A quarterly newsletter by the Alberta Geological Survey

Last Revised: May 31, 2007 (Version 5)
Methods Protocol for the Human Mortality Database
J.R. Wilmoth, K. Andreev, D. Jdanov, and D.A. Glei
with the assistance of
1C. Boe, M. Bubenheim, D. Philipov, V. Shkolnikov, P. Vachon


Table of Contents
Introduction.................................................................................................................................................1
General principles.......................................................................................................................................2
Notation and terminology for age and time...............................................................................................2
Lexis diagram..................................................................................................................2
Standard configurations of age and time...................................................................................................4
Female / male / total ..................................................................................................................................6
Periods and cohorts ...................................................................................................................................6
Adjustments to raw data............................................................................................................................7
Format of data files ...................................................................................................................................7
Steps for computing mortality rates and life tables .................................................................................7
Common adjustments to raw data ............................................................................................................9
Distributing deaths of unknown age..........................................................................................................9
Splitting 1x1 death counts into Lexis triangles .......................................................................................11
Splitting 5x1 nto 1x1 data .................................................................................................14
Splitting death counts in open age intervals into Lexis triangles ............................................................14
Population estimates (January 1st)............15
Linear interpolation .................................................................................................................................15
Intercensal survival methods...................................................................................................................16
Specific example ..................................................................................................................................16
Generalizing the method......................................................................................................................20
Pre- and postcensal survival method...................................................................................................25
Intercensal survival with census data in n-year age groups................................................................26
Extinct cohorts methods..................27
Survivor ratio...........................................................................................................................................29
Death rates.................................................................................................................................................32
Life tables...............................34
Period life tables......................................................................................................................................35
Cohort life tables........................39
Multi-year cohorts..................41

1 This document grew out of a series of discussions held in various locations beginning in June 2000. The
four individuals listed as authors wrote the original version and/or have actively contributed to subsequent
versions, including through the development of additional methods. Several others assisted with the
creation of this document through their active participation in meetings and ongoing discussions via
email. The authors are fully responsible for any errors or ambiguities. They thank Georg Heilmann for
his assistance with the graphs.
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Almost-extinct cohorts .........................................................................................................................42
Abridged life tables .................................................................................................................................44
Appendix A. Linear model for splitting 1x1 death counts ...................................................................45
Appendix B. Computational methods for fitting cubic splines ............................................................52
Splitting nx1 data into 1x1 format...........................................................................................................52
Splitting period-cohort parallelograms covering n cohorts .....................................................................54
Appendix C. Method for splitting deaths in an open age interval.......................................................55
Correction for unusual fluctuations in deaths..........................................................................................56
Correction for cohort size........................................................................................................................59
Appendix D. Adjustments for changes in population coverage...........................................................63
Birth counts used in splitting 1x1 deaths.................................................................................................63
Extinct cohort methods............................................................................................................................65
Intercensal survival methods...................................................................................................................67
Linear interpolation .................................................................................................................................70
Period death rates around the time of a territorial change.......................................................................70
Cohort mortality estimates around the time of a territorial change.........................................................70
Other changes in population coverage ....................................................................................................71
Appendix E. Computing death rates and probabilities of death72
Uniform distribution of deaths ................................................................................................................72
Cohort death rates and probabilities.............73
Period death ..............75
Appendix F. Special methods used for selected populations................................................................78
References..................................................................................................................................................80

List of Figures
Figure 1. Example of a Lexis diagram.........................................................................................................3
Figure 2. Illustration of Lexis triangles........................................................................................................4
Figure 3. Intercensal survival method (example).......................................................................................17
Figure 4. Intercensal survival method (in general) ....................................................................................21
Figure 5. Pre- and postcensal survival method ..........................................................................................26
Figure 6. Methods used for population estimates.......28
Figure 7. Illustration of extinction rule (with l = 5 and x = ω - 1) ...........................................................29
Figure 8. Survivor ratio method (at age x = ω - 1, with k = m = 5)31
Figure 9. Data for period death rates and probabilities..............................................................................33
Figure 10. Data for cohort death rates and probabilities............................................................................34
Figure 11. Illustration of five-year cohort (assuming no migration)..........................................................42
Figure 12. Life table calculations for almost-extinct cohorts ....................................................................43
* *Figure 13. Liost-extinct cohorts aged to in year t .....................44 x x + 4 n

Figure A-1. Proportion of male infant deaths in lower triangle.................................................................48
Figure A-2. male age 80 deaths in lower triangle49

Figure C-1. First differences in deaths, West German females, 1999 .......................................................57
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