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

Do senescent declines in elite tennis players differ across the sexes?

Aging is characterized by rising mortality, declining fertility and declines in physiological function with age (functional senescence). Sex differences in the tempo and severity of survival and fertility declines are widespread, but it is less clear how often and how much trajectories of functional senescence diverge between the sexes. We tested how physiological function changed with age in male and female elite tennis players using first-serve speed (power) and first-serve accuracy as performance measures. We found absolute differences between the sexes with men serving faster, but less accurately than women. Both power and accuracy showed senescent declines but these began earlier for power. There were signals of trait-compensation, where players with pronounced power declines showed relative increases in accuracy, which might partially buffer against power deterioration. However, there were no sex differences in how either trait changed with age, contrasting with other sports. Sex differences in functional senescence are probably shaped by interactions between natural and sexual selection, the proximate costs of trait expression and a trait’s genetic architecture, and so are highly trait-specific. We discuss the strengths and potential pitfalls of using data from elite athletes to disentangle these complex interactions

New Approaches in Mortality Modelling and Forecasting

Mortality modelling and forecasting are deeply rooted in demographic and actuarial sciences. Models to describe mortality patterns over age and time have long been used and developed since John Graunt (1662) introduced one of the first models of mortality, the life table. Forecasts of mortality have also been produced for many years: the first examples trace back to the beginning of the twentieth century, when English actuaries started to measure the financial burden of unanticipated longevity improvements on insurance and pension providers’ reserves. Today, the study of human mortality still occupies a central role in demographic and actuarial analyses. Most of the attention received by this area of research has been stimulated by two pressing challenges faced by modern societies: population ageing and longevity risk. According to the latest World Population Prospects, virtually every country of the world is experiencing growth in the number and proportion of older persons, resulting from continuous mortality and fertility declines (United Nations, 2019). Furthermore, the demographic transition has been impacting both public and private pension systems, whose retirement liabilities lie between $60 and$80 trillions in developed economies due to unexpected mortality improvements (Michaelson and Mulholland, 2014). Funding public policies and retirement products for the elderly becomes increasingly difficult as working-age populations shrink and dependency ratios increase worldwide. The enormous size of unexpected public and private retirement liabilities is the result of overly conservative forecasts of mortality during most recent decades. Despite the great advances in the field of mortality forecasting, including the shift from deterministic to stochastic approaches, currently and widely used methods have repeatedly failed to anticipate the sustained rate of mortality improvements observed in many low-mortality countries. The need for novel models that can predict longevity improvements more accurately than established methodologies is evident and timely. Therefore, this dissertation aims to bring new insights to the analysis and forecasting of human mortality by introducing novel statistical methods that offer different perspectives on mortality developments. This dissertation comprises six chapters, five of which are studies that have been devised to address this goal. Each study takes the form of a research manuscript, which has been published or submitted to scientific journals; furthermore, routines for reproducing the results presented in the thesis have been made publicly available. The first chapter introduces the basic notions and measuresemployedinthestudyofhumanmortality, reviewsthemaincontributionsinthehistory ofmodellingandforecastingmortality, and provides a short overview of the five studies developed in the thesis. In Chapter 2, we illustrate a general framework for modelling adult mortality that reconciles the well-known laws of mortality into a single flexible family. Re-parameterizing mortality models in terms of the proposed location–scale family has two important advantages: the model’s parameters have a direct demographic interpretation, and their estimation is more precise due to their lower correlation. From the third to the fifth chapters, the attention is shifted from mortality rates to age-atdeath distributions as an alternative, yet informative (and neglected), function for modelling and forecasting human mortality. Chapter 3 proposes a relational approach to model and forecast adult mortality by transforming the age-axis of a standard distribution of deaths. The proposed Segmented Transformation Age-at-death Distributions (STAD) model successfully captures mortality developments over age and time, and its forecasts are more accurate and optimistic than those obtained with the seminal Lee-Carter (LC) model (Lee and Carter, 1992) and its extensions. The STAD model is further employed and generalized in the following two chapters. In Chapter 4, the methodology is extended to the entire age-range. The age-pattern of mortality is first smoothly decomposed into three independent components that operate upon childhood, middle and old ages (as originally proposed by Thiele, 1871). The three components are then modelled and forecast with specialized versions of the STAD model. The resulting forecasts are shown to be more accurate and optimistic than those of traditional and well-established models. Chapter 5 presents a generalization and application of the STAD methodology for modelling and forecasting cohort mortality data. Models developed to forecast cohort data are very scarce in the literature, and our proposed approach allows us to precisely complete the mortality experience of partially observed cohorts. Finally, Chapter 6 proposes a new extension of the influential LC model that overcomes some of its known drawbacks. Working in a penalized composite link framework, we simultaneously smooth and decompose the mortality pattern into three independent components, which are modelled, estimated and forecast within an LC smooth framework. Fitted and forecast mortality profiles do not show the jaggedness typically displayed by the LC model; furthermore, mortality rates can vary more flexibly across age and time, as they result from a combination of three component-specific schedules of mortality changes

Epilocal: A real-time tool for local epidemic monitoring

BACKGROUND The novel coronavirus (SARS-CoV-2) emerged as a global threat at the beginning of 2020, spreading around the globe at different times and rates. Within a country, such differences provide the opportunity for strategic allocations of health care resources. OBJECTIVE We aim to provide a tool to estimate and visualize differences in the spread of the pandemic at the subnational level. Specifically, we focus on the case of Italy, a country that has been harshly hit by the virus. METHODS We model the number of SARS-CoV-2 reported cases and deaths as well as the number of hospital admissions at the Italian subnational level with Poisson regression. We employ parametric and nonparametric functional forms for the hazard function. In the parametric approach, model selection is performed using an automatic criterion based on the statistical significance of the estimated parameters and on goodness-of-fit assessment. In the nonparametric approach, we employ out-of-sample forecasting error minimization. RESULTS For each province and region, fitted models are plotted against observed data, demonstrating the appropriateness of the modeling approach. Moreover, estimated counts and rates of change for each outcome variable are plotted on maps of the country. This provides a direct visual assessment of the geographic distribution of risk areas as well as insights on the evolution of the pandemic over time. CONTRIBUTION The proposed Epilocal software provides researchers and policymakers with an open-access real-time tool to monitor the most recent trends of the COVID-19 pandemic in Italian regions and provinces with informative graphical outputs. The software is freely available and can be easily modified to fit other countries as well as future pandemics

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

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

Epilocal: a real-time tool for local epidemic monitoring

We describe Epilocal, a simple R program designed to automatically download the most recent data on reported infected SARS-CoV-2 cases for all Italian provinces and regions, and to provide a simple descriptive analysis. For each province the cumulative number of reported infected cases is available each day. In addition, the current numbers of hospitalized patients (separately for intensive care or not) and the cumulative number of deceased individuals are available at the region level. The data are analyzed through Poisson generalized linear models with logarithmic link function and polynomial regression on time. For cumulative data, we also consider a logistic parameterisation of the hazard function. Automatic model selection is performed to choose among the different model specifications, based on the statistical significance of the corresponding estimated parameters and on goodness-of-fit assessment. The chosen model is used to produce up-to-today estimates of the growth rate of the counts. Results are plotted on a map of the country to allow for a visual assessment of the geographic distribution of the areas with differential prevalence and rates of growth

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