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Concepts and Basic Measures of Mortality

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The Demography and Epidemiology of Human Health and Aging

Abstract

Death statistics are a basic element in measuring progress toward improved health and increased longevity of a population. They are needed both for demographic studies and for public health administration. Death statistics are used in the analysis of the past and present demographic status of a population as well as its prospective growth; in serving the administrative and research needs of public health agencies in connection with the development, operation, and evaluation of public health programs; and in basic research and analysis of the health, survival, and longevity of a population or some group within it. Death statistics are needed to conduct analyses of past population changes as well as past changes in the health and longevity of the population. These analyses are required to make projections of mortality, population size, and other demographic characteristics, and to prepare, interpret, and evaluate projections of the health status of the population.

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Notes

  1. 1.

    World Health Organization. (1950). Official records No. 28 (Third World Health Assembly 3.6) (pp. 16–17). Geneva: World Health Organization.

  2. 2.

    U.S. National Office of Vital Statistics. (1950). International recommendations on definitions of live birth and fetal deaths. Washington, DC: Public Health Service. See also U.S. National Center for Health Statistics, Physicians’ Handbook on Medical Certification of Death, 2003 Revision, and Hospitals’ and Physicians’ Handbook on Birth Registration and Fetal Death Reporting, 2003 Revision.

  3. 3.

    In mathematical terms it is the integral of a specified function of the population (px) for the period, usually a year, or X ∫x + 1 fpx dx, where the subscript x refers to time, as do the limits of the integral.

  4. 4.

    It is important to note that neither Gompertz nor Makeham intended that their formulas be applied to the advanced ages. Gompertz himself intended that his formula apply only to the population aged 20–60 and Makeham extended this range to age 80.

  5. 5.

    A logistic model is a special model where the “population” tends toward a specified asymptotic upper limit. The general form of the logistic equation is \(f(x) = a \div (1 +{ \mathit{be}}^{\mathit{-cx}})\), where a, b, and c are positive numbers. Typically f(x) denotes the population as a function of time x and the population tends toward a limit represented by a in the equation. The curve has a sigmoid shape, and hence upper and lower asymptotes and a point of inflection at midway.

  6. 6.

    Other logistic formulas with additional parameters have been proposed by Horiuchi and Wilmoth (1998), Thatcher et al. (1998), and Beard (1971). In addition to these formulas, several others have been proposed to model the entire age range – childhood, adulthood, and old age. They employ a component technique, that is, one that describes mortality in terms of particular segments of the age cycle. The formulas usually have three component parts and include several parameters to allow for changes in the parts. The Heligman and Pollard (1980) model is an additive component model with three components and eight parameters. The Thiele (1872) model also has three components: A decreasing Gompertz curve for the childhood ages, a normal curve for accident mortality, and an increasing Gompertz curve for the older ages. Mode and Busby (1982) also proposed a three-component model. Rogers and Little (1994) describe an exponential component model that has four components, each with one or more parameters. (For more information, see Suchindran (2004); Siegel and Swanson (2004)).

  7. 7.

    A rectangular distribution of a variable (e.g., deaths) in an age group (e.g., 5-year group) is one in which equal parts (e.g., one-fifth) of the variable fall in equal intervals of the age group (e.g., single ages). For a discussion of interpolation techniques and an illustrative calculation of the median age see Siegel and Swanson (2004).

  8. 8.

    Note that, as the median age of deaths rises, the interquartile range and the relative interquartile range tend to fall. This applies to the coefficient of variation and its components also. As Wilmoth and Horiuchi (1999) note, to combine changes in a measure of variation with changes in average age is to combine components that move in opposite directions. It is difficult to separate these two effects and it is difficult, therefore, to interpret the changes in the composite measure.

  9. 9.

    Specifically, if a distribution is multiplied by a factor f, its variance is multiplied by f 2 and its standard deviation is multiplied by f.

  10. 10.

    To measure differences in the age patterns of age-specific death rates, we can apply the same formula to the rates as to the absolute numbers. Because of the very high level of death rates at the later ages as compared with the earlier ages, particularly under general conditions of low mortality, the distribution of death rates is dominated by the rates at these higher ages. It is desirable, therefore, to reduce the weight of the rates at the highest ages by reweighting them. The reweighting can be accomplished by multiplying the rates by the population age distribution. The age distribution of the population tapers sharply at the advanced ages and so, by the weighting process, less weight is given to mortality at these ages. The calculation would convert the percent distribution of death rates to a different function of deaths by age, namely the percent distribution of deaths:

    $$\begin{array}{rcl} & \mbox{ Weighting age} -\mbox{ specific death rates} = {({d}_{a} \div {p}_{a})}^{{_\ast}}({p}_{a} \div \sum \nolimits {p}_{a}) = ({d}_{a} \div \sum \nolimits {p}_{a}) = {d}_{a} \div P& \\ & \mbox{ Converting to a percent distribution} = ({d}_{a} \div P) \div \sum \nolimits ({d}_{a} \div P) = {d}_{a} \div \sum \nolimits {d}_{a} = r & \\ \end{array}$$
  11. 11.

    Currently NCHS uses an automated scheme called ACME (“Automated Classification for Medical Entities”) for coding the underlying cause of death for each certificate in accordance with WHO rules. NCHS has developed two supplementary systems, one to automate coding of multiple causes of death called MICAR, and the other to allow for literal entry of the multiple cause-of-death text as reported by the certifier called SuperMICAR. Records that cannot be automatically processed by MICAR or SuperMICAR are manually coded with respect to cause and then further processed through ACME.

  12. 12.

    A fuller explanation of the basis for the introduction of the new standard population and of the effect of introducing it on U.S. mortality trends and sex-race differences is given in the following reports of the U.S. National Center for Health Statistics: Age standardization of death rates: Implementation of the year 2000 standard. In R.N. Anderson & H.M. Rosenberg, National VitalStatistics Reports, 47(3), 1998; and Age-adjusted death rates: Trend data based on the year 2000 standard population. By D.L. Hoyert & R.N. Anderson, National Vital Statistics Reports, 49(9), 2001.

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  1. J. Stuart Siegel Demographic Services, Nicholson Lane 5809 Unit 808, 20852-5710, North Bethesda, Maryland, USA

    Jacob S. Siegel

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Siegel, J.S. (2012). Concepts and Basic Measures of Mortality. In: The Demography and Epidemiology of Human Health and Aging. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1315-4_3

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