Global estimation of child mortality using a Bayesian B-spline Bias-reduction model

Estimates of the under-five mortality rate (U5MR) are used to track progress in reducing child mortality and to evaluate countries' performance related to Millennium Development Goal 4. However, for the great majority of developing countries without well-functioning vital registration systems, estimating the U5MR is challenging due to limited data availability and data quality issues. We describe a Bayesian penalized B-spline regression model for assessing levels and trends in the U5MR for all countries in the world, whereby biases in data series are estimated through the inclusion of a multilevel model to improve upon the limitations of current methods. B-spline smoothing parameters are also estimated through a multilevel model. Improved spline extrapolations are obtained through logarithmic pooling of the posterior predictive distribution of country-specific changes in spline coefficients with observed changes on the global level. The proposed model is able to flexibly capture changes in U5MR over time, gives point estimates and credible intervals reflecting potential biases in data series and performs reasonably well in out-of-sample validation exercises. It has been accepted by the United Nations Inter-agency Group for Child Mortality Estimation to generate estimates for all member countries.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS768 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Probabilistic projections of HIV prevalence using Bayesian melding

The Joint United Nations Programme on HIV/AIDS (UNAIDS) has developed the Estimation and Projection Package (EPP) for making national estimates and short-term projections of HIV prevalence based on observed prevalence trends at antenatal clinics. Assessing the uncertainty about its estimates and projections is important for informed policy decision making, and we propose the use of Bayesian melding for this purpose. Prevalence data and other information about the EPP model's input parameters are used to derive a probabilistic HIV prevalence projection, namely a probability distribution over a set of future prevalence trajectories. We relate antenatal clinic prevalence to population prevalence and account for variability between clinics using a random effects model. Predictive intervals for clinic prevalence are derived for checking the model. We discuss predictions given by the EPP model and the results of the Bayesian melding procedure for Uganda, where prevalence peaked at around 28% in 1990; the 95% prediction interval for 2010 ranges from 2% to 7%.Comment: Published at http://dx.doi.org/10.1214/07-AOAS111 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Probabilistic projections of HIV prevalence using Bayesian melding

The Joint United Nations Programme on HIV/AIDS (UNAIDS) has developed the Estimation and Projection Package (EPP) for making national estimates and short-term projections of HIV prevalence based on observed prevalence trends at antenatal clinics. Assessing the uncertainty about its estimates and projections is important for informed policy decision making, and we propose the use of Bayesian melding for this purpose. Prevalence data and other information about the EPP model's input parameters are used to derive a probabilistic HIV prevalence projection, namely a probability distribution over a set of future prevalence trajectories. We relate antenatal clinic prevalence to population prevalence and account for variability between clinics using a random effects model. Predictive intervals for clinic prevalence are derived for checking the model. We discuss predictions given by the EPP model and the results of the Bayesian melding procedure for Uganda, where prevalence peaked at around 28% in 1990; the 95% prediction interval for 2010 ranges from 2% to 7%.Comment: Published at http://dx.doi.org/10.1214/07-AOAS111 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Temporal models for demographic and global health outcomes in multiple populations: Introducing a new framework to review and standardize documentation of model assumptions and facilitate model comparison

There is growing interest in producing estimates of demographic and global health indicators in populations with limited data. Statistical models are needed to combine data from multiple data sources into estimates and projections with uncertainty. Diverse modeling approaches have been applied to this problem, making comparisons between models difficult. We propose a model class, Temporal Models for Multiple Populations (TMMPs), to facilitate documentation of model assumptions in a standardized way and comparison across models. The class distinguishes between latent trends and the observed data, which may be noisy or exhibit systematic biases. We provide general formulations of the process model, which describes the latent trend of the indicator of interest. We show how existing models for a variety of indicators can be written as TMMPs and how the TMMP-based description can be used to compare and contrast model assumptions. We end with a discussion of outstanding questions and future directions.Comment: 32 pages, 7 figure

Interview with Adrian Raftery

Professor Adrian E. Raftery is the Boeing International Professor of Statistics and Sociology, and an adjunct professor of Atmospheric Sciences, at the University of Washington in Seattle. He was born in Dublin, Ireland, and obtained a B.A. in Mathematics and an M.Sc. in Statistics and Operations Research at Trinity College Dublin. He obtained a doctorate in mathematical statistics from the Universit\'e Pierre et Marie Curie under the supervision of Paul Deheuvels. He was a lecturer in statistics at Trinity College Dublin, and then an associate and full professor of statistics and sociology at the University of Washington. He was the founding Director of the Center for Statistics and Social Sciences. Professor Raftery has published over 200 articles in peer-reviewed statistical, sociological and other journals. His research focuses on Bayesian model selection and Bayesian model averaging, model-based clustering, inference for deterministic models, and the development of new statistical methods for demography, sociology, and the environmental and health sciences. He is a member of the United States National Academy of Sciences, a Fellow of the American Academy of Arts and Sciences, an Honorary Member of the Royal Irish Academy, a member of the Washington State Academy of Sciences, a Fellow of the American Statistical Association, a Fellow of the Institute of Mathematical Statistics, and an elected Member of the Sociological Research Association. He has won multiple awards for his research. He was Coordinating and Applications Editor of the Journal of the American Statistical Association and Editor of Sociological Methodology. He was identified as the world's most cited researcher in mathematics for the period 1995-2005. Thirty-three students have obtained Ph.D.'s working under Raftery's supervision, of whom 21 hold or have held tenure-track university faculty positions.Comment: 17 pages, 8 figure

National, regional, and global sex ratios of infant, child, and under-5 mortality and identifi cation of countries with outlying ratios: a systematic assessment

Background Under natural circumstances, the sex ratio of male to female mortality up to the age of 5 years is greater than one but sex discrimination can change sex ratios. The estimation of mortality by sex and identifi cation of countries with outlying levels is challenging because of issues with data availability and quality, and because sex ratios might vary naturally based on diff erences in mortality levels and associated cause of death distributions. Methods For this systematic analysis, we estimated country-specifi c mortality sex ratios for infants, children aged 1–4 years, and children under the age of 5 years (under 5s) for all countries from 1990 (or the earliest year of data collection) to 2012 using a Bayesian hierarchical time series model, accounting for various data quality issues and assessing the uncertainty in sex ratios. We simultaneously estimated the global relation between sex ratios and mortality levels and constructed estimates of expected and excess female mortality rates to identify countries with outlying sex ratios. Findings Global sex ratios in 2012 were 1·13 (90% uncertainty interval 1·12–1·15) for infants, 0·95 (0·93–0·97) for children aged 1–5 years, and 1·08 (1·07–1·09) for under 5s, an increase since 1990 of 0·01 (–0·01 to 0·02) for infants, 0·04 (0·02 to 0·06) for children aged 1–4 years, and 0·02 (0·01 to 0·04) for under 5s. Levels and trends varied across regions and countries. Sex ratios were lowest in southern Asia for 1990 and 2012 for all age groups. Highest sex ratios were seen in developed regions and the Caucasus and central Asia region. Decreasing mortality was associated with increasing sex ratios, except at very low infant mortality, where sex ratios decreased with total mortality. For 2012, we identifi ed 15 countries with outlying under-5 sex ratios, of which ten countries had female mortality higher than expected (Afghanistan, Bahrain, Bangladesh, China, Egypt, India, Iran, Jordan, Nepal, and Pakistan). Although excess female mortality has decreased since 1990 for the vast majority of countries with outlying sex ratios, the ratios of estimated to expected female mortality did not change substantially for most countries, and worsened for India. Interpretation Important diff erences exist between boys and girls with respect to survival up to the age of 5 years. Survival chances tend to improve more rapidly for girls compared with boys as total mortality decreases, with a reversal of this trend at very low infant mortality. For many countries, sex ratios follow this pattern but important exceptions exist. An explanation needs to be sought for selected countries with outlying sex ratios and action should be undertaken if sex discrimination is present

Levels and trends in contraceptive prevalence, unmet need, and demand for family planning for 29 states and union territories in India: a modelling study using the Family Planning Estimation Tool

Background Improving access to reproductive health services and commodities is central to development. Eff orts to assess progress on this front have been largely focused on national estimates, but such analyses can mask local disparities. We assessed progress in reproductive health services subnationally in India. Methods We developed a statistical model to generate estimates and projections of levels and trends in family planning indicators for subpopulations. The model builds onto the UN Population Division’s Family Planning Estimation Model and uses data from multiple rounds of the Demographic and Health Survey, the District Level Household & Facility Survey, and the Annual Health Survey. We present annual estimates and projections of levels and trends in the prevalence of modern contraceptive use, and unmet need and demand for family planning for 29 states and union territories in India from 1990 to 2030. We also compared projections of demand satisfi ed with modern methods with the proposed goal of 75%. Findings There is a large amount of heterogeneity in India, with a diff erence of up to 55·1 percentage points (95% uncertainty interval 46·4–62·1) in modern contraceptive use in 2015 between subregions. States such as Andhra Pradesh, with 92·7% (90·9–94·2) demand satisfi ed with modern methods, are performing well above the national average (71·8%, 56·7–83·6), whereas Manipur, with 26·8% (16·7–38·5) of demand satisfi ed, and Meghalaya, with 45·0% (40·1–50·0), consistently lag behind the rest of the country. Manipur and Meghalaya require the highest percentage increase in modern contraceptive use to achieve 75% demand satisfi ed with modern methods by 2030. In terms of absolute numbers, Uttar Pradesh requires the greatest increase, needing 9·2 million (5·5–12·6 million) additional users of modern contraception by 2030 to meet the target of 75%. Interpretation The demand for family planning among the states and union territories in India is highly diverse. Greatest attention is needed in Uttar Pradesh, Manipur, and Meghalaya to meet UN targets. The analysis can be generalised to other countries as well as other subpopulations