The Dangers of Drawing Cohort Profiles From Period Data: A Research Note.

Drawing cohort profiles and cohort forecasts from grids of age-period data is common practice in demography. In this research note, we (1) show how demographic measures artificially fluctuate when calculated from the diagonals of age-period rates because of timing and cohort-size bias, (2) estimate the magnitude of these biases, and (3) illustrate how prediction intervals for cohort indicators of mortality may become implausible when drawn from Lee-Carter methods and age-period grids. These biases are surprisingly large, even when the cohort profiles are created from single-age, single-year period data. The danger is that we overinterpret deviations from expected trends that were induced by our own data manipulation.

Evaluation of age-specific causes of death in the context of the Italian longevity transition.

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.

Drewnowski's index to measure lifespan variation: Revisiting the Gini coefficient of the life table.

The Gini coefficient of the life table is a concentration index that provides information on lifespan variation. Originally proposed by economists to measure income and wealth inequalities, it has been widely used in population studies to investigate variation in ages at death. We focus on the complement of the Gini coefficient, Drewnowski's index, which is a measure of equality. We study its mathematical properties and analyze how changes over time relate to changes in life expectancy. Further, we identify the threshold age below which mortality improvements are translated into decreasing lifespan variation and above which these improvements translate into increasing lifespan inequality. We illustrate our theoretical findings simulating scenarios of mortality improvement in the Gompertz model, and showing an example of application to Swedish life table data. Our experiments demonstrate how Drewnowski's index can serve as an indicator of the shape of mortality patterns. These properties, along with our analytical findings, support studying lifespan variation alongside life expectancy trends in multiple species.

Explaining regional differences in mortality during the first wave of Covid-19 in Italy.

Italy was hit harshly by the Covid-19 pandemic, registering more than 35,000 Covid-19 deaths between February and July 2020. During this first wave of the epidemic, the virus spread unequally across the country, with northern regions witnessing more cases and deaths. We investigate demographic and socio-economic factors contributing to the diverse regional impact of the virus during the first wave. Using generalized additive mixed models, we find that Covid-19 mortality at regional level is negatively associated with the degree of intergenerational co-residence, number of intensive care unit beds per capita, and delay in the outbreak of the epidemic. Conversely, we do not find strong associations for several variables highlighted in recent literature, such as population density or the share of the population who are older or have at least one chronic disease. Our results underscore the importance of context-specific analysis for the study of a pandemic.

Smoothing, Decomposing and Forecasting Mortality Rates.

The Lee-Carter (LC) model represents a landmark paper in mortality forecasting. While having been widely accepted and adopted, the model has some limitations that hinder its performance. Some variants of the model have been proposed to deal with these drawbacks individually, none coped with them all at the same time. In this paper, we propose a Three-Component smooth Lee-Carter (3C-sLC) model which overcomes many of the issues simultaneously. It decomposes mortality development into childhood, early-adult and senescent mortality, which are described, individually, by a smooth variant of the LC model. Smoothness is enforced to avoid irregular patterns in projected life tables, and complexity in the forecasting methodology is unaltered with respect to the original LC model. Component-specific schedules are considered in projections, providing additional insights into mortality forecasts. We illustrate the proposed approach to mortality data for ten low-mortality populations. The 3C-sLC captures mortality developments better than a smooth improved version of the LC model, and it displays wider prediction intervals. The proposed approach provides actuaries, demographers, epidemiologists and social scientists in general with a unique and valuable tool to simultaneously smooth, decompose and forecast mortality.

Assessing excess mortality in times of pandemics based on principal component analysis of weekly mortality data-the case of COVID-19.

The COVID-19 outbreak has called for renewed attention to the need for sound statistical analyses to monitor mortality patterns and trends over time. Excess mortality has been suggested as the most appropriate indicator to measure the overall burden of the pandemic in terms of mortality. As such, excess mortality has received considerable interest since the outbreak of COVID-19 began. Previous approaches to estimate excess mortality are somewhat limited, as they do not include sufficiently long-term trends, correlations among different demographic and geographic groups, or autocorrelations in the mortality time series. This might lead to biased estimates of excess mortality, as random mortality fluctuations may be misinterpreted as excess mortality. We propose a novel approach that overcomes the named limitations and draws a more realistic picture of excess mortality. Our approach is based on an established forecasting model that is used in demography, namely, the Lee-Carter model. We illustrate our approach by using the weekly age- and sex-specific mortality data for 19 countries and the current COVID-19 pandemic as a case study. Our findings show evidence of considerable excess mortality during 2020 in Europe, which affects different countries, age, and sex groups heterogeneously. Our proposed model can be applied to future pandemics as well as to monitor excess mortality from specific causes of death.

Linking excess mortality to mobility data during the first wave of COVID-19 in England and Wales.

Non-pharmaceutical interventions have been implemented worldwide to curb the spread of COVID-19. However, the effectiveness of such governmental measures in reducing the mortality burden remains a key question of scientific interest and public debate. In this study, we leverage digital mobility data to assess the effects of reduced human mobility on excess mortality, focusing on regional data in England and Wales between February and August 2020. We estimate a robust association between mobility reductions and lower excess mortality, after adjusting for time trends and regional differences in a mixed-effects regression framework and considering a five-week lag between the two measures. We predict that, in the absence of mobility reductions, the number of excess deaths could have more than doubled in England and Wales during this period, especially in the London area. The study is one of the first attempts to quantify the effects of mobility reductions on excess mortality during the COVID-19 pandemic.

Dynamics of life expectancy and life span equality.

As people live longer, ages at death are becoming more similar. This dual advance over the last two centuries, a central aim of public health policies, is a major achievement of modern civilization. Some recent exceptions to the joint rise of life expectancy and life span equality, however, make it difficult to determine the underlying causes of this relationship. Here, we develop a unifying framework to study life expectancy and life span equality over time, relying on concepts about the pace and shape of aging. We study the dynamic relationship between life expectancy and life span equality with reliable data from the Human Mortality Database for 49 countries and regions with emphasis on the long time series from Sweden. Our results demonstrate that both changes in life expectancy and life span equality are weighted totals of rates of progress in reducing mortality. This finding holds for three different measures of the variability of life spans. The weights evolve over time and indicate the ages at which reductions in mortality increase life expectancy and life span equality: the more progress at the youngest ages, the tighter the relationship. The link between life expectancy and life span equality is especially strong when life expectancy is less than 70 y. In recent decades, life expectancy and life span equality have occasionally moved in opposite directions due to larger improvements in mortality at older ages or a slowdown in declines in midlife mortality. Saving lives at ages below life expectancy is the key to increasing both life expectancy and life span equality.

Location-Scale Models in Demography: A Useful Re-parameterization of Mortality Models.

Several parametric mortality models have been proposed to describe the age pattern of mortality since Gompertz introduced his "law of mortality" almost two centuries ago. However, very few attempts have been made to reconcile most of these models within a single framework. In this article, we show that many mortality models used in the demographic and actuarial literature can be re-parameterized in terms of a general and flexible family of models, the family of location-scale (LS) models. These models are characterized by two parameters that have a direct demographic interpretation: the location and scale parameters, which capture the shifting and compression dynamics of mortality changes, respectively. Re-parameterizing a model in terms of the LS family has several advantages over its classic formulation. In addition to aiding parameter interpretability and comparability, the statistical estimation of the LS parameters is facilitated due to their significantly lower correlation. The latter, in turn, further improves parameter interpretability and reduces estimation bias. We show the advantages of the LS family over the typical parameterization of mortality models with two illustrations using the Human Mortality Database.

Modelling and forecasting adult age-at-death distributions.

Age-at-death distributions provide an informative description of the mortality pattern of a population but have generally been neglected for modelling and forecasting mortality. In this paper, we use the distribution of deaths to model and forecast adult mortality. Specifically, we introduce a relational model that relates a fixed 'standard' to a series of observed distributions by a transformation of the age axis. The proposed Segmented Transformation Age-at-death Distributions (STAD) model is parsimonious and efficient: using only three parameters, it captures and disentangles mortality developments in terms of shifting and compression dynamics. Additionally, mortality forecasts can be derived from parameter extrapolation using time-series models. We illustrate our method and compare it with the Lee-Carter model and variants for females in four high-longevity countries. We show that the STAD fits the observed mortality pattern very well, and that its forecasts are more accurate and optimistic than the Lee-Carter variants.

Diet has independent effects on the pace and shape of aging in Drosophila melanogaster.

Studies examining how diet affects mortality risk over age typically characterise mortality using parameters such as aging rates, which condense how much and how quickly the risk of dying changes over time into a single measure. Demographers have suggested that decoupling the tempo and the magnitude of changing mortality risk may facilitate comparative analyses of mortality trajectories, but it is unclear what biologically meaningful information this approach offers. Here, we determine how the amount and ratio of protein and carbohydrate ingested by female Drosophila melanogaster affects how much mortality risk increases over a time-standardised life-course (the shape of aging) and the tempo at which animals live and die (the pace of aging). We find that pace values increased as flies consumed more carbohydrate but declined with increasing protein consumption. Shape values were independent of protein intake but were lowest in flies consuming ~90 µg of carbohydrate daily. As protein intake only affected the pace of aging, varying protein intake rescaled mortality trajectories (i.e. stretched or compressed survival curves), while varying carbohydrate consumption caused deviation from temporal rescaling (i.e. changed the topography of time-standardised survival curves), by affecting pace and shape. Clearly, the pace and shape of aging may vary independently in response to dietary manipulation. This suggests that there is the potential for pace and shape to evolve independently of one another and respond to different physiological processes. Understanding the mechanisms responsible for independent variation in pace and shape, may offer insight into the factors underlying diverse mortality trajectories.

Longevity and concentration in survival times: the log-scale-location family of failure time models.

Evidence suggests that the increasing life expectancy levels at birth witnessed over the past centuries are associated with a decreasing concentration of the survival times. The purpose of this work is to study the relationships that exist between longevity and concentration measures for some regression models for the evolution of survival. In particular, we study a family of survival models that can be used to capture the observed trends in longevity and concentration over time. The parametric family of log-scale-location models is shown to allow for modeling different trends of expected value and concentration of survival times. An extension towards mixture models is also described in order to take into account scenarios where a fraction of the population experiences short term survival. Some results are also presented for such framework. The use of both the log-scale-location family and the mixture model is illustrated through an application to period life tables from the Human Mortality Database.