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How to Measure the Burden of Mortality? L Bonneux
J Epidemiol Community Health: first published as 10.1136/jech.56.2.128 on 1 February 2002. Downloaded from 128 THEORY AND METHODS How to measure the burden of mortality? L Bonneux ............................................................................................................................. J Epidemiol Community Health 2002;56:128–131 Objectives: To explore various methods to quantify the burden of mortality, with a special interest for the more recent method at the core of calculations of disability adjusted life years (DALY). Design: Various methods calculating the age schedule at death are applied to two historical life table populations. One method calculates the “years of life lost”, by multiplying the numbers of deaths at age ....................... L Bonneux, Department of x by the residual life expectancy. This residual life expectancy may be discounted and age weighted. Public Health, Erasmus The other method calculates the “potential years of life lost” by multiplying the numbers of deaths at age University Rotterdam, the x by the years missing to reach a defined threshold (65 years or 75 years). Netherlands Methods: The period life tables describing the mortality of Dutch male populations from 1900–10 Correspondence to: (high mortality) and from 1990–1994 (low mortality). Dr L Bonneux, Department Results: A standard life table with idealised long life expectancy increases the burden of death more of Public Health, Erasmus if mortality is lower. People at old age, more prevalent if mortality is low, lose more life years in an ide- University Rotterdam, PO alised life table. The discounted life table decreases the burden of death strongly if mortality is high: Box 1738, 3000 DR Rotterdam, the the life lost by a person dying at a young age is discounted. -
Using Dynmaic Reliability in Estimating Mortality at Advanced
Using Dynamic Reliability in Estimating Mortality at Advanced Ages Fanny L.F. Lin, Professor Ph.D. Graduate Institute of Statistics and Actuarial Science Feng Chia University P.O. Box 25-181 Taichung 407, Taiwan Tel: +886-4-24517250 ext. 4013, 4012 Fax: +886-4-24507092 E-mail: [email protected] Abstract Traditionally, the Gompertz’s mortality law has been used in studies that show mortality rates continue to increase exponentially with age. The ultimate mortality rate has no maximum limit. In the field of engineering, the reliability theory has been used to measure the hazard-rate function that is dependent on system reliability. Usually, the hazard rate ( H ) and the reliability (R ) have a strong negative coefficient of correlation. If reliability decreases with increasing hazard rate, this type of hazard rate can be expressed as a power function of failure probability, 1- R . Many satisfactory results were found in quality control research in industrial engineering. In this research, this concept is applied to human mortality rates. The reliability R(x) is the probability a newborn will attain age x . Assuming the model between H(x) and R(x) is H(x) = B + C(1- R(x) A ) D , where A represents the survival decaying memory characteristics, B/C is the initial mortality strength, C is the strength of mortality, and D is the survival memory characteristics. Eight Taiwan Complete Life Tables from 1926 to 1991 were used as the data source. Mortality rates level off at a constant B+C for very high ages in the proposed model but do not follow Gompertz’s mortality law to the infinite. -
Incidence, Mortality, Disability-Adjusted Life Years And
Original article The global burden of injury: incidence, mortality, disability-adjusted life years and time trends from the Global Burden of Disease study 2013 Juanita A Haagsma,1,60 Nicholas Graetz,1 Ian Bolliger,1 Mohsen Naghavi,1 Hideki Higashi,1 Erin C Mullany,1 Semaw Ferede Abera,2,3 Jerry Puthenpurakal Abraham,4,5 Koranteng Adofo,6 Ubai Alsharif,7 Emmanuel A Ameh,8 9 10 11 12 Open Access Walid Ammar, Carl Abelardo T Antonio, Lope H Barrero, Tolesa Bekele, Scan to access more free content Dipan Bose,13 Alexandra Brazinova,14 Ferrán Catalá-López,15 Lalit Dandona,1,16 Rakhi Dandona,16 Paul I Dargan,17 Diego De Leo,18 Louisa Degenhardt,19 Sarah Derrett,20,21 Samath D Dharmaratne,22 Tim R Driscoll,23 Leilei Duan,24 Sergey Petrovich Ermakov,25,26 Farshad Farzadfar,27 Valery L Feigin,28 Richard C Franklin,29 Belinda Gabbe,30 Richard A Gosselin,31 Nima Hafezi-Nejad,32 Randah Ribhi Hamadeh,33 Martha Hijar,34 Guoqing Hu,35 Sudha P Jayaraman,36 Guohong Jiang,37 Yousef Saleh Khader,38 Ejaz Ahmad Khan,39,40 Sanjay Krishnaswami,41 Chanda Kulkarni,42 Fiona E Lecky,43 Ricky Leung,44 Raimundas Lunevicius,45,46 Ronan Anthony Lyons,47 Marek Majdan,48 Amanda J Mason-Jones,49 Richard Matzopoulos,50,51 Peter A Meaney,52,53 Wubegzier Mekonnen,54 Ted R Miller,55,56 Charles N Mock,57 Rosana E Norman,58 Ricardo Orozco,59 Suzanne Polinder,60 Farshad Pourmalek,61 Vafa Rahimi-Movaghar,62 Amany Refaat,63 David Rojas-Rueda,64 Nobhojit Roy,65,66 David C Schwebel,67 Amira Shaheen,68 Saeid Shahraz,69 Vegard Skirbekk,70 Kjetil Søreide,71 Sergey Soshnikov,72 Dan J Stein,73,74 Bryan L Sykes,75 Karen M Tabb,76 Awoke Misganaw Temesgen,77 Eric Yeboah Tenkorang,78 Alice M Theadom,79 Bach Xuan Tran,80,81 Tommi J Vasankari,82 Monica S Vavilala,57 83 84 85 ▸ Vasiliy Victorovich Vlassov, Solomon Meseret Woldeyohannes, Paul Yip, Additional material is 86 87 88,89 1 published online only. -
Lecture Notes 3
4 Testing Hypotheses The next lectures will look at tests, some in an actuarial setting, and in the last subsection we will also consider tests applied to graduation. 4.1 Tests in the regression setting 1) A package will produce a test of whether or not a regression coefficient is 0. It uses properties of mle’s. Let the coefficient of interest be b say. Then the null hypothesis is HO : b =0and the alternative is HA : b =0. At the 5% significance level, HO will be accepted if the p-value p>0.05, and rejected otherwise. 2) In an AL parametric model if α is the shape parameter then we can test HO :logα =0against the alternative HA :logα =0. Again mle properties are used and a p-value is produced as above. In the case of the Weibull if we accept log α =0then we have the simpler exponential distribution (with α =1). 3) We have already mentioned that, to test Weibull v. exponential with null hypothesis HO : exponential is an acceptable fit, we can use 2 2logLweib − 2logLexp ∼ χ (1), asymptotically. 4.2 Non-parametric testing of survival between groups We will just consider the case where the data splits into two groups. There is a relatively easy extension to k(>2) groups. We need to set up some notation. d =#events at t in group 1, Notation: i1 i ni1 =#in risk set at ti from group 1, similarly di2,ni2. Event times are (0 <)t1 <t2 < ···<tm. di =#events at ti ni =#in risk set at ti di = di1 + di2,ni = ni1 + ni2 All the tests are based on the following concepts: Observed # events in group 1 at time ti, = di1 di Expected # events in group 1 at time ti, = ni1 n under the null hypothesis below i H O : there is no difference between the hazard rates of the two groups Usually the alternative hypothesis for all tests is 2-sided and simply states that there is a difference in the hazard rates. -
A Review of Life Table Construction
Biometrics & Biostatistics International Journal Research Article Open Access A review of life table construction Abstract Volume 5 Issue 3 - 2017 Life table is the one of the oldest statistical techniques and is extensively used by Ilker Etikan, Sulaiman Abubakar, Rukayya medical statisticians and actuaries. It is also the scheme for expressing the form of mortality in terms of probabilities. The life table is constructed from census data Alkassim Near East University Faculty of Medicine Department of and death registration data, it can also be constructed from vital registration or Biostatistics, Nicosia-TRNC, Cyprus retrospective surveys. Generally, they are constructed for age, gender, ethnic groups and occupational groups and so on. Some classification of life table such as cohort Correspondence: Ilker Etikan, Near East University Faculty of or current life table which are classified according to the reference year, unabridged Medicine Department of Biostatistics, Nicosia-TRNC, Cyprus, (complete) or abridge life table classified according to length of age interval and single Email or multiple decrement life table classified according to the number of characteristics considered were discussed in the article. Received: November 24, 2016 | Published: March 02, 2017 Keywords: life tables, survival analysis, kaplan meirer Introduction In 1693, the first mortality table is usually credited to Edmund halley who constructed a life table base on the data from Breslau city in A life table is a terse way of showing the probabilities of a member Poland. The table thought to be the first and as well as best of its kind. 1 of a particular population living to or dying at a precise age. -
Life Tables for 191 Countries: Data, Methods and Results
LIFE TABLES FOR 191 COUNTRIES: DATA, METHODS AND RESULTS Alan D Lopez Joshua Salomon Omar Ahmad Christopher JL Murray Doris Mafat GPE Discussion Paper Series: No.9 EIP/GPE/EBD World Health Organization 1 I Introduction The life table is a key summary tool for assessing and comparing mortality conditions prevailing in populations. From the time that the first modern life tables were constructed by Graunt and Halley during the latter part of the 17th century, life tables have served as a valuable analytical tool for demographers, epidemiologists, actuaries and other scientists. The basic summary measure of mortality from the life table, the expectation of life at birth, is widely understood by the general public and trends in life expectancy are closely monitored as the principal measure of changes in a population's health status. The construction of a life table requires reliable data on a population's mortality rates, by age and sex. The most reliable source of such data is a functioning vital registration system where all deaths are registered. Deaths at each age are related to the size of the population in that age group, usually estimated from population censuses, or continuous registration of all births, deaths and migrations. The resulting age-sex-specific death rates are then used to calculate a life table. While the legal requirement for the registration of deaths is virtually universal, the cost of establishing and maintaining a system to record births and deaths implies that reliable data from routine registration is generally only available in the more economically advanced countries. Reasonably complete national data to calculate life tables in the late 1990s was only available for about 65 countries, covering about one-third of the deaths estimated to have occurred in 1999. -
Disability Adjusted Life Years (Dalys)
Article Disability Adjusted Life Years (DALYs) in Terms of Years of Life Lost (YLL) Due to Premature Adult Mortalities and Postneonatal Infant Mortalities Attributed to PM2.5 and PM10 Exposures in Kuwait Ali Al-Hemoud 1,*, Janvier Gasana 2, Abdullah N. Al-Dabbous 1, Ahmad Al-Shatti 3 and Ahmad Al-Khayat 4 1 Crisis Decision Support Program, Environment and Life Sciences Research Center, Kuwait Institute for Scientific Research, P.O. Box 24885, 13109 Safat, Kuwait; [email protected] 2 Faculty of Public Health, Health Sciences Center, Kuwait University, P.O. Box 24923, 13110 Hawalli, Kuwait; [email protected] 3 Occupational Health Department, Kuwait Ministry of Health, P.O. Box 51360, 53454 Riqqa, Kuwait; [email protected] 4 Techno-Economics Division, Kuwait Institute for Scientific Research, P.O. Box 24885, 13109 Safat, Kuwait; [email protected] * Correspondence: [email protected]; Tel.: +09-652-498-9464 Received: 9 October 2018; Accepted: 17 November 2018; Published: 21 November 2018 Abstract: Ambient air pollution in terms of fine and coarse particulate matter (PM2.5 and PM10) has been shown to increase adult and infant mortalities. Most studies have estimated the risk of mortalities through attributable proportions and number of excess cases with no reference to the time lost due to premature mortalities. Disability adjusted life years (DALYs) are necessary to measure the health impact of PM over time. In this study, we used life-tables for three years (2014–2016) to estimate the years of life lost (YLL), a main component of DALYs, for adult mortalities (age 30+ years) and postneonatal infant mortalities (age 28+ days–1 year) associated with PM2.5 exposure and PM10 exposure, respectively. -
A New Look at Halley's Life Table
J. R. Statist. Soc. A (2011) 174, Part 3, pp. 823–832 A new look at Halley’s life table David R. Bellhouse University of Western Ontario, London, Canada [Received March 2010. Revised November 2010] Summary. Edmond Halley published his Breslau life table in 1693, which was arguably the first in the world based on population data. By putting Halley’s work into the scientific context of his day and through simple plots and calculations, new insights into Halley’s work are made. In particular, Halley tended to round his numbers and to massage his data for easier presentation and calculation. Rather than highlighting outliers as would be done in a modern analysis, Halley instead smoothed them out. Halley’s method of life table construction for early ages is exam- ined. His lifetime distribution at higher ages, which is missing in his paper, is reconstructed and a reason is suggested for why Halley neglected to include these ages in his table. Keywords: Data analysis; Demographic statistics; Life tables; 17th century; Smoothing 1. Introduction In 1693 Edmond Halley constructed a life table or more correctly, as noted by Greenwood (1941, 1943), a population table. It was based on data collected for the years 1687–1691 from the city of Breslau, which is now called Wrocław, by the Protestant pastor of the town, Caspar Neumann. The data that Halley used were the numbers of births and deaths recorded in the parish registers of the town, which was then under the control of the Habsburg monarchy of Austria. It was a town in a Polish area comprised predominantly of German speakers adhering to Lutheranism within an officially Roman Catholic empire (Davies and Moorhouse (2002), pages 159–160, 180). -
Let F(X) Be a Life Cumulative Distribution Function for Some Element Under Consideration
TRANSACTIONS OF SOCIETY OF ACTUARIES 1961 VOL. 13 NO. 36AB A JUSTIFICATION OF SOME COMMON LAWS OF MORTALITY DAVID R.. BRILLINGER m~ objectives of this paper are twofold. The first one is to intro- duce the modem concepts and definitions of the statistical subject T of life testing and to tie them in with the corresponding concepts of actuarial science. The second half of the paper presents a justification of some common laws of mortality (Gompertz's, Makeham's I, Makeham's II), and also gives a very general form of a mortality law that may prove useful. Let F(x) be a life cumulative distribution function for some element under consideration. F(x) is thus the probability that this element fails before reaching age x. Associated with F(x) is a life density function, f(x) = dF(x)/dx and a failure rate at age x, #(x) = f(x)/[1 -- F(x)]. From the equation, [1 -F (x) ] ~,(x),ax = f (x)ZXx, (1) one sees that #(x) may be interpreted as the conditional probability of failure in the next interval of length Ax, given that the element has survived to age x. This follows from the fact that [I -- F(x)] is the prob- ability that the element survives to age x and f(x)zXx is the probability that the element fails in the next interval of length Ax. E.g., if the element is a life aged x, F (x) =,q0 = 1 --*P0 = 1 --1,/Io f (x) = - dxa__ (l,/l,) 1 d ~, (x) = -~ d---~ l, = ~,, the force of mortality at age x. -
National Vital Statistics Reports Volume 69, Number 12 November 17, 2020
National Vital Statistics Reports Volume 69, Number 12 November 17, 2020 United States Life Tables, 2018 by Elizabeth Arias, Ph.D., and Jiaquan Xu, M.D., Division of Vital Statistics Abstract Introduction Objectives—This report presents complete period life tables There are two types of life tables: the cohort (or generation) for the United States by Hispanic origin, race, and sex, based on life table and the period (or current) life table. The cohort life age-specific death rates in 2018. table presents the mortality experience of a particular birth Methods—Data used to prepare the 2018 life tables are cohort—all persons born in the year 1900, for example—from 2018 final mortality statistics; July 1, 2018 population estimates the moment of birth through consecutive ages in successive based on the 2010 decennial census; and 2018 Medicare data calendar years. Based on age-specific death rates observed for persons aged 66–99. The methodology used to estimate through consecutive calendar years, the cohort life table reflects the life tables for the Hispanic population remains unchanged the mortality experience of an actual cohort from birth until no from that developed for the publication of life tables by Hispanic lives remain in the group. To prepare just a single complete origin for data year 2006. The methodology used to estimate cohort life table requires data over many years. It is usually the 2018 life tables for all other groups was first implemented not feasible to construct cohort life tables entirely on the basis with data year 2008. In 2018, all 50 states and the District of of observed data for real cohorts due to data unavailability or Columbia reported deaths by race based on the 1997 Office of incompleteness (1). -
Product Preview
PUBLICATIONS e Experts In Actuarial Career Advancement Product Preview For More Information: email [email protected] or call 1(800) 282-2839 Chapter 1 – Actuarial Notation 1 CHAPTER 1 – ACTUARIAL NOTATION There is a specific notation used for expressing probabilities, called “actuarial notation”. You must become familiar with this notation, as it is used extensively in the study material and on the exams. The notation txp means “the probability of a person age x living t or more years”. Example 1.1 – Interpret 57p Answer – The probability of a person age 7 living five or more years. Conversely, txq means “the probability of a person age x dying within the next t years”. Example 1.2 – Interpret 57q Answer – The probability of a person age 7 dying at or before age 12. In the case where we are only looking for the probability over the course of one year we use the shorthand notation px or qx . Example 1.3 – Interpret q0 Answer – The probability of a person age 0 dying at or before age 1. Even though we are using a different notation we still follow the same rules of probability. One of the more common rules used is that if you have two (and only two) possible events, A and B, then PA() PB () 1. The probabilities of these two events are compliments of each other. Example 1.4 – Given 510p 0.9 , find 510q Answer – These two values are compliments of each other so we can say 510qp1 5 10 1 0.9 0.1 Because of the way we write the notation, it can be a little confusing to try to relate the different probabilities to each other. -
Vital and Health Statistic, Series 2, No
Series 2 No. 129 Vital and Health Statistics From the CENTERS FOR DISEASE CONTROL AND PREVENTION / National Center for Health Statistics Method for Constructing Complete Annual U.S. Life Tables December 1999 U.S. DEPARTMENT OF HEALTH AND HUMAN SERVICES Centers for Disease Control and Prevention National Center for Health Statistics Copyright Information All material appearing in this report is in the public domain and may be reproduced or copied without permission; citation as to source, however, is appreciated. Suggested citation Anderson RN. Method for constructing complete annual U.S. life tables. National Center for Health Statistics. Vital Health Stat 2(129). 1999. Library of Congress Cataloging-in-Publication Data Anderson, Robert N. Method for constructing complete annual U.S. life tables / [by Robert N. Anderson]. p. cm. — (Vital and health statistics. Series 2, Data evaluation and methods research ; no. 129) (DHHS publication ; no. (PHS) 99-1329) ‘‘This report describes a method for constructing complete annual U.S. life tables and for extending ...’’ ‘‘November, 1999.’’ Includes bibliographical references. ISBN 0-8406-0560-9 1. United States—Statistics, Vital—Methodology. 2. Insurance, Life—United States—Statistical methods. 3. Insurance, Health—United States—Statistical methods. 4. Mortality—United States—Statistical methods. 5. Public health—United States—Statistical methods. I. National Center for Health Statistics (U.S.) II. Title. III. Series. IV. Series: DHHS publication ; no. (PHS) 99-1329 RA409.U45 no. 129 [HB1335.A3] 362.1'0723 s—dc21 [614.4'273'0727] 99-058350 For sale by the U.S. Government Printing Office Superintendent of Documents Mail Stop: SSOP Washington, DC 20402-9328 Printed on acid-free paper.