Thirty years on: A review of the Lee–Carter method for forecasting mortality

Basellini, Ugofilippo; Camarda, Carlo Giovanni; Booth, Heather

doi:10.1016/j.ijforecast.2022.11.002

Cited by 26 publications

(7 citation statements)

References 72 publications

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“…Since in low mortality countries, mortality decline is decelerating at younger ages and accelerating at older ages [ 56 ], the static assumption of mortality decline of traditional Lee-Carter model would be anomalous in long-term projection. LC_ER is a time-varying Lee-Carter model considering the changes of mortality decline between different age groups when modeling, which was widely recognized and adopted by World Population Prospects 2022 [ 57 , 58 ]. Therefore, potential LTCI demands change caused by changes in old-age mortality decline in long-term projections could be captured by LC_ER.…”

Section: Methodsmentioning

confidence: 99%

Life expectancy, long-term care demand and dynamic financing mechanism simulation: an empirical study of Zhejiang Pilot, China

Xu,

Li,

2024

BMC Health Serv Res

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Background China has piloted Long-Term Care Insurance (LTCI) to address increasing care demand. However, many cities neglected adjusting LTCI premiums since the pilot, risking the long-term sustainability of LTCI. Therefore, using Zhejiang Province as a case, this study simulated mortality-adjusted long-term care demand and the balance of LTCI funds through dynamic financing mechanism under diverse life expectancy and disability scenarios. Methods Three-parameter log-quadratic model was used to estimate the mortality from 1990 to 2020. Mortality with predicted interval from 2020 to 2080 was projected by Lee-Carter method extended with rotation. Cohort-component projection model was used to simulate the number of older population with different degrees of disability. Disability data of the older people is sourced from China Health and Retirement Longitudinal Study 2018. The balance of LTCI fund was simulated by dynamic financing actuarial model. Results Life expectancy of Zhejiang for male (female) is from 80.46 (84.66) years in 2020 to 89.39 [86.61, 91.74] (91.24 [88.90, 93.25]) years in 2080. The number of long-term care demand with severe disability in Zhejiang demonstrates an increasing trend from 285 [276, 295] thousand in 2023 to 1027 [634, 1657] thousand in 2080 under predicted mean of life expectancy. LTCI fund in Zhejiang will become accumulated surplus from 2024 to 2080 when annual premium growth rate is 5.25% [4.20%, 6.25%] under various disability scenarios, which is much higher than the annual growth of unit cost of long-term care services (2.25%). The accumulated balance of LTCI fund is sensitive with life expectancy. Conclusions Dynamic growth of LTCI premium is essential in dealing with current deficit around 2050 and realizing Zhejiang’s LTCI sustainability in the long-run. The importance of dynamic monitoring disability and mortality information is emphasized to respond immediately to the increase of premiums. LTCI should strike a balance between expanding coverage and controlling financing scale. This study provides implications for developing countries to establish or pilot LTCI schemes.

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Section: Methodsmentioning

confidence: 99%

Life expectancy, long-term care demand and dynamic financing mechanism simulation: an empirical study of Zhejiang Pilot, China

Xu,

Li,

2024

BMC Health Serv Res

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“…The evaluation of the Lee-Carter model served as an exemplary choice to showcase the application of our validation design. The Lee-Carter model itself has proven problems that have been addressed and solved by multiple extensions (for a review of models see Basellini et al (2022)). However, the comparison of different models was not in the scope of this research.…”

Section: Limitationsmentioning

confidence: 99%

“…This workflow aims at assessing the suitability of a forecasting method depending on the prevailing mortality regime in the population of interest. Since the introduction of the Lee-Carter model in 1992 (Lee and Carter, 1992), several extensions have been proposed (Booth et al, 2006;Booth and Tickle, 2008;Basellini et al, 2022). For example, considering the advancement of survival improvements to increasingly older ages (Rau et al, 2008), more recent approaches account for trends in rates of mortality improvement and in the distribution of ages at death (Haberman and Renshaw, 2012;Li et al, 2013;Ševčíková et al, 2016;de Beer et al, 2017;Bardoutsos et al, 2018;Basellini and Camarda, 2019;Camarda, 2019).…”

Section: Introductionmentioning

confidence: 99%

A validation workflow for mortality forecasting

Duerst¹,

Schöley²,

Bohk-Ewald³

2023

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“…The main reason for this is the fundamental difference in the spaces in which members of fundamentally different populations live and interact. In this context, the mathematical apparatus of time series analysis is suitable for describing the development of cyber epidemics [34][35][36][37][38] . However, the disadvantage of this approach is the strength of compartmental models-time series analysis models do not take into account the specifics of the development of the cyber epidemic.Machine learning is a powerful tool for determining the relationship between input and output data for processes that are difficult to analyze analytically.…”

mentioning

confidence: 99%

“…Patrolla in 2004 proposed an agent-oriented model 37,38 , which expands the capabilities of cellular automata in the context of tracking the spread of infection, taking into account mutual contacts between individuals united in a certain social group. Such a model is embodied in the scheme of possible contacts as a dynamic or static graph, the vertices of which correspond to objects with a finite, but sufficiently detailed, set of individual properties inherent to individuals or their classes.…”

mentioning

confidence: 99%

Stochastic forecasting of variable small data as a basis for analyzing an early stage of a cyber epidemic

Kovtun,

Grochla,

Kharchenko

et al. 2023

Sci Rep

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Security Information and Event Management (SIEM) technologies play an important role in the architecture of modern cyber protection tools. One of the main scenarios for the use of SIEM is the detection of attacks on protected information infrastructure. Consorting that ISO 27001, NIST SP 800-61, and NIST SP 800-83 standards objectively do not keep up with the evolution of cyber threats, research aimed at forecasting the development of cyber epidemics is relevant. The article proposes a stochastic concept of describing variable small data on the Shannon entropy basis. The core of the concept is the description of small data by linear differential equations with stochastic characteristic parameters. The practical value of the proposed concept is embodied in the method of forecasting the development of a cyber epidemic at an early stage (in conditions of a lack of empirical information). In the context of the research object, the stochastic characteristic parameters of the model are the generation rate, the death rate, and the independent coefficient of variability of the measurement of the initial parameter of the research object. Analytical expressions for estimating the probability distribution densities of these characteristic parameters are proposed. It is assumed that these stochastic parameters of the model are imposed on the intervals, which allows for manipulation of the nature and type of the corresponding functions of the probability distribution densities. The task of finding optimal functions of the probability distribution densities of the characteristic parameters of the model with maximum entropy is formulated. The proposed method allows for generating sets of trajectories of values of characteristic parameters with optimal functions of the probability distribution densities. The example demonstrates both the flexibility and reliability of the proposed concept and method in comparison with the concepts of forecasting numerical series implemented in the base of Matlab functions.

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Thirty years on: A review of the Lee–Carter method for forecasting mortality

Cited by 26 publications

References 72 publications

Life expectancy, long-term care demand and dynamic financing mechanism simulation: an empirical study of Zhejiang Pilot, China

Life expectancy, long-term care demand and dynamic financing mechanism simulation: an empirical study of Zhejiang Pilot, China

A validation workflow for mortality forecasting

Stochastic forecasting of variable small data as a basis for analyzing an early stage of a cyber epidemic

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