Incorporating testing volume into estimation of effective reproduction number dynamics.

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.

Rejoinder to the discussion on "The central role of the identifying assumption in population size estimation".

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 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 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.

A small area model to assess temporal trends and sub-national disparities in healthcare quality.

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.

Early effects of COVID-19 on maternal and child health service disruption in Mozambique.

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.

The WHO estimates of excess mortality associated with the COVID-19 pandemic.

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 20201. 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.

Incorporating testing volume into estimation of effective reproduction number dynamics.

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.

Global, regional, and national trends in under-5 mortality between 1990 and 2019 with scenario-based projections until 2030: a systematic analysis by the UN Inter-agency Group for Child Mortality Estimation.

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.

Combining information to estimate adherence in studies of pre-exposure prophylaxis for HIV prevention: Application to HPTN 067.

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.

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.

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.

Naomi: a new modelling tool for estimating HIV epidemic indicators at the district level in sub-Saharan Africa.

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.

Global, regional, and national estimates and trends in stillbirths from 2000 to 2019: a systematic assessment.

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.

Estimating seroprevalence of SARS-CoV-2 in Ohio: A Bayesian multilevel poststratification approach with multiple diagnostic tests.

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.

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.

Estimation of health and demographic indicators with incomplete geographic information.

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.

Modeling and presentation of vaccination coverage estimates using data from household surveys.

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.

Space-time modeling of child mortality at the Admin-2 level in a low and middle income countries context.

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.

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 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.

Child mortality estimation incorporating summary birth history data.

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.