Relation of the Weibull Shape Parameter with the Healthy Life Years Lost Estimates: Analytic Derivation and Estimation from an Extended Life Table

Matsushita et al (1992) have done an interesting finding. They observed that the shape parameter of the Weibull model presented systematic changes over time and age when applied to mortality data for males and females in Japan. They have also estimated that this parameter was smaller in the 1891-1898 data in Japan compared to the 1980 mortality data and they presented an illustrative figure for females where the values of the shape parameter are illustrated on the diagram close to the corresponding survival curves. However, they have not provided an analytical explanation of this behavior of the shape parameter of the Weibull model. The cumulative hazard of this model can express the additive process of applying a force in a material for enough time before cracking. To pass to the human data, the Weibull model and the cumulative hazard can express the additive process which disabilities and diseases cause the human organism during the life span leading to healthy life years lost. In this paper we further analytically derive a more general model of survival-mortality in which we estimate a parameter related to the Healthy Life Years Lost (HLYL) and leading to the Weibull model and the corresponding shape parameter as a specific case. We have also demonstrated that the results found for the general HLYL parameter we have proposed provides results similar to those provided by the World Health Organization for the Healthy Life Expectancy (HALE) and the corresponding HLYL estimates. An analytic derivation of the mathematical formulas is presented along with an easy to apply Excel program. This program is an extension of the classical life table including four more columns to estimate the cumulative mortality, the average mortality, the person life years lost and finally the HLYL parameter bx. The latest versions of this program appear in the Demographics2019 websit

Chaos in Simple Rotation-Translation Models

The chaotic properties of simple two-dimensional rotation-translation models are explored and simulated. The models are given in difference equation forms, while the corresponding differential equations systems are studied and the resulting trajectories in the plane are explored and illustrated in the computer experiments done. Characteristic patterns, egg-shaped forms and central chaotic bulges are present when particles are introduced in the rotating system. The resulting forms and chaotic attractors mainly depend on the form of the nonlinear function expressing the rotation angle. Several cases are studied corresponding to a central force rotation system.Comment: 18 pages, 28 figure

Properties of a Stochastic Model for Life Table Data: Exploring Life Expectancy Limits

In this paper we explore the life expectancy limits by based on the stochastic modeling of mortality and applying the first exit or hitting time theory of a stochastic process. The main assumption is that the health state or the "vitality", according to Strehler and Mildvan, of an individual is a stochastic variable and thus it was introduced and applied a first exit time density function to mortality data. The model is used to estimate the development of mortality rates in the late stages of the human life span, to make better fitting to population mortality data including the infant mortality, to compare it with the classical Gompertz curve, and to make comparisons between the Carey med-fly data and the population mortality data estimating the health state or "vitality" functions. Furthermore, we apply the model to the life table data of Italy, France, USA, Canada, Sweden, Norway and Japan, and we analyze the characteristic parameters of the model and make forecasts.Comment: 9 pages, 2 figure

A Quantitative Method for Estimating the Human Development Stages by Based on the Health State Function Theory and the Resulting Deterioration Process

The Health State Function theory is applied to find a quantitative estimate of the Human Development Stages by defining and calculating the specific age groups and subgroups. Early and late adolescence stages, first, second and third stages of adult development are estimated along with the early, middle and old age groups and subgroups. We briefly present the first exit time theory used to find the health state function of a population and then we give the details of the new theoretical approach with the appropriate applications to support and validate the theoretical assumptions. Our approach is useful for people working in several scientific fields and especially in medicine, biology, anthropology, psychology, gerontology, probability and statistics. The results are connected with the speed and acceleration of the deterioration of the human organism during age as a consequence of the changes in the first, second and third differences of the Health State Function and of the Deterioration Function. Keywords: Human development stages, Deterioration, Deterioration function, Human Mortality Database, HMD, World Health Organization, WHO, Quantitative methods, Health State Function, Erikson's stages of psychosocial development, Piaget method, Sullivan method, Disability stages, Light disability, Moderate disability, Severe disability stage, Old ages, Critical ages.Comment: 19 pages, 9 figures, 8 table

A Method for Estimating the Total Loss of Healthy Life Years: Applications and Comparisons in UK and Scotland

We propose a method of estimating the Total Loss of Healthy Life Years based on the first exit time theory for a stochastic process, the resulting Health State Function and the Deterioration Function estimated as the curvature of the health state function. We have done many applications in UK and Scotland and Sweden supporting our theory. Furthermore it was proven that both the WHO and EU estimates of the healthy life expectancy can result from our method. The WHO system takes into account the severe and moderate causes in estimating the loss of healthy life years; instead the EU system calculates the total loss of healthy life years. For both cases our methodology provides both estimators from only death and population data. The advantages of our method are straightforward. We do not need survey data to make the calculations. The resulting estimates should be used to test and improve the existing survey based methodologies. While the WHO and EU systems tend to approach each other differences continue to appear based on the methodology of the related surveys and the analysis of data. Two main schools are working to these directions one based on USA the Institute for Health Metrics and Evaluation (IHME) headed by Christopher J.L. Murray and contributors in all over the world and the European Health and Life Expectancy Information System (EHLEIS) with Jean-Marie Robine and a team from the EU member states. Keywords: Deterioration, Loss of healthy years, HALE, DALE, World Health Organization, WHO, European Union, EU, EHEMU, IHME, EHLEIS, Healthy life expectancy, Life expectancy.Comment: 15 pages, 8 figures, 4 table

Modeling the Health Expenditure in Japan, 2011. A Healthy Life Years Lost Methodology

The Healthy Life Years Lost Methodology (HLYL) is introduced to model and estimate the Health Expenditure in Japan in 2011. The HLYL theory and estimation methods are presented in our books in the Springer Series on Demographic Methods and Population Analysis vol. 45 and 46 titled: Exploring the Health State of a Population by Dynamic Modeling Methods and Demography and Health Issues: Population Aging, Mortality and Data Analysis. Special applications appear in Chapters of these books as in The Health-Mortality Approach in Estimating the Healthy Life Years Lost Compared to the Global Burden of Disease Studies and Applications in World, USA and Japan and in Estimation of the Healthy Life Expectancy in Italy Through a Simple Model Based on Mortality Rate by Skiadas and Arezzo. Here further to present the main part of the methodology with more details and illustrations, we develop and extend a life table important to estimate the healthy life years lost along with the fitting to the health expenditure in the related case. The application results are quite promising and important to support decision makers and health agencies with a powerful tool to improve the health expenditure allocation and the future predictions.Comment: 9 pages, 7 figure

The Health State Function, the Force of Mortality and other Characteristics resulting from the First Exit Time Theory applied to Life Table Data

In this paper we summarize the main parts of the first exit time theory developed in connection to the life table data and the resulting theoretical and applied issues. Several new tools arise from the development of this theory and especially the Health State Function and some important characteristics of this function. Special attention has being done in the presentation of the health state function along with the well established theory for the Force of Mortality and the related applications as are the life tables and the estimation of life expectancies. A main part of this work is the formulation of the appropriate non-linear analysis program including a model which provides an almost perfect fit to life table data. This model, proposed in 1995 is now expanded as to include the mortality excess for the age group from 15-30 years. A version of the program is given in Excel and provided at the website: http://www.cmsim.netComment: 20 pages, 12 figure

Estimating the Healthy Life Expectancy from the Health State Function of a Population in Connection to the Life Expectancy at Birth

Following our previous works on the health state of a population and the related health state function we proceed in developing a method to estimate the Healthy Life Expectancy in connection to the relative impact of the Mortality Area in the health state function graph. The resulting tools are applied to the data sets for 1990, 2000 and 2009 for the Countries of the World Health Organization (WHO). The application is done in the Excel Chart and it is ready to be used for other time periods. The results are compared with the estimates presented in the WHO report for 2000 showing a good relationship between the estimates of the two methods. However, our proposed method, not based on collection of data for diseases and other causes affecting a healthy life, is more flexible. We can estimate the healthy life years from various time periods when information related to diseases is missing. Keywords: Health state function, Healthy life expectancy, Deterioration, Loss of healthy years, HALE, DALE, World Health Organization, WHOComment: 17 pages, 8 figures, 4 table

Direct Healthy Life Expectancy Estimates from Life Tables with a Sullivan Extension. Bridging the Gap Between HALE and Eurostat Estimates

The analytic derivation of a more general model of survival-mortality and the estimation of a parameter bx related to the Healthy Life Years Lost (HLYL) is followed with the formulation of a computer program providing results similar to those of the World Health Organization for the Healthy Life Expectancy (HALE) and the corresponding HLYL estimates. This program is an extension of the classical life table including more columns to estimate the cumulative mortality, the average mortality, the person life years lost and finally the HLYL parameter bx. Evenmore, a further extension of the Excel program based on the Sullivan method provides estimates of the Healthy Life Expectancy at every year of the lifespan for five different types of estimates that are the Direct, WHO, Eurostat, Equal and Other. Estimates for several countries are presented. It is also presented a methodology and a program to bridge the gap between the World Health Organization (HALE) and Eurostat (HLE) healthy life expectancy estimates. The latest version of this program (SKI-6) appear in the Demographics2020 website.Comment: 14 pages, 10 figures, 2 tables. arXiv admin note: substantial text overlap with arXiv:1904.1012

Verifying the HALE measures of the Global Burden of Disease Study: Quantitative Methods Proposed

To verify the Global Burden of Disease Study and the provided healthy life expectancy (HALE) estimates from the World Health Organization (WHO) we propose a very simple model based on the mortality {\mu}x of a population provided in a classical life table and a mortality diagram. We use the abridged life tables provided by WHO. Our estimates are compared with the HALE estimates for the World territories and the WHO countries. Even more we have developed the related simple program in Excel which provides immediately the Life Expectancy, the Loss of Healthy Life Years and the Healthy Life Expectancy estimate. We also apply the health state function theory to have more estimates and comparisons. The results suggest improved WHO estimates in recent years for the majority of the cases. Keywords: Health state function, Healthy life expectancy, Mortality Diagram, Loss of healthy years, LHLY, HALE, DALE, World Health Organization, WHO, Global burden of Disease, Health status.Comment: 29 pages, 9 figures, 6 Tables (3 Tables with full estimated figures