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Ungrouping of the age-at-death distribution for neoplasms (A, log10(λ) = 6.5), diseases of the blood and blood-forming organs and disorders involving the immune mechanism (B, log10(λ) = 5.25), and infectious and parasitic diseases (C, log10(λ) = 5.25), United States, 2009. Histogram, original data from the Centers for Disease Control and Prevention database (black line with overplotted points) and results from ungrouping (solid gray line). Optimal values of the smoothing parameter were chosen by minimizing Akaike's Information Criterion.
Source publication
Ungrouping binned data can be desirable for many reasons: Bins can be too coarse to allow for accurate analysis; comparisons can be hindered when different grouping approaches are used in different histograms; and the last interval is often wide and open-ended and, thus, covers a lot of information in the tail area. Age group-specific disease incid...
Citations
... Demographers preparing inputs for a cohort-component model have an number of methods they can choose from within the four broad classes of parametric (Bermúdez et al., 2012;de Beer & Janssen, 2016;Wilson, 2020), polynomial (Campbell, 1996;Grigoriev & Jdanov, 2015;Hsieh, 1991;McNeil et al., 1977), relational (Booth, 1984;Brass, 1971;Smith et al., 2013), and non-parametric (Bernard & Bell, 2015;Kostaki et al., 2009Kostaki et al., , 2011Rizzi et al., 2015) methods. We have seen that for projecting the population of an SPA, a method must have a number of desirable features: producing plausible profiles in the presence of large uncertainty in observed rates (large noise), producing accurate profiles for the rest of the country (small noise), the ability to include non-polynomial features into the profile such as jumps or spikes in a rate (non-polynomial), flexibility in controlling the profile over an open age interval (extrapolate), the ability to include views on what a profile should look like (expert view), and the ability to handle deviations from orthodox profiles (flexibility). ...
Sparsely populated areas of developed countries are regions of great demographic diversity and dynamism. While they remain strategically and economically important, trends in urbanization and technology have increased their relative sparsity and isolation making centralized government, service delivery and planning a challenge. Populations of their sub-jurisdictions are small and often exhibit significant heterogeneity in key demographic characteristics, not least between their Indigenous first residents and non-Indigenous citizens. Development of projection models for these areas is challenged by significant input data paucity, biases and structural issues related to the data collection and estimation architectures in place to gather input data across diverse and small populations. While this is the case, the demand for and importance of projections is no less for sparsely populated areas than elsewhere. Variants of the cohort component model are important tools for population projections for SPAs, with their grounding in the demographic accounting equation and modest input requirements. Nevertheless, to attain fit-for-purpose input data requires demographers to consider and select from a growing number of methods for smoothing issues with input data for projections for these regions. In this article we analyze the contributions of recent advances in methods for estimating fertility, mortality, and migration rates for small and diverse populations such as those in SPAs, focusing on the very sparsely populated jurisdiction of the Northern Territory of Australia. In addition to the contributions of our method itself, results at the detailed level demonstrate how abnormal and challenging ‘doing’ projections for sparsely populated areas can be.
... Five-year abridged life tables were constructed for all the 27 countries, with 16 age groups ranging from 5 to 9 years to 85+ years. Given that the mortality data of the US are only available in 10-year intervals, this study used the ungrouping method proposed by Rizzi, Gampe, and Eilers (2015) to estimate 5-year-age-group death rate for the US. This technique has been recognised as producing satisfying results in ungrouping binned data (Rizzi et al., 2015) (for ungrouping results, see Supplementary Material 1). ...
... Given that the mortality data of the US are only available in 10-year intervals, this study used the ungrouping method proposed by Rizzi, Gampe, and Eilers (2015) to estimate 5-year-age-group death rate for the US. This technique has been recognised as producing satisfying results in ungrouping binned data (Rizzi et al., 2015) (for ungrouping results, see Supplementary Material 1). Life expectancy was estimated from age 5 years rather than from birth because mortality rates at age zero and at age 1-4 years were unavailable for 23 of the 27 countries, and the COVID-19 case fatality rate is almost negligible for children under the age of 5 years (Signorelli & Odone, 2020). ...
Background
The World Health Organization declared COVID-19 no longer a global health emergency on 5th May 2023; however, the impact of COVID-19 on life expectancy throughout the pandemic period is not clear. This study aimed to quantify and decompose the changes in life expectancy during 2019–2023 and corresponding age and gender disparities in 27 countries.
Methods
Data were sourced from the Human Mortality Database, the World Population Prospects 2022 and the United Kingdom's Office for National Statistics. Life expectancy was estimated using the abridged life table method, while differentials of life expectancies were decomposed using the age-decomposition algorithm.
Results
There was an overall reduction in life expectancy at age 5 among the 27 countries in 2020. Life expectancy rebounded in Western, Northern and Southern Europe in 2021 but further decreased in the United States, Chile and Eastern Europe in the same year. In 2022 and after, lost life expectancy years in the United States, Chile and Eastern Europe were slowly regained; however, as of 7th May 2023, life expectancy in 22 of the 27 countries had not fully recovered to its pre-pandemic level. The reduced life expectancy in 2020 was mainly driven by reduced life expectancy at age 65+, while that in subsequent years was mainly driven by reduced life expectancy at age 45–74. Women experienced a lower reduction in life expectancy at most ages but a greater reduction at age 85+.
Conclusions
The pandemic has caused substantial short-term mortality variations during 2019–2023 in the 27 countries studied. Although most of the 27 countries experienced increased life expectancy after 2022, life expectancy in 22 countries still has not entirely regained its pre-pandemic level by May 2023. Threats of COVID-19 are more prominent for older adults and men, but special attention is needed for women aged 85+ years.
... , it is assumed that the counts of deaths have a Poisson distribution with parameter eˆµ, where e and µ denote the vectors of central exposures and transition intensities, respectively. This assumption is commonly used with Penalized Composite Link Models, as in Eilers (2007), Remund et al. (2017) or Rizzi et al. (2015). Therefore, ...
... 15,358,195 7,603,377 7,754,752 7,767,493 3,801,601 3,965,935 778,521 77,977 154,355 85,490 51,165 169,733 95,372 72,100 statistics of deaths published by the ABS. 4 Given that the ABS only publishes annual statistics of death by place of birth in ten-year age group from age 5 years onwards (i.e. 0 year, 1-4 years, and ten-year age groups from 5 to 14 years to 75-84 years, and 85 years and older), this study uses the Penalized Composite Link Model, proposed by Rizzi et al. (2015), to ungroup the annual statistics of death into age-specific level (for ungrouped age-specific death number, see Supplementary Material 2). ...
Whether the ‘healthy migrant effect’ exhibits different patterns in mortality and morbidity and how such patterns change during the life course have not been adequately understood in the literature. Using the datasets of the Australian Bureau of Statistics, this study presents an in-depth investigation of the healthy migrant effect and its age variations in Australia. Specifically, this study estimates life expectancy (LE) and healthy life expectancy (HLE) of the Australia-born and overseas-born populations, as well as eight Australian migrant groups, and decomposes the HLE differences into mortality and morbidity differences from three dimensions: age, gender and country of birth. The results reveal that compared with the Australia-born population, the overseas-born population enjoys a prominently longer LE; however, they suffer a similar or lower HLE after age 65 and a lower HLE/LE ratio throughout all ages. Young overseas-born adults manifest a more significant health advantage in both mortality and morbidity than early-life and older overseas-born individuals; however, the morbidity advantage of young migrants, particularly those who are female and originated from culturally different countries, declines dramatically with ageing. The results suggest that overall, migrants do not have the same advantage in morbidity as they do in mortality and that health advantages of migrants decreases with time in both dimensions of health and more rapidly for morbidity. The results suggest that pertinent policies are needed to reduce acculturation-related challenges and to mitigate the decline in migrants’ health in the post-migration environment to ensure better quality of life outcomes of migrants.
... We ungrouped and re-aggregated age-specific death counts by cause using the well-established 'pclm' function from the 'ungroup' R package in order to derive SDRs based on the same age intervals as for the other countries. 27,28 Moreover, we rely on a regression-based approach for estimating the cause-specific contributions to the change in SMDs over time. This method was pioneered by Preston 29 and has been used for examining sex differences in mortality previously. ...
Background:
Male excess mortality is mostly related to non-biological factors, and is thus of high social- and health-policy concern. Previous research has mainly focused on national patterns, while subnational disparities have been less in the focus. This study takes a spatial perspective on subnational patterns, covering seven European countries at the crossroad between Eastern and Western Europe.
Methods:
We analyze a newly gathered spatially detailed data resource comprising 228 regions with well-established demographic methods to assess the contribution of specific causes of death to the evolution of sex mortality differentials (SMDs) since the mid-1990s.
Results:
Our results show that declines in SMDs were mostly driven by a reduction of male excess mortality from cardiovascular diseases and neoplasms (about 50-60% and 20-30%, respectively). In Western Europe, trends in deaths from neoplasms contributed more to the reduction of SMDs, while among regions located in Eastern-Central Europe narrowing SMDs were mostly driven by changes in cardiovascular disease-related deaths. Moreover, men show up to three times higher mortality levels from external causes as compared to women in several analyzed regions. But in absolute terms, external deaths play only a minor role in explaining SMDs due to their small contribution to overall mortality.
Conclusions:
We conclude that examining the regional development of SMDs is useful for introducing targeted social and health policies in order to reduce and prevent mortality inequalities between women and men.
... Under these conditions, spline methods can be used to derive a complete schedule from abridged data (Elandt-Johnson and Johnson 1980;Hsieh 1991;Wilmoth et al. 2007). Spline methods have also been extended to handle moderate levels of noise, using P-splines (Rizzi et al. 2015(Rizzi et al. , 2019. Relational methods borrow the age structure of rates from an existing complete schedule (the standard) and apply adjustments to fit abridged rates approximately (Brass 1971) or exactly (Kostaki 2000). ...
... If two methods differ in mean loss by more than five, then the one with the lower loss is more accurate than the other. We compare the performance of CS with the performance of a popular spline method (Elandt-Johnson and Johnson 1980), a relational method (Kostaki 2000), a parametric method (Heligman and Pollard 1980), a non-parametric method (Rizzi et al. 2015), and a hybrid parametric method (adjusted Heligman-Pollard; Kostaki 1991). Details of the procedures for fitting these alternative models are given in the Appendix. ...
... For Rizzi et al.'s (2015) Penalized Composite Link Model (PCLM) method, we used linear P-splines, a quadratic penalty optimized using the Akaike Information Criterion (Akaike 1974), and a population exposed to Estimating mortality with calibrated splines 5 the risk of dying given by a stationary distribution with total number 12.5 million, approximately the number of females/males in a population the size of Australia. Following Rizzi et al. (2015), we spaced spline knots one year apart, from age 0 to age 110. The results show that apart from Heligman-Pollard, the methods are equally accurate over the age range 20 to 80. Below age 20 the accuracy of Elandt-Johnson, PCLM, and Kostaki begins to degrade, while Heligman-Pollard shows relative improvement. ...
Demographers have developed a number of methods for expanding abridged mortality data into a complete schedule; however, these can be usefully applied only under certain conditions, and the presence or absence of one or more additional sources of incompleteness can degrade their relative accuracy, lead to implausible profiles, or even cause the methods to fail. We develop a new method for expanding an abridged schedule based on calibrated splines; this method is accurate and robust in the presence of errors in mortality rates, missing values, and truncation. We compare its performance with the performance of existing methods for expanding abridged data and find that it is superior to current methods at producing accurate and plausible complete schedules over a broad range of data-quality conditions. The method when applied is a valuable addition to existing tools for estimating mortality, especially for small nations, countries with incomplete vital statistics, and subnational populations.
... To end up with data by single year of age-in line with the HMD data and the aim of our analysis-we smoothed the age-specific deaths from WHO and the HCD and created an upper open-ended age group of 110+. For this purpose, in line with and Wensink et al. (2020), we used the efficient estimation of smooth distributions by Rizzi et al. (2015), which was implemented in the R package 'ungroup' (Pascariu et al. 2018). This smoothing technique maintains total deaths across ages for the different causes of death. ...
Much less is known about the sex gap in lifespan variation, which reflects inequalities in the length of life, than about the sex gap in life expectancy (average length of life). We examined the contributions of age groups and causes of death to the sex gap in lifespan variation for 28 European countries, grouped into five European regions. In 2010-15, males in Europe displayed a 6.8-year-lower life expectancy and a 2.3-year-higher standard deviation in lifespan than females, with clear regional differences. Sex differences in lifespan variation are attributable largely to higher external mortality among males aged 30-39, whereas sex differences in life expectancy are due predominantly to higher smoking-related and cardiovascular disease mortality among males aged 60-69. The distinct findings for the sex gap in lifespan variation and the sex gap in life expectancy provide additional insights into the survival differences between the sexes.
... We implement two existing non-parametric models to estimate age-specific death rates from raw death counts and exposures: 1) P-splines [Eilers and Marx, 1996], and 2) PCLM, the penalized composite link method [Rizzi et al., 2015]. Both methods share a common statistical basis, but the latter has been found particularly suitable for reconstructing the tail of a distribution. ...
... We finally use the observed exposures 85-109 from HMD to calculate corresponding age-specific death rates. Readers are referred to Rizzi et al. [2015] and Pascariu et al. [2018] for additional details. ...
Age-specific mortality improvements are non-uniform, neither across ages nor across time. We propose a two-step procedure to estimate the rates of mortality improvement (RMI) in age-specific death rates (ASDR) at ages 85 and above for ten European countries from 1950 to 2019. In the first step, we smooth the raw death counts and estimate ASDR using four different methods: one parametric (gamma-Gompertz-Makeham), two non-parametric (P-splines and PCLM), and a novel Bayesian procedure to handle fluctuations resulting from ages with zero death counts. We compare the goodness of fit of the four smoothing methods and calculate the year-to-year ASDR differences according to the best-fitting one. We fit a piecewise linear function to these differences in the second step. The slope in each linear segment captures the average RMI in the respective year range. For each age, we calculate the goodness of fit in the last linear segment to assess how informative the estimated RMI of current mortality change is. The estimated rates of mortality improvement or deterioration (RMI) can be used to make short-term social, health, and social planning, as well as more precise mortality forecasts.
... The use of grouped data might result in unre li able esti ma tions of sages and related mea sures. A pos si ble CORRECTED PROOFS approach to tackle this issue is to apply non para met ric mod els to ungroup binned data (Rizzi et al. 2015) before the cal cu la tion of sages. ...
Everyone has a chronological age. Because survivorship declines relentlessly in populations with age-specific death rates greater than zero, everyone also has a survivorship age ("s-age"), the age at which a proportion s of the population is still alive. S-ages can be estimated for both periods and cohorts. While trajectories of mortality over chronological ages differ (e.g., across populations, over time, by sex, or by any subpopulation), mortality trajectories over s-ages are similar, a sign that populations experience similar mortality dynamics at specific levels of survivorship. We show that this important demographic regularity holds for 23 sex-specific populations analyzed during a period comprising more than 100 years.
... Since cause-of-death data are available in 5-year age groups, we employ the Penalized Composite Link Model (PCLM) 34,35 to ungroup data into single years of age. The method is based on the composite link model 36 , with a penalty added to ensure the smoothness of the target distribution 37 . ...
In many low-mortality countries, life expectancy at birth increased steadily over the last century. In particular, both Italian females and males benefited from faster improvements in mortality compared to other high-income countries, especially from the 1960s, leading to an exceptional increase in life expectancy. However, Italy has not become the leader in longevity. Here, we investigate life expectancy trends in Italy during the period 1960–2015 for both sexes. Additionally, we contribute to the existing literature by complementing life expectancy with an indicator of dispersion in ages at death, also known as lifespan inequality. Lifespan inequality underlies heterogeneity over age in populating health improvements and is a marker of uncertainty in the timing of death. We further quantify the contributions of different age groups and causes of death to recent trends in life expectancy and lifespan inequality. Our findings highlight the contributions of cardiovascular diseases and neoplasms to the recent increase in life expectancy but not necessarily to the decrease in lifespan inequality. Our results also uncover a more recent challenge across Italy: worsening mortality from infectious diseases and mortality at older age.
