arXiv2022

Estimating Global and Country-Specific Excess Mortality During the COVID-19 Pandemic

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.

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arXiv2021

A Bayesian hierarchical small-area population model accounting for data source specific methodologies from American Community Survey, Population Estimates Program, and Decennial Census data

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.

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arXiv2021

Statistical implications of relaxing the homogeneous mixing assumption in time series Susceptible-Infectious-Removed models

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.

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arXiv2021

A flexible Bayesian framework to estimate age- and cause-specific child mortality over time from sample registration data

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.

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arXiv2021

A linear noise approximation for stochastic epidemic models fit to partially observed incidence counts

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.

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arXiv2021

A Statistical Introduction to Template Model Builder: A Flexible Tool for Spatial Modeling

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.

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arXiv2020

Harmonizing Child Mortality Data at Disparate Geographic Levels

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.

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arXiv2020

Estimating Seroprevalence of SARS-CoV-2 in Ohio: A Bayesian Multilevel Poststratification Approach with Multiple Diagnostic Tests

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.

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arXiv2020

A Probabilistic Model for Analyzing Summary Birth History Data

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.

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