The United Nations recently released population projections based on data until 2012 and a Bayesian probabilistic methodology. Analysis of these data reveals that, contrary to previous literature, world population is unlikely to stop growing this century. There is an 80% probability that world population, now 7.2 billion, will increase to between 9.6 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 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.The United Nations (UN) is the leading agency that projects world population into the future on a regular basis (2). Every two years it publishes revised data of the populations of all countries by age and sex, as well as fertility, mortality and migration rates, in a biennial publication called the World Population Prospects (WPP). In July 2014, probabilistic projections for individual countries to 2100 were released Unlike previous projections, they allow us to quantify our confidence in projected future trends using established methods of statistical inference. They are based on recent data, including the results of the 2010 round of censuses and recent surveys until 2012, as well as the most recent data on incidence, ‡

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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 65þ) will almost certainly decline dramatically in most countries over the coming decades.double logistic function | Lee-Carter method | life expectancy at birth | predictive distribution | United Nations World Population Prospects P rojections of countries' future populations, broken down by age and sex, are used by governments for social, economic, and infrastructure planning by international organizations for development planning and monitoring and global modeling, by the private sector for strategic and marketing decisions, and by academic and other researchers as inputs to social and health research.Most population projections are currently done deterministically, using the cohort component method (1, 2). This is an ageand sex-structured version of the basic demographic identity that the population of a country at the next time point is equal to the population at the current time point, plus the number of births, minus the number of deaths, plus the number of immigrants minus the number of emigrants. It was formulated in matrix form by Leslie (3) and is described in detail in ref. (4, chap. 6).Population projections are currently produced by many organizations, including national and local governments and private companies. The main organizations that have produced population projections for all or most of the world's countries are the United Nations (UN) (5), the World Bank (6), and the United States Census Bureau (7), all of which use the standard deterministic approach. Among these, the UN produces ...

We describe a Bayesian projection model to produce country-specific projections of the total fertility rate (TFR) for all countries. The model decomposes the evolution of TFR into three phases: pre-transition high fertility, the fertility transition, and post-transition low fertility. The model for the fertility decline builds on the United Nations Population Division’s current deterministic projection methodology, which assumes that fertility will eventually fall below replacement level. It models the decline in TFR as the sum of two logistic functions that depend on the current TFR level, and a random term. A Bayesian hierarchical model is used to project future TFR based on both the country’s TFR history and the pattern of all countries. It is estimated from United Nations estimates of past TFR in all countries using a Markov chain Monte Carlo algorithm. The post-transition low fertility phase is modeled using an autoregressive model, in which long-term TFR projections converge toward and oscillate around replacement level. The method is evaluated using out-of-sample projections for the period since 1980 and the period since 1995, and is found to be well calibrated.

In developed countries, mortality decline is decelerating at younger ages and accelerating at old ages, which we call a “rotation”. We expect that this rotation will also occur in developing countries as they attain high life expectancies. But the rotation is subtle and has proved difficult to handle in mortality models that include all age groups. Without taking it into account, however, long-term mortality projections will produce questionable results. Here we simplify the problem by focusing on the relative magnitude of death rates at two ages, 0 and 15–19, while making assumptions about changes in rates of decline at other ages. We extend the Lee-Carter method to incorporate this subtle rotation in projection. We suggest that the extended Lee-Carter method could provide plausible projections of the age pattern of mortality for populations that currently have very high life expectancies as well as others. Detailed examples are given using data from Japan and the US.

We propose a Bayesian hierarchical model for producing probabilistic forecasts of male period life expectancy at birth for all the countries of the world from the present to 2100. Such forecasts would be an input to the production of probabilistic population projections for all countries, which is currently being considered by the United Nations. To evaluate the method, we did an out-of-sample cross-validation experiment, fitting the model to the data from 1950–1995, and using the estimated model to forecast for the subsequent ten years. The ten-year predictions had a mean absolute error of about 1 year, about 40% less than the current UN methodology. The probabilistic forecasts were calibrated, in the sense that (for example) the 80% prediction intervals contained the truth about 80% of the time. We illustrate our method with results from Madagascar (a typical country with steadily improving life expectancy), Latvia (a country that has had a mortality crisis), and Japan (a leading country). We also show aggregated results for South Asia, a region with eight countries. Free publicly available software packages called and are available to implement the method.

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.

Summary Background Documentation of the demographic and geographical details of changes in cause-specific neonatal (younger than 1 month) and 1–59-month mortality in India can guide further progress in reduction of child mortality. In this study we report the changes in cause-specific child mortality between 2000 and 2015 in India. Methods Since 2001, the Registrar General of India has implemented the Million Death Study (MDS) in 1.3 million homes in more than 7000 randomly selected areas of India. About 900 non-medical surveyors do structured verbal autopsies for deaths recorded in these homes. Each field report is assigned randomly to two of 404 trained physicians to classify the cause of death, with a standard process for resolution of disagreements. We combined the proportions of child deaths according to the MDS for 2001–13 with annual UN estimates of national births and deaths (partitioned across India’s states and rural or urban areas) for 2000–15. We calculated the annual percentage change in sex-specific and cause-specific mortality between 2000 and 2015 for neonates and 1–59-month-old children. Findings The MDS captured 52 252 deaths in neonates and 42 057 deaths at 1–59 months. Examining specific causes, the neonatal mortality rate from infection fell by 66% from 11.9 per 1000 livebirths in 2000 to 4.0 per 1000 livebirths in 2015 and the rate from birth asphyxia or trauma fell by 76% from 9.0 per 1000 livebirths in 2000 to 2.2 per 1000 livebirths in 2015. At 1–59 months, the mortality rate from pneumonia fell by 63% from 11.2 per 1000 livebirths in 2000 to 4.2 per 1000 livebirths in 2015 and the rate from diarrhoea fell by 66% from 9.4 per 1000 livebirths in 2000 to 3.2 per 1000 livebirths in 2015 (with narrowing girl–boy gaps). The neonatal tetanus mortality rate fell from 1.6 per 1000 livebirths in 2000 to less than 0.1 per 1000 livebirths in 2015 and the 1–59-month measles mortality rate fell from 3.3 per 1000 livebirths in 2000 to 0.3 per 1000 livebirths in 2015. By contrast, mortality rates for prematurity or low birthweight rose from 12.3 per 1000 livebirths in 2000 to 14.3 per 1000 livebirths in 2015, driven mostly by increases in term births with low birthweight in poorer states and rural areas. 29 million cumulative child deaths occurred from 2000 to 2015. The average annual decline in mortality rates from 2000 to 2015 was 3.3% for neonates and 5.4% for children aged 1–59 months. Annual declines from 2005 to 2015 (3.4% decline for neonatal mortality and 5.9% decline in 1–59-month mortality) were faster than were annual declines from 2000 to 2005 (3.2% decline for neonatal mortality and 4.5% decline in 1–59-month mortality). These faster declines indicate that India avoided about 1 million child deaths compared with continuation of the 2000–05 declines. Interpretation To meet the 2030 Sustainable Development Goals for child mortality, India will need to maintain the current trajectory of 1–59-month mortality and accelerate declines in neonatal mortality (to >5% annually) from 2015 onwar...