Bayesian inference under cluster sampling with probability proportional to size.

Cluster sampling is common in survey practice, and the corresponding inference has been predominantly design based. We develop a Bayesian framework for cluster sampling and account for the design effect in the outcome modeling. We consider a two-stage cluster sampling design where the clusters are first selected with probability proportional to cluster size, and then units are randomly sampled inside selected clusters. Challenges arise when the sizes of the nonsampled cluster are unknown. We propose nonparametric and parametric Bayesian approaches for predicting the unknown cluster sizes, with this inference performed simultaneously with the model for survey outcome, with computation performed in the open-source Bayesian inference engine Stan. Simulation studies show that the integrated Bayesian approach outperforms classical methods with efficiency gains, especially under informative cluster sampling design with small number of selected clusters. We apply the method to the Fragile Families and Child Wellbeing study as an illustration of inference for complex health surveys.

A Bayesian evidence synthesis approach to estimate disease prevalence in hard-to-reach populations: hepatitis C in New York City.

Existing methods to estimate the prevalence of chronic hepatitis C (HCV) in New York City (NYC) are limited in scope and fail to assess hard-to-reach subpopulations with highest risk such as injecting drug users (IDUs). To address these limitations, we employ a Bayesian multi-parameter evidence synthesis model to systematically combine multiple sources of data, account for bias in certain data sources, and provide unbiased HCV prevalence estimates with associated uncertainty. Our approach improves on previous estimates by explicitly accounting for injecting drug use and including data from high-risk subpopulations such as the incarcerated, and is more inclusive, utilizing ten NYC data sources. In addition, we derive two new equations to allow age at first injecting drug use data for former and current IDUs to be incorporated into the Bayesian evidence synthesis, a first for this type of model. Our estimated overall HCV prevalence as of 2012 among NYC adults aged 20-59 years is 2.78% (95% CI 2.61-2.94%), which represents between 124,900 and 140,000 chronic HCV cases. These estimates suggest that HCV prevalence in NYC is higher than previously indicated from household surveys (2.2%) and the surveillance system (2.37%), and that HCV transmission is increasing among young injecting adults in NYC. An ancillary benefit from our results is an estimate of current IDUs aged 20-59 in NYC: 0.58% or 27,600 individuals.

The Millennium Villages Project: a retrospective, observational, endline evaluation.

BACKGROUND: The Millennium Villages Project (MVP) was a 10 year, multisector, rural development project, initiated in 2005, operating across ten sites in ten sub-Saharan African countries to achieve the Millennium Development Goals (MDGs). In this study, we aimed to estimate the project's impact, target attainment, and on-site spending. METHODS: In this endline evaluation of the MVP, we retrospectively selected comparison villages that best matched the project villages on possible confounding variables. Cross-sectional survey data on 40 outcomes of interest were collected from both the project and the comparison villages in 2015. Using these data, as well as on-site spending data collected during the project, we estimated project impacts as differences in outcomes between the project and comparison villages; target attainment as differences between project outcomes and prespecified targets; and on-site spending as expenditures reported by communities, donors, governments, and the project. Spending data were not collected in the comparison villages. FINDINGS: Averaged across the ten project sites, we found that impact estimates for 30 of 40 outcomes were significant (95% uncertainty intervals [UIs] for these outcomes excluded zero) and favoured the project villages. In particular, substantial effects were seen in agriculture and health, in which some outcomes were roughly one SD better in the project villages than in the comparison villages. The project was estimated to have no significant impact on the consumption-based measures of poverty, but a significant favourable impact on an index of asset ownership. Impacts on nutrition and education outcomes were often inconclusive (95% UIs included zero). Averaging across outcomes within categories, the project had significant favourable impacts on agriculture, nutrition, education, child health, maternal health, HIV and malaria, and water and sanitation. A third of the targets were met in the project sites. Total on-site spending decreased from US$132 per person in the first half of the project (of which $66 was from the MVP) to $109 per person in the second half of the project (of which $25 was from the MVP). INTERPRETATION: The MVP had favourable impacts on outcomes in all MDG areas, consistent with an integrated rural development approach. The greatest effects were in agriculture and health, suggesting support for the project's emphasis on agriculture and health systems strengthening. The project conclusively met one third of its targets. FUNDING: The Open Society Foundations, the Islamic Development Bank, and the governments of Japan, South Korea, Mali, Senegal, and Uganda.

Social sector expenditure and child mortality in India: a state-level analysis from 1997 to 2009.

BACKGROUND: India is unlikely to meet the Millennium Development Goal for child mortality. As public policy impacts child mortality, we assessed the association of social sector expenditure with child mortality in India. METHODS AND FINDINGS: Mixed-effects regression models were used to assess the relationship of state-level overall social sector expenditure and its major components (health, health-related, education, and other) with mortality by sex among infants and children aged 1-4 years from 1997 to 2009, adjusting for potential confounders. Counterfactual models were constructed to estimate deaths averted due to overall social sector increases since 1997. Increases in per capita overall social sector expenditure were slightly higher in less developed than in more developed states from 1997 to 2009 (2.4-fold versus 2-fold), but the level of expenditure remained 36% lower in the former in 2009. Increase in public expenditure on health was not significantly associated with mortality reduction in infants or at ages 1-4 years, but a 10% increase in health-related public expenditure was associated with a 3.6% mortality reduction (95% confidence interval 0.2-6.9%) in 1-4 years old boys. A 10% increase in overall social sector expenditure was associated with a mortality reduction in both boys (6.8%, 3.5-10.0%) and girls (4.1%, 0.8-7.5%) aged 1-4 years. We estimated 119,807 (95% uncertainty interval 53,409-214,662) averted deaths in boys aged 1-4 years and 94,037 (14,725-206,684) in girls in India in 2009 that could be attributed to increases in overall social sector expenditure since 1997. CONCLUSIONS: Further reduction in child mortality in India would be facilitated if policymakers give high priority to the social sector as a whole for resource allocation in the country's 5-year plan for 2012-2017, as public expenditure on health alone has not had major impact on reducing child mortality.

Determinants of condom uptake among HIV voluntary counselling and testing clients: experiences from a hospital-based study in south India.

BACKGROUND: HIV voluntary counselling and testing was a key HIV prevention strategy brought to scale by India's National AIDS Control Organization. Condom uptake is an essential metric of intervention impact given the expansion of the epidemic into an increasingly diverse population. With only 20% of first-time counselling and testing clients at the largest HIV treatment hospital in south India reporting previous condom use, the question of intervention impact on condom use deserves investigation. In this study, we track intervention impact across various demographic groups and identify the added value of more thorough counselling. METHODS: Data were collected from 8,865 individuals who attended counselling multiple times at the Tamil Nadu Government Hospital of Thoracic Medicine over the years 2004-2009. Counsellors recorded client demographic characteristics, HIV risk behaviours reported, and counselling services provided after each counselling session. Matching and regression methods were used to determine the probability of condom uptake by serostatus, gender, and receipt of personalized risk reduction counselling while controlling for other characteristics. RESULTS: HIV counselling and testing was associated with condom uptake among 29.2% of HIV positive women (CI 24.5-34.4%), 31.7% of HIV positive men (CI 27.8-35.4%), 15.5% of HIV negative women (CI 11.2-20.8%), and only 3.6% of HIV negative men (CI 1.9-5.9%) who had previously never used condoms. Personalized risk reduction counselling increased impact in some groups; for example an additional 18% of HIV negative women (CI 11.3-24.4%) and 17% of HIV positive men (CI 10.9-23.4%) started using condoms. The number of sexual partners was not associated with the impact of counselling completeness. CONCLUSIONS: Because the components of testing and counselling impact the condom use habits of men and women differently, understanding the dynamics of condom use negotiation between partners is essential to optimizing impact on Indian couples. Clients' predicted condom uptake ranged between 4% and 47% depending on factors like gender, serostatus, and services provided. Personalized risk reduction counselling is associated with increased chance of condom use, with larger gains in HIV negative women and HIV positive men. HIV negative men are least likely to start using condoms and least impacted by additional counselling.

Algorithms for enhancing public health utility of national causes-of-death data.

BACKGROUND: Coverage and quality of cause-of-death (CoD) data varies across countries and time. Valid, reliable, and comparable assessments of trends in causes of death from even the best systems are limited by three problems: a) changes in the International Statistical Classification of Diseases and Related Health Problems (ICD) over time; b) the use of tabulation lists where substantial detail on causes of death is lost; and c) many deaths assigned to causes that cannot or should not be considered underlying causes of death, often called garbage codes (GCs). The Global Burden of Disease Study and the World Health Organization have developed various methods to enhance comparability of CoD data. In this study, we attempt to build on these approaches to enhance the utility of national cause-of-death data for public health analysis. METHODS: Based on careful consideration of 4,434 country-years of CoD data from 145 countries from 1901 to 2008, encompassing 743 million deaths in ICD versions 1 to 10 as well as country-specific cause lists, we have developed a public health-oriented cause-of-death list. These 56 causes are organized hierarchically and encompass all deaths. Each cause has been mapped from ICD-6 to ICD-10 and, where possible, they have also been mapped to the International List of Causes of Death 1-5. We developed a typology of different classes of GCs. In each ICD revision, GCs have been identified. Target causes to which these GCs should be redistributed have been identified based on certification practice and/or pathophysiology. Proportionate redistribution, statistical models, and expert algorithms have been developed to redistribute GCs to target codes for each age-sex group. RESULTS: The fraction of all deaths assigned to GCs varies tremendously across countries and revisions of the ICD. In general, across all country-years of data available, GCs have declined from more than 43% in ICD-7 to 24% in ICD-10. In some regions, such as Australasia, GCs in 2005 are as low as 11%, while in some developing countries, such as Thailand, they are greater than 50%. Across different age groups, the composition of GCs varies tremendously - three classes of GCs steadily increase with age, but ambiguous codes within a particular disease chapter are also common for injuries at younger ages. The impact of redistribution is to change the number of deaths assigned to particular causes for a given age-sex group. These changes alter ranks across countries for any given year by a number of different causes, change time trends, and alter the rank order of causes within a country. CONCLUSIONS: By mapping CoD through different ICD versions and redistributing GCs, we believe the public health utility of CoD data can be substantially enhanced, leading to an increased demand for higher quality CoD data from health sector decision-makers.

Maternal mortality for 181 countries, 1980-2008: a systematic analysis of progress towards Millennium Development Goal 5.

BACKGROUND: Maternal mortality remains a major challenge to health systems worldwide. Reliable information about the rates and trends in maternal mortality is essential for resource mobilisation, and for planning and assessment of progress towards Millennium Development Goal 5 (MDG 5), the target for which is a 75% reduction in the maternal mortality ratio (MMR) from 1990 to 2015. We assessed levels and trends in maternal mortality for 181 countries. METHODS: We constructed a database of 2651 observations of maternal mortality for 181 countries for 1980-2008, from vital registration data, censuses, surveys, and verbal autopsy studies. We used robust analytical methods to generate estimates of maternal deaths and the MMR for each year between 1980 and 2008. We explored the sensitivity of our data to model specification and show the out-of-sample predictive validity of our methods. FINDINGS: We estimated that there were 342,900 (uncertainty interval 302,100-394,300) maternal deaths worldwide in 2008, down from 526,300 (446,400-629,600) in 1980. The global MMR decreased from 422 (358-505) in 1980 to 320 (272-388) in 1990, and was 251 (221-289) per 100,000 livebirths in 2008. The yearly rate of decline of the global MMR since 1990 was 1.3% (1.0-1.5). During 1990-2008, rates of yearly decline in the MMR varied between countries, from 8.8% (8.7-14.1) in the Maldives to an increase of 5.5% (5.2-5.6) in Zimbabwe. More than 50% of all maternal deaths were in only six countries in 2008 (India, Nigeria, Pakistan, Afghanistan, Ethiopia, and the Democratic Republic of the Congo). In the absence of HIV, there would have been 281 500 (243,900-327,900) maternal deaths worldwide in 2008. INTERPRETATION: Substantial, albeit varied, progress has been made towards MDG 5. Although only 23 countries are on track to achieve a 75% decrease in MMR by 2015, countries such as Egypt, China, Ecuador, and Bolivia have been achieving accelerated progress. FUNDING: Bill & Melinda Gates Foundation.