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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. Vital and Health Statistics Method for Constructing Complete Annual U.S. Life Tables Series 2: Data Evaluation and Methods Research No. 129 U.S. DEPARTMENT OF HEALTH AND HUMAN SERVICES Centers for Disease Control and Prevention National Center for Health Statistics Hyattsville, Maryland December 1999 DHHS Publication No. (PHS) 2000-1329 National Center for Health Statistics Edward J. Sondik, Ph.D., Director Jack R. Anderson, Deputy Director Jack R. Anderson, Acting Associate Director for International Statistics Lester R. Curtin, Ph.D., Acting Associate Director for Research and Methodology Jennifer H. Madans, Ph.D., Acting Associate Director for Analysis, Epidemiology, and Health Promotion P. Douglas Williams, Acting Associate Director for Data Standards, Program Development, and Extramural Programs Edward L. Hunter, Associate Director for Planning, Budget, and Legislation Jennifer H. Madans, Ph.D., Acting Associate Director for Vital and Health Statistics Systems Douglas L. Zinn, Acting Associate Director for Management Charles J. Rothwell, Associate Director for Data Processing and Services Division of Vital Statistics Mary Anne Freedman, Director James A. Weed, Ph.D., Deputy Director Harry M. Rosenberg, Ph.D., Chief, Mortality Statistics Branch Contents Abstract ................................................................................................. 1 Introduction ............................................................................................. 1 Background .............................................................................................. 1 Complete versus Abridged Life Tables ...................................................................... 1 Extending the Open-Ended Age Interval to 100 Years and Over ................................................. 2 Heterogeneity of Mortality Risk ........................................................................... 2 Age Misstatement ....................................................................................... 2 Medicare Data as a Standard .............................................................................. 3 Methods ................................................................................................ 4 Adjustment for Deaths for Which Age Was Not Reported ...................................................... 4 Interpolation of Px and Dx ................................................................................ 4 Calculation of q0 ....................................................................................... 6 Calculation of qx for Ages 1–84 Years ...................................................................... 6 Use of Medicare Data at Ages 85–99 Years .................................................................. 6 Survivor Function lx ..................................................................................... 7 Decrement Function dx ................................................................................... 7 Stationary Population Lx .................................................................................. 7 Person-Years Lived at and Over Age xTx ................................................................... 8 Life Expectancy at Age xex .............................................................................. 8 Results ................................................................................................. 8 Conclusions ............................................................................................. 10 References .............................................................................................. 10 Text Tables A. Interpolation coefficients based on Beer’s ordinary formula for the subdivision of grouped data into fifths ........... 5 B. Births in 1995 and 1996, deaths in 1996 of infants born in 1995 and 1996, and separation factors by race and sex: United States ...................................................................................... 6 C. k values by age, race, and sex based on insured Medicare data: United States, 1996 ............................ 7 D. Slope of the changes in k values by age, race, and sex .................................................... 8 E. Comparison of 1996 probabilities of dying by race and sex based on vital statistics and Medicare data ............. 8 F. Life expectancy by age, race, and sex from 1996 complete U.S. life tables, 1996 abridged U.S. life tables, and 1989–91 U.S. decennial life tables ............................................................................. 9 Figures 1. Vital statistics death rates, aged 65 years and over: United States, 1970, 1980, and 1990 ......................... 3 2. Probability of dying by single years of age, 65–99 years for white males based on vital statistics data and Medicare data: United States, 1996 ............................................................................ 3 3. Probability of dying by single years of age, 65–99 years for white females based on vital statistics data and Medicare data: United States, 1996 ............................................................................ 4 4. Probability of dying by single years of age, 65–99 years for black males based on vital statistics data and Medicare data: United States, 1996 ............................................................................ 4 iii 5. Probability of dying by single years of age, 65–99 years for black females based on vital statistics data and Medicare data: United States, 1996 ............................................................................ 5 6. k values by age, race, and sex based on insured Medicare data: United States, 1996 ............................. 7 Detailed Tables 1. Life table for the total population: United States, 1996 .................................................... 11 2. Life table for males: United States, 1996 ............................................................... 13 3. Life table for females: United States, 1996 .............................................................. 15 4. Life table for the white population: United States, 1996 ................................................... 17 5. Life table for white males: United States, 1996 .......................................................... 19 6. Life table for white females: United States, 1996 ......................................................... 21 7. Life table for the black population: United States, 1996 ................................................... 23 8. Life table for black males: United States, 1996 .......................................................... 25 9. Life table for black females: United States, 1996 ......................................................... 27 iv Objectives This report describes a method for A Method for Constructing constructing complete annual U.S. life tables and for extending the age Complete Annual U.S. Life coverage of the life table to age 100. Previously, annual life tables were based on an abridged methodology and Tables were closed with the age category 85 years and over. In the United States, by Robert N. Anderson, Ph.D., Division of Vital Statistics approximately one-third of the population survives beyond age 85 years. This fact, coupled with Introduction life tables with the age category 100 improvements in age reporting and the years and over. availability of higher quality old-age The report first provides some mortality data, recommends that the life he purpose of this report is to background and a brief review of the table be closed at an older age. describe a method for theoretical and empirical literature on T constructing complete annual U.S. which the method is based. Next, the Methods life tables. Previously, the annual life mathematical details
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