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.

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.

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.

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.

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.

Age patterns and sex ratios of adult mortality in countries with high HIV prevalence.

OBJECTIVE: To compare the 2016 United Nations Programme on HIV/AIDS (UNAIDS) modelled estimates of adult mortality in sub-Saharan Africa to empirical estimates. DESIGN: Age-specific mortality rates were obtained from nationally representative sibling survival data, recent household deaths and vital registration, and directly compared with UNAIDS estimates. Orphanhood prevalence derived from UNAIDS mortality estimates was compared with survey and census reports on the survival of children's parents. METHODS: Age-specific mortality rates for adults aged 15-59 years were calculated from Demographic and Health Surveys and deaths reported in censuses or vital registration, adjusted for underreporting, whenever possible. Proportions of orphans were extracted from censuses and surveys for children aged 5-9 years. RESULTS: UNAIDS estimates were significantly higher than sibling mortality estimates, except among men in countries with very high HIV prevalence. There was a better agreement between rates based on household deaths or vital registration and model outputs. Sex ratios (M/F) of adult mortality were lower in UNAIDS estimates. The modelled orphan prevalence was significantly higher than in surveys and censuses, again with the exception of paternal orphans in countries with very high HIV prevalence. Ratios of paternal-to-maternal orphans were lower in the UNAIDS model than surveys and censuses. Among women, increases in mortality due to AIDS were more concentrated in the age range 25-50 years in model outputs, as compared with empirical estimates. CONCLUSION: Discrepancies in levels, sex ratios and age patterns of adult mortality between empirical and UNAIDS estimates call for additional data quality assessments and improvements in estimation methods.

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.

The United Nations Probabilistic Population Projections: An Introduction to Demographic Forecasting with Uncertainty.

The United Nations publishes projections of populations around the world and breaks these down by age and sex. Traditionally, they are produced with standard demographic methods based on assumptions about future fertility rates, survival probabilities, and migration counts. Such projections, however, were not accompanied by formal statements of uncertainty expressed in probabilistic terms. In July 2014 the UN for the first time issued official probabilistic population projections for all countries to 2100. These projections quantify uncertainty associated with future fertility and mortality trends worldwide. This review article summarizes the probabilistic population projection methods and presents forecasts for population growth over the rest of this century.

Age-specific and sex-specific adult mortality risk in India in 2014: analysis of 0·27 million nationally surveyed deaths and demographic estimates from 597 districts.

BACKGROUND: As child mortality decreases rapidly worldwide, premature adult mortality is becoming an increasingly important contributor to global mortality. Any possible worldwide reduction of premature adult mortality before the age of 70 years will depend on progress in India. Indian districts increasingly have responsibility for implementing public health programmes. We aimed to assess age-specific and sex-specific adult mortality risks in India at the district level. METHODS: We analysed data from five national surveys of 0·27 million adult deaths at an age of 15-69 years together with 2014 demographic data to estimate age-specific and sex-specific adult mortality risks for 597 districts. Cause of death data were drawn from the verbal autopsies in the Registrar General of India's ongoing Million Death Study. FINDINGS: In 2014, about two-fifths of India's men aged 15-69 years lived in the 253 districts where the conditional probability of a man dying at these ages exceeded 50%, and more than a third of India's women aged 15-69 years lived in the 222 districts where the conditional probability of a woman dying exceeded 40%. The probabilities of a man or woman dying by the age of 70 years in high-mortality districts was 62% and 54%, respectively, whereas the probability of a man or woman dying by the age of 70 years in low-mortality districts was 40% and 30%, respectively. The roughly 10-year survival gap between high-mortality and low-mortality districts was nearly as extreme as the survival gap between the entire Indian population and people living in high-income countries. Adult mortality risks at ages 15-69 years was highest in east India and lowest in west India, by contrast with the north-south divide for child mortality. Vascular disease, tuberculosis, malaria and other infections, and respiratory diseases accounted for about 60% of the absolute gap in adult mortality risk at ages 15-69 years between high-mortality and low-mortality districts. Most of the variation in adult mortality could not be explained by known determinants or risk factors for premature mortality. INTERPRETATION: India's large variation in adult mortality by district, notably the higher death rates in eastern India, requires further aetiological research, particularly to explore whether high levels of adult mortality risks from infections and non-communicable diseases are a result of historical childhood malnutrition and infection. Such research can be complemented by an expanded coverage of known effective interventions to reduce adult mortality, especially in high-mortality districts. FUNDING: National Institutes of Health, Canadian Institutes of Health Research, University of Toronto.

Bayesian Reconstruction of Two-Sex Populations by Age: Estimating Sex Ratios at Birth and Sex Ratios of Mortality.

The original version of Bayesian reconstruction, a method for estimating age-specific fertility, mortality, migration and population counts of the recent past with uncertainty, produced estimates for female-only populations. Here we show how two-sex populations can be similarly reconstructed and probabilistic estimates of various sex ratio quantities obtained. We demonstrate the method by reconstructing the populations of India from 1971 to 2001, Thailand from 1960 to 2000, and Laos from 1985 to 2005. We found evidence that in India, sex ratio at birth exceeded its conventional upper limit of 1.06, and, further, increased over the period of study, with posterior probability above 0.9. In addition, almost uniquely, we found evidence that life expectancy at birth (e0) was lower for females than for males in India (posterior probability for 1971-1976 equal to 0.79), although there was strong evidence for a narrowing of the gap through to 2001. In both Thailand and Laos, we found strong evidence for the more usual result that e0 was greater for females and, in Thailand, that the difference increased over the period of study.

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.

Letter to the Editor: Probabilistic population forecasts for informed decision making.

Demographic forecasts are inherently uncertain. Nevertheless, an appropriate description of this uncertainty is a key underpinning of informed decision making. In recent decades various methods have been developed to describe the uncertainty of future populations and their structures, but the uptake of such tools amongst the practitioners of official population statistics has been lagging behind. In this letter we revisit the arguments for the practical uses of uncertainty assessments in official population forecasts, and address their implications for decision making. We discuss essential challenges, both for the forecasters and forecast users, and make recommendations for the official statistics community.

World population stabilization unlikely this century.

The United Nations (UN) recently released population projections based on data until 2012 and a Bayesian probabilistic methodology. Analysis of these data reveals that, contrary to previous literature, the world population is unlikely to stop growing this century. There is an 80% probability that world population, now 7.2 billion people, will increase to between 9.6 billion and 12.3 billion in 2100. This uncertainty is much smaller than the range from the traditional UN high and low variants. Much of the increase is expected to happen in Africa, in part due to higher fertility rates and a recent slowdown in the pace of fertility decline. Also, the ratio of working-age people to older people is likely to decline substantially in all countries, even those that currently have young populations.

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.