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There is interest in learning about the causal effect of family planning (FP) on empowerment related outcomes. Experimental data related to this question are available from trials in which FP programs increase access to FP. While program assignment is unconfounded, FP uptake and subsequent empowerment may share common causes. We use principal stratification to estimate the causal effect of an intermediate FP outcome on a primary outcome of interest, among women affected by a FP program. Within strata defined by the potential reaction to the program, FP uptake is unconfounded. To minimize the need for parametric assumptions, we propose to use Bayesian Additive Regression Trees (BART) for modeling stratum membership and outcomes of interest. We refer to the combined approach as Prince BART. We evaluate Prince BART through a simulation study and use it to assess the causal effect of modern contraceptive use on employment in six cities in Nigeria, based on quasi-experimental data from a FP program trial during the first half of the 2010s. We show that findings differ between Prince BART and alternative modeling approaches based on parametric assumptions.

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 figures

Aggregate measures of family planning are used to monitor demand for and usage of contraceptive methods in populations globally, for example as part of the FP2030 initiative. Family planning measures for low- and middle-income countries are typically based on data collected through cross-sectional household surveys. Recently proposed measures account for sexual activity through assessment of the distribution of time-between-sex (TBS) in the population of interest. In this paper, we propose a statistical approach to estimate the distribution of TBS using data typically available in low- and middle-income countries, while addressing two major challenges. The first challenge is that timing of sex information is typically limited to women's time-since-last-sex (TSLS) data collected in the cross-sectional survey. In our proposed approach, we adopt the current duration method to estimate the distribution of TBS using the available TSLS data, from which the frequency of sex at the population level can be derived. Furthermore, the observed TSLS data are subject to reporting issues because they can be reported in different units and may be rounded off. To apply the current duration approach and account for these data reporting issues, we develop a flexible Bayesian model, and provide a detailed technical description of the proposed modeling approach.

Several demographic and health indicators, including the total fertility rate (TFR) and modern contraceptive use rate (mCPR), evolve similarly over time, characterized by a transition between stable states. Existing approaches for estimation or projection of transitions in multiple populations have successfully used parametric functions to capture the relation between the rate of change of an indicator and its level. However, incorrect parametric forms may result in bias or incorrect coverage in long-term projections. We propose a new class of models to capture demographic transitions in multiple populations. Our proposal, the B-spline Transition Model (BTM), models the relationship between the rate of change of an indicator and its level using B-splines, allowing for data-adaptive estimation of transition functions. Bayesian hierarchical models are used to share information on the transition function between populations. We apply the BTM to estimate and project country-level TFR and mCPR and compare the results against those from extant parametric models. For TFR, BTM projections have generally lower error than the comparison model. For mCPR, while results are comparable between BTM and a parametric approach, the B-spline model generally improves out-of-sample predictions. The case studies suggest that the BTM may be considered for demographic applications, Comment: 31 pages, 16 figures (not including supplementary material.)

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 figures

Accurate estimates of subnational populations are important for policy formulation and monitoring population health indicators. For example, estimates of the number of women of reproductive age are important to understand the population at risk to maternal mortality and unmet need for contraception. However, in many low-income countries, data on population counts and components of population change are limited, and so levels and trends subnationally are unclear. We present a Bayesian constrained cohort component model for the estimation and projection of subnational populations. The model builds on a cohort component projection framework, incorporates census data and estimates from the United Nation's World Population Prospects, and uses characteristic mortality schedules to obtain estimates of population counts and the components of population change, including internal migration. The data required as inputs to the model are minimal and available across a wide range of countries, including most low-income countries. The model is applied to estimate and project populations by county in Kenya for 1979-2019, and validated against the 2019 Kenyan census.

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

Unintended pregnancy and abortion estimates are needed to inform and motivate investment in global health programmes and policies. Variability in the availability and reliability of data poses challenges for producing estimates. We developed a Bayesian model that simultaneously estimates incidence of unintended pregnancy and abortion for 195 countries and territories. Our modelling strategy was informed by the proximate determinants of fertility with (i) incidence of unintended pregnancy defined by the number of women (grouped by marital and contraceptive use status) and their respective pregnancy rates, and (ii) abortion incidence defined by group-specific pregnancies and propensities to have an abortion. Hierarchical random walk models are used to estimate country-group-period-specific pregnancy rates and propensities to abort.

The sex ratio at birth (SRB) is defined as the ratio of male to female live births. The SRB imbalance in parts of the world over the past several decades is a direct consequence of sex-selective abortion, driven by the co-existence of son preference, readily available technology of prenatal sex determination, and fertility decline. Estimation and projection of the degree of SRB imbalance is complicated because of variability in SRB reference levels and because of the uncertainty associated with SRB observations. We develop Bayesian hierarchical time series mixture models for SRB estimation and scenario-based projections for all countries from 1950 to 2100. We model the SRB regional and national reference levels, and the fluctuation around national reference levels. We identify countries at risk of SRB imbalances and model both (i) the absence or presence of sex ratio transitions in such countries and, if present, (ii) the transition process. The transition model of SRB imbalance captures three stages (increase, stagnation and convergence back to SRB baselines). The model identifies countries with statistical evidence of SRB inflation in a fully Bayesian approach. The scenario-based SRB projections are based on the sex ratio transition model with varying assumptions regarding the occurrence of a sex ratio transition in at-risk countries. Projections are used to quantify the future burden of missing female births due to sex-selective abortions under different scenarios.

Civil registration vital statistics (CRVS) data are used to produce national estimates of maternal mortality, but are often subject to substantial reporting errors due to misclassification of maternal deaths. The accuracy of CRVS systems can be assessed by comparing CRVS-based counts of maternal and non-maternal deaths to those obtained from specialized studies, which are rigorous assessments of maternal mortality for a given country-period. We developed a Bayesian bivariate random walk model to estimate sensitivity and specificity of the reporting on maternal mortality in CRVS data, and associated CRVS adjustment factors. The model was fitted to a global data set of CRVS and specialized study data. Validation exercises suggest that the model performs well in terms of predicting CRVS-based proportions of maternal deaths for country-periods without specialized studies. The new model is used by the UN Maternal Mortality Inter-Agency Group to account for misclassification errors when estimating maternal mortality using CRVS data.

In recent years, much of the focus in monitoring child mortality has been on assessing changes in the under-five mortality rate (U5MR). However, as the U5MR decreases, the share of neonatal deaths (within the first month) tends to increase, warranting increased efforts in monitoring this indicator in addition to the U5MR. A Bayesian splines regression model is presented for estimating neonatal mortality rates (NMR) for all countries. In the model, the relationship between NMR and U5MR is assessed and used to inform estimates, and spline regression models are used to capture country-specific trends. As such, the resulting NMR estimates incorporate trends in overall child mortality while also capturing data-driven trends. The model is fitted to 195 countries using the database from the United Nations Interagency Group for Child Mortality Estimation, producing estimates from 1990, or earlier if data are available, until 2015. The results suggest that, above a U5MR of 34 deaths per 1000 live births, at the global level, a 1 per cent increase in the U5MR leads to a 0.6 per cent decrease in the ratio of NMR to U5MR. Below a U5MR of 34 deaths per 1000 live births, the proportion of deaths under-five that are neonatal is constant at around 54 per cent. However, the relationship between U5MR and NMR varies across countries. The model has now been adopted by the United Nations Inter-agency Group for Child Mortality Estimation.

The maternal mortality ratio (MMR) is defined as the number of maternal deaths in a population per 100,000 live births. Country-specific MMR estimates are published on a regular basis by the United Nations Maternal Mortality Estimation Inter-agency Group (UN MMEIG) to track progress in reducing maternal deaths and to evaluate regional and national performance related to Millennium Development Goal (MDG) 5, which calls for a 75% reduction in the MMR between 1990 and 2015. Until 2014, the UN MMEIG used a multilevel regression model for producing estimates for countries without sufficient data from vital registration systems. While this model worked well in the past to assess MMR levels for countries with limited data, it was deemed unsatisfactory for final MDG 5 reporting for countries where longer time series of observations had become available because by construction, estimated trends in the MMR were covariate-driven only and did not necessarily track data-driven trends. We developed a Bayesian maternal mortality estimation model, which extends upon the UN MMEIG multilevel regression model. The new model assesses data-driven trends through the inclusion of an ARIMA time series model that captures accelerations and decelerations in the rate of change in the MMR. Varying reporting and data quality issues are accounted for in source-specific data models. The revised model provides data-driven estimates of MMR levels and trends and will be used for MDG 5 reporting for all countries.

The United Nations regularly publishes projections of the populations of all the world's countries broken down by age and sex. These projections are the de facto standard and are widely used by international organizations, governments and researchers. Like almost all other population projections, they are produced using the standard deterministic cohort-component projection method and do not yield statements of uncertainty. We describe a Bayesian method for producing probabilistic population projections for most countries which are projections that the United Nations could use. It has at its core Bayesian hierarchical models for the total fertility rate and life expectancy at birth. We illustrate the method and show how it can be extended to address concerns about the UN's current assumptions about the long-term distribution of fertility. The method is implemented in the R packages bayesTFR, bayesLife, bayesPop and bayesDem., Comment: Published in at http://dx.doi.org/10.1214/13-STS419 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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)

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)