Modeling Age Patterns of Under-5 Mortality: Results From a Log-Quadratic Model Applied to High-Quality Vital Registration Data.

Information about how the risk of death varies with age within the 0-5 age range represents critical evidence for guiding health policy. This study proposes a new model for summarizing regularities about how under-5 mortality is distributed by detailed age. The model is based on a newly compiled database that contains under-5 mortality information by detailed age in countries with high-quality vital registration systems, covering a wide array of mortality levels and patterns. It uses a log-quadratic approach in predicting a full mortality schedule between ages 0 and 5 on the basis of only one or two parameters. With its larger number of age-groups, the proposed model offers greater flexibility than existing models in terms of both entry parameters and model outcomes. We present applications of this model for evaluating and correcting under-5 mortality information by detailed age in countries with problematic mortality data.

Systematic assessment of the sex ratio at birth for all countries and estimation of national imbalances and regional reference levels.

The sex ratio at birth (SRB; ratio of male to female live births) imbalance in parts of the world over the past few decades is a direct consequence of sex-selective abortion, driven by the coexistence of son preference, readily available technology of prenatal sex determination, and fertility decline. Estimation of the degree of SRB imbalance is complicated because of unknown SRB reference levels and because of the uncertainty associated with SRB observations. There are needs for reproducible methods to construct SRB estimates with uncertainty, and to assess SRB inflation due to sex-selective abortion. We compile an extensive database from vital registration systems, censuses and surveys with 10,835 observations, and 16,602 country-years of information from 202 countries. We develop Bayesian methods for SRB estimation for all countries from 1950 to 2017. We model the SRB regional and national reference levels, the fluctuation around national reference levels, and the inflation. The estimated regional reference levels range from 1.031 (95% uncertainty interval [1.027; 1.036]) in sub-Saharan Africa to 1.063 [1.055; 1.072] in southeastern Asia, 1.063 [1.054; 1.072] in eastern Asia, and 1.067 [1.058; 1.077] in Oceania. We identify 12 countries with strong statistical evidence of SRB imbalance during 1970-2017, resulting in 23.1 [19.0; 28.3] million missing female births globally. The majority of those missing female births are in China, with 11.9 [8.5; 15.8] million, and in India, with 10.6 [8.0; 13.6] million.

Probabilistic projection of subnational total fertility rates.

BACKGROUND: We consider the problem of probabilistic projection of the total fertility rate (TFR) for subnational regions. OBJECTIVE: We seek a method that is consistent with the UN's recently adopted Bayesian method for probabilistic TFR projections for all countries and works well for all countries. METHODS: We assess various possible methods using subnational TFR data for 47 countries. RESULTS: We find that the method that performs best in terms of out-of-sample predictive performance and also in terms of reproducing the within-country correlation in TFR is a method that scales each national trajectory from the national predictive posterior distribution by a region-specific scale factor that is allowed to vary slowly over time. CONCLUSIONS: Probabilistic projections of TFR for subnational units are best produced by scaling the national projection by a slowly time-varying region-specific scale factor. This supports the hypothesis of Watkins (1990, 1991) that within-country TFR converges over time in response to country-specific factors, and thus extends the Watkins hypothesis to the last 50 years and to a much wider range of countries around the world. CONTRIBUTION: We have developed a new method for probabilistic projection of subnational TFR that works well and outperforms other methods. This also sheds light on the extent to which within-country TFR converges over time.

Global, regional, and national levels and trends in under-5 mortality between 1990 and 2015, with scenario-based projections to 2030: a systematic analysis by the UN Inter-agency Group for Child Mortality Estimation.

BACKGROUND: In 2000, world leaders agreed on the Millennium Development Goals (MDGs). MDG 4 called for a two-thirds reduction in the under-5 mortality rate between 1990 and 2015. We aimed to estimate levels and trends in under-5 mortality for 195 countries from 1990 to 2015 to assess MDG 4 achievement and then intended to project how various post-2015 targets and observed rates of change will affect the burden of under-5 deaths from 2016 to 2030. METHODS: We updated the UN Inter-agency Group for Child Mortality Estimation (UN IGME) database with 5700 country-year datapoints. As of July, 2015, the database contains about 17 000 country-year datapoints for mortality of children younger than 5 years for 195 countries, and includes all available nationally-representative data from vital registration systems, population censuses, household surveys, and sample registration systems. We used these data to generate estimates, with uncertainty intervals, of under-5 (age 0-4 years) mortality using a Bayesian B-spline bias-reduction model (B3 model). This model includes a data model to adjust for systematic biases associated with different types of data sources. To provide insights into the global and regional burden of under-5 deaths associated with post-2015 targets, we constructed five scenario-based projections for under-5 mortality from 2016 to 2030 and estimated national, regional, and global under-5 mortality rates up to 2030 for each scenario. RESULTS: The global under-5 mortality rate has fallen from 90·6 deaths per 1000 livebirths (90% uncertainty interval 89·3-92·2) in 1990 to 42·5 (40·9-45·6) in 2015. During the same period, the annual number of under-5 deaths worldwide dropped from 12·7 million (12·6 million-13·0 million) to 5·9 million (5·7 million-6·4 million). The global under-5 mortality rate reduced by 53% (50-55%) in the past 25 years and therefore missed the MDG 4 target. Based on point estimates, two regions-east Asia and the Pacific, and Latin America and the Caribbean-achieved the MDG 4 target. 62 countries achieved the MDG 4 target, of which 24 were low-income and lower-middle income countries. Between 2016 and 2030, 94·4 million children are projected to die before the age of 5 years if the 2015 mortality rate remains constant in each country, and 68·8 million would die if each country continues to reduce its mortality rate at the pace estimated from 2000 to 2015. If all countries achieve the Sustainable Development Goal of an under-5 mortality rate of 25 or fewer deaths per 1000 livebirths by 2030, we project 56·0 million deaths by 2030. About two-thirds of all sub-Saharan African countries need to accelerate progress to achieve this target. INTERPRETATION: Despite substantial progress in reducing child mortality, concerted efforts remain necessary to avoid preventable under-5 deaths in the coming years and to accelerate progress in improving child survival further. Urgent actions are needed most in the regions and countries with high under-5 mortality rates, particularly those in sub-Saharan Africa and south Asia. FUNDING: None.

Bayesian population reconstruction of female populations for less developed and more developed countries.

We show that Bayesian population reconstruction, a recent method for estimating past populations by age, works for data of widely varying quality. Bayesian reconstruction simultaneously estimates age-specific population counts, fertility rates, mortality rates, and net international migration flows from fragmentary data, while formally accounting for measurement error. As inputs, Bayesian reconstruction uses initial bias-reduced estimates of standard demographic variables. We reconstruct the female populations of three countries: Laos, a country with little vital registration data where population estimation depends largely on surveys; Sri Lanka, a country with some vital registration data; and New Zealand, a country with a highly developed statistical system and good quality vital registration data. In addition, we extend the method to countries without censuses at regular intervals. We also use it to assess the consistency of results between model life tables and available census data, and hence to compare different model life table systems.

Bayesian probabilistic population projections for all countries.

Projections of countries' future populations, broken down by age and sex, are widely used for planning and research. They are mostly done deterministically, but there is a widespread need for probabilistic projections. We propose a bayesian method for probabilistic population projections for all countries. The total fertility rate and female and male life expectancies at birth are projected probabilistically using bayesian hierarchical models estimated via Markov chain Monte Carlo using United Nations population data for all countries. These are then converted to age-specific rates and combined with a cohort component projection model. This yields probabilistic projections of any population quantity of interest. The method is illustrated for five countries of different demographic stages, continents and sizes. The method is validated by an out of sample experiment in which data from 1950-1990 are used for estimation, and applied to predict 1990-2010. The method appears reasonably accurate and well calibrated for this period. The results suggest that the current United Nations high and low variants greatly underestimate uncertainty about the number of oldest old from about 2050 and that they underestimate uncertainty for high fertility countries and overstate uncertainty for countries that have completed the demographic transition and whose fertility has started to recover towards replacement level, mostly in Europe. The results also indicate that the potential support ratio (persons aged 20-64 per person aged 65+) will almost certainly decline dramatically in most countries over the coming decades.

Bayesian Population Projections for the United Nations.

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 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.

Joint Probabilistic Projection of Female and Male Life Expectancy.

BACKGROUND: The United Nations (UN) produces population projections for all countries every two years. These are used by international organizations, governments, the private sector and researchers for policy planning, for monitoring development goals, as inputs to economic and environmental models, and for social and health research. The UN is considering producing fully probabilistic population projections, for which joint probabilistic projections of future female and male life expectancy at birth are needed. OBJECTIVE: We propose a methodology for obtaining joint probabilistic projections of female and male life expectancy at birth. METHODS: We first project female life expectancy using a one-sex method for probabilistic projection of life expectancy. We then project the gap between female and male life expectancy. We propose an autoregressive model for the gap in a future time period for a particular country, which is a function of female life expectancy and a t-distributed random perturbation. This method takes into account mortality data limitations, is comparable across countries, and accounts for shocks. We estimate all parameters based on life expectancy estimates for 1950-2010. The methods are implemented in the bayesLife and bayesPop R packages. RESULTS: We evaluated our model using out-of-sample projections for the period 1995-2010, and found that our method performed better than several possible alternatives. CONCLUSIONS: We find that the average gap between female and male life expectancy has been increasing for female life expectancy below 75, and decreasing for female life expectancy above 75. Our projections of the gap are lower than the UN's 2008 projections for most countries and so lead to higher projections of male life expectancy.

AIDS exceptionalism: another constituency heard from.

Amidst current debates over resources for AIDS, we examine the policy preferences of the people who are navigating AIDS in their daily lives. Survey and ethnographic data on the prioritization of HIV/AIDS interventions were collected in a longitudinal cohort study in rural Malawi. Study participants gave higher priority to problems other than AIDS. Confining analysis to HIV-positive survey respondents only weakly raises the prioritization of HIV/AIDS services. The ethnographic data are consistent with these findings: although rural Malawians are fully aware of the risk of dying from AIDS, other problems are perceived as more pressing for their community.

Child mortality estimation: a global overview of infant and child mortality age patterns in light of new empirical data.

BACKGROUND: The under-five mortality rate (the probability of dying between birth and age 5 y, also denoted in the literature as U5MR and (5)q(0)) is a key indicator of child health, but it conceals important information about how this mortality is distributed by age. One important distinction is what amount of the under-five mortality occurs below age 1 y ((1)q(0)) versus at age 1 y and above ((4)q(1)). However, in many country settings, this distinction is often difficult to establish because of various types of data errors. As a result, it is common practice to resort to model age patterns to estimate (1)q(0) and (4)q(1) on the basis of an observed value of (5)q(0). The most commonly used model age patterns for this purpose are the Coale and Demeny and the United Nations systems. Since the development of these models, many additional sources of data for under-five mortality have become available, making possible a general evaluation of age patterns of infant and child mortality. In this paper, we do a systematic comparison of empirical values of (1)q(0) and (4)q(1) against model age patterns, and discuss whether observed deviations are due to data errors, or whether they reflect true epidemiological patterns not addressed in existing model life tables. METHODS AND FINDINGS: We used vital registration data from the Human Mortality Database, sample survey data from the World Fertility Survey and Demographic and Health Surveys programs, and data from Demographic Surveillance Systems. For each of these data sources, we compared empirical combinations of (1)q(0) and (4)q(1) against combinations provided by Coale and Demeny and United Nations model age patterns. We found that, on the whole, empirical values fall relatively well within the range provided by these models, but we also found important exceptions. Sub-Saharan African countries have a tendency to exhibit high values of (4)q(1) relative to (1)q(0), a pattern that appears to arise for the most part from true epidemiological causes. While this pattern is well known in the case of western Africa, we observed that it is more widespread than commonly thought. We also found that the emergence of HIV/AIDS, while perhaps contributing to high relative values of (4)q(1), does not appear to have substantially modified preexisting patterns. We also identified a small number of countries scattered in different parts of the world that exhibit unusually low values of (4)q(1) relative to (1)q(0), a pattern that is not likely to arise merely from data errors. Finally, we illustrate that it is relatively common for populations to experience changes in age patterns of infant and child mortality as they experience a decline in mortality. CONCLUSIONS: Existing models do not appear to cover the entire range of epidemiological situations and trajectories. Therefore, model life tables should be used with caution for estimating (1)q(0) and (4)q(1) on the basis of (5)q(0). Moreover, this model-based estimation procedure assumes that the input value of (5)q(0) is correct, which may not always be warranted, especially in the case of survey data. A systematic evaluation of data errors in sample surveys and their impact on age patterns of (1)q(0) and (4)q(1) is urgently needed, along with the development of model age patterns of under-five mortality that would cover a wider range of epidemiological situations and trajectories. Please see later in the article for the Editors' Summary.

Estimating trends in the total fertility rate with uncertainty using imperfect data: Examples from West Africa.

BACKGROUND: Estimating the total fertility rate is challenging for many developing countries because of limited data and varying data quality. A standardized, reproducible approach to produce estimates that include an uncertainty assessment is desired. METHODS: We develop a method to estimate and assess uncertainty in the total fertility rate over time, based on multiple imperfect observations from different data sources, including surveys and censuses. We take account of measurement error in observations by decomposing it into bias and variance, and assess both by linear regression on a variety of data quality covariates. We estimate the total fertility rate using a local smoother, and assess uncertainty using the weighted likelihood bootstrap. RESULTS: We apply our method to data from seven countries in West Africa and construct estimates and uncertainty intervals for the total fertility rate. Based on cross-validation exercises, we find that accounting for differences in data quality between observations gives better calibrated confidence intervals and reduces bias. CONCLUSIONS: When working with multiple imperfect observations from different data sources to estimate the total fertility rate, or demographic indicators in general, potential biases and differences in error variance should be taken into account to improve the estimates and their uncertainty assessment.

Divergent age patterns of under-5 mortality in south Asia and sub-Saharan Africa: a modelling study.

BACKGROUND: Understanding the age pattern of under-5 mortality is essential for identifying the most vulnerable ages and underlying causes of death, and for assessing why the decline in child mortality is slower in some countries and subnational areas than others. The aim of this study is to detect age patterns of under-5 mortality that are specific to low-income and middle-income countries (LMICs). METHODS: In this modelling study, we used data from 277 Demographic and Health Surveys (DHSs), 58 Health and Demographic Surveillance Systems (HDSSs), two cohort studies, and two sample-registration systems. From these sources, we collected child date of birth and date of death (or age at death) from LMICs between 1966 and 2020. We computed 22 deaths rates from each survey with the following age breakdowns: 0, 7, 14, 21, and 28 days; 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, and 21 months; and 2, 3, 4, and 5 years. We assessed how probabilities of dying estimated for the 22 age groups deviated from predictions generated by a vital registration model that reflects the historical mortality of 25 high-income countries. FINDINGS: We calculated mortality rates of 81 LMICs between 1966 and 2020. In contrast with the other regions of the world, we found that under-5 mortality in south Asia and sub-Saharan Africa was characterised by increased mortality at both ends of the age range (ie, younger than 28 days and older than 6 months) at a given level of mortality. Observed mortality in these regions was up to 2 times higher than predicted by the vital registration model for the younger-than-28 days age bracket, and up to 10 times higher than predicted for the older-than-6 months age bracket. This age pattern of under-5 mortality is significant in 17 countries in south Asia and sub-Saharan Africa. Excess mortality in children older than 6 months without excess mortality in children younger than 28 days was found in 38 countries. In south Asia, results were consistent across data sources. In sub-Saharan Africa, excess mortality in children younger than 28 days was found mostly in DHSs; the majority of HDSSs did not show this excess mortality. We have attributed this difference in data sources mainly to omissions of early deaths in HDSSs. INTERPRETATION: In countries with age patterns of under-5 mortality that diverge from predictions, evidence-based public health interventions should focus on the causes of excess of mortality; notably, the effect of fetal growth restriction and infectious diseases. The age pattern of under-5 mortality will be instrumental in assessing progress towards the decline of under-5 mortality and the Sustainable Development Goals. FUNDING: Eunice Kennedy Shriver National Institute of Child Health and Human Development of the National Institutes of Health.

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.

Projecting sex imbalances at birth at global, regional and national levels from 2021 to 2100: scenario-based Bayesian probabilistic projections of the sex ratio at birth and missing female births based on 3.26 billion birth records.

INTRODUCTION: Skewed levels of the sex ratio at birth (SRB) due to sex-selective abortions have been observed in several countries since the 1970s. They will lead to long-term sex imbalances in more than one-third of the world's population with yet unknown social and economic impacts on affected countries. Understanding the potential evolution of sex imbalances at birth is therefore essential for anticipating and planning for changing sex structures across the world. METHODS: We produced probabilistic SRB projections from 2021 to 2100 based on different scenarios of sex ratio transition and assessed their implications in terms of missing female births at global, regional and national levels. Based on a comprehensive SRB database with 3.26 billion birth records, we project the skewed SRB and missing female births with a Bayesian hierarchical time series mixture model. The SRB projections under reference scenario S1 assumed SRB transitions only for countries with strong statistical evidence of SRB inflation, and the more extreme scenario S2 assumed a sex ratio transition for countries at risk of SRB inflation but with no or limited evidence of ongoing inflation. RESULTS: Under scenario S1, we projected 5.7 (95% uncertainty interval (1.2; 15.3)) million additional missing female births to occur by 2100. Countries affected will be those already affected in the past by imbalanced SRB, such as China and India. If all countries at risk of SRB inflation experience a sex ratio transition as in scenario S2, the projected missing female births increase to 22.1 (12.2; 39.8) million with a sizeable contribution of sub-Saharan Africa. CONCLUSION: The scenario-based projections provide important illustrations of the potential burden of future prenatal sex discrimination and the need to monitor SRBs in countries with son preference. Policy planning will be needed in the years to come to minimise future prenatal sex discrimination and its impact on social structures.

Global, regional, and national mortality trends in youth aged 15-24 years between 1990 and 2019: a systematic analysis.

BACKGROUND: The global health community is devoting considerable attention to adolescents and young people, but risk of death in this population is poorly measured. We aimed to reconstruct global, regional, and national mortality trends for youths aged 15-24 years between 1990 and 2019. METHODS: In this systematic analysis, we used all publicly available data on mortality in the age group 15-24 years for 195 countries, as compiled by the UN Inter-agency Group for Child Mortality Estimation. We used nationally representative vital registration data, estimated the completeness of death registration, and extracted mortality rates from surveys with sibling histories, household deaths reported in censuses, and sample registration systems. We used a Bayesian B-spline bias-reduction model to generate trends in 10q15, the probability that an adolescent aged 15 years would die before reaching age 25 years. This model treats observations of the 10q15 probability as the product of the actual risk of death and an error multiplier that varies depending on the data source. The main outcome that we assessed was the levels of and trends in youth mortality and the global and regional mortality rates from 1990 to 2019. FINDINGS: Globally, the probability of an individual dying between age 15 years and 24 years was 11·2 deaths (90% uncertainty interval [UI] 10·7-12·5) per 1000 youths aged 15 in 2019, which is about 2·5 times less than infant mortality (28·2 deaths [27·2-30·0] by age 1 year per 1000 live births) but is higher than the risk of dying from age 1 to 5 (9·7 deaths [9·1-11·1] per 1000 children aged 1 year). The probability of dying between age 15 years and 24 years declined by 1·4% per year (90% UI 1·1-1·8) between 1990 and 2019, from 17·1 deaths (16·5-18·9) per 1000 in 1990; by contrast with this total decrease of 34% (27-41), under-5 mortality declined by 59% (56-61) in this period. The annual number of deaths declined from 1·7 million (90% UI 1·7-1·9) in 1990 to 1·4 million (1·3-1·5) in 2019. In sub-Saharan Africa, the number of deaths increased by 20·8% from 1990 to 2019. Although 18·3% of the population aged 15-24 years were living in sub-Saharan Africa in 2019, the region accounted for 37·9% (90% UI 34·8-41·9) of all worldwide deaths in youth. INTERPRETATION: It is urgent to accelerate progress in reducing youth mortality. Efforts are particularly needed in sub-Saharan Africa, where the burden of mortality is increasingly concentrated. In the future, a growing number of countries will see youth mortality exceeding under-5 mortality if current trends continue. FUNDING: UN Children's Fund, Bill & Melinda Gates Foundation, United States Agency for International Development.

Modelling HIV epidemics in the antiretroviral era: the UNAIDS Estimation and Projection package 2009.

OBJECTIVE: The UNAIDS Estimation and Projection Package (EPP) is a tool for country-level estimation and short-term projection of HIV/AIDS epidemics based on fitting observed HIV surveillance data on prevalence. This paper describes the adaptations made in EPP 2009, the latest version of this tool, as new issues have arisen in the global response, in particular the global expansion of antiretroviral therapy (ART). RESULTS: By December 2008 over 4 million people globally were receiving ART, substantially improving their survival. EPP 2009 required modifications to correctly adjust for the effects of ART on incidence and the resulting increases in HIV prevalence in populations with high ART coverage. Because changing incidence is a better indicator of program impact, the 2009 series of UNAIDS tools also focuses on calculating incidence alongside prevalence. Other changes made in EPP 2009 include: an improved procedure, incremental mixture importance sampling, for efficiently generating more accurate uncertainty estimates; provisions to vary the urban/rural population ratios in generalised epidemics over time; introduction of a modified epidemic model that accommodates behaviour change in low incidence settings; and improved procedures for calibrating models. This paper describes these changes in detail, and discusses anticipated future changes in the next version of EPP.

Hotspots and Coldspots: Household and village-level variation in orphanhood prevalence in rural Malawi.

We explore the characteristics of households and villages in which orphans are resident in two areas of Malawi. We first review pertinent themes in qualitative data collected in our research sites. Then, using spatial analysis, we show how positive and negative clusters of orphans - which we term orphanhood "hotspots" and "coldspots" - can be found at the village and sub-village levels. In the third and longest section of the paper, and using multilevel analyses with both simple and complex variance structures, we evaluate the relationship between the presence of orphans and a range of individual, household and village-level characteristics, including households' spatial relationship to each other and to other local sites of significance. This series of analyses shows that the most important covariates of orphan presence are household size, wealth, and religious characteristics, with all measured simultaneously at both household and village-level. In addition, most of these have heterogenous effects across villages. We conclude by reviewing some difficulties in explaining causal mechanisms underlying these observed relationships, and discuss conceptual, theoretical and programmatic implications.

Probabilistic population aging.

We merge two methodologies, prospective measures of population aging and probabilistic population forecasts. We compare the speed of change and variability in forecasts of the old age dependency ratio and the prospective old age dependency ratio as well as the same comparison for the median age and the prospective median age. While conventional measures of population aging are computed on the basis of the number of years people have already lived, prospective measures are computed also taking account of the expected number of years they have left to live. Those remaining life expectancies change over time and differ from place to place. We compare the probabilistic distributions of the conventional and prospective measures using examples from China, Germany, Iran, and the United States. The changes over time and the variability of the prospective indicators are smaller than those that are observed in the conventional ones. A wide variety of new results emerge from the combination of methodologies. For example, for Germany, Iran, and the United States the likelihood that the prospective median age of the population in 2098 will be lower than it is today is close to 100 percent.