STANDARDIZED CLASS INTERVALS AND RATE COMPUTATION IN STATISTICAL MAPS OF MORTALITY

ABSTRACT

The standard deviation of a set of mortality or morbidity rates for areal units can be used to establish class intervals for mapping. Use of standard, rather than arbitrarily selected, mapping categories will reduce bias and error in map interpretation. The method of rate calculation employed will affect variation among rate values as well as the nature of the frequency distribution. Crude and age-adjusted rates are chosen to suit the purpose of the map, but once the choice has been made the technical characteristics of the method and its affect on variation and frequency of distribution should be considered.

Notes

1 The author would like to thank Dr. John Storck, Consultant to the National Center for Health Statistics, U. S. Public Health Service, for suggesting the application of the standard deviation in the form presented here and also for his valuable comments on the paper in draft form.

2 Good examples for different countries can be found in G. M. Howe on behalf of the Royal Geographical Society, National Atlas of Disease Mortality in the United Kingdom (London: Thomas Nelson and Sons Ltd., 1963); G. M. Howe, “The Geography of Death in England and Wales, 1960,”The Lancet (April 13, 1963), pp. 818 20; M. A. Murray, “The Geography of Death in England and Wales,”Annals, Association of American Geographers, Vol. 52 (1962), pp. 130 49; M. A. Murray, “Geography of Death in the United States and the United Kingdom,”Annals, Association of American Geographers, Vol. 57 (1967), pp. 301 14; Bundesministerium Für Gesundheitswesen, Das Gesundheitswesen der Bundesrepublik Deutschland (Statistical Atlas on Public Health in the Federal Republic of Germany), Vol. 1 (Stuttgart: Kohlhammer, 1963); and J. Sigurjonsson, “Geographical Variations in Mortality from Cancer in Iceland, with Particular Reference to Stomach Cancer,”Journal of the National Cancer Institute, Vol. 37 (1966), pp. 337 46.

3 Data problesm are discussed by Murray, op. cit., footnote 2 (1962), and by F. E. Linder and R. D. Grove, “Definition and Interpretation of Vital Statistics Rates,”Vital Statistics Rates in the United States, 1900–1940 (Washington, D. C.: Government Printing Office, 1959), Chapter III, pp. 27–59.

4 N. D. McGlashan, “The Medical Geographer's Work,”International Pathology, Vol. 7 (1966), pp. 81 83.

5 The notation used in the following expressions is after M. Spiegelman, Introduction to Demography (Chicago: Society of Actuaries, 1955), pp. 54–71, to whom reference should be made for a more thorough treatment.

Where D is the total number of deaths among a population in a given area and time period; i, a specified cause of death; P the population at risk; and k, a constant unit of population—usually 1,000 or 100,000.

The expression nMx is the mortality rate at age x for the administrative unit in question and nPxs is the number of persons in the equivalent age group of a standard population, s. The standard population is usually the national group for a specified time; for example, the total population of the United States in 1960 could serve as a standard for calculating rates for each state. The procedure is to multiply the age specific death rates for a state by the corresponding population of the United States. This yields expected deaths which are summed to a total for all ages. The total of expected deaths is then divided by the total population of the standard to give the age-adjusted death rate for the state in question.

In fact, however, the age-specific death rates for sub-groups of the population are often not available and in these cases an indirect method of calculating the age-adjusted rate may be employed.

(2′) Age-adjusted Death Rate (Indirect Method) This is the ratio of the total reported deaths in the particular administrative unit, D, to the number expected on the basis of age-specific death rates in a standard population, multiplied by the crude death rate of the standard population. The result is an age-adjusted rate comparable to, but not the same as, that derived from the direct method. For a discussion of the merits of these two methods see T. D. Woolsey, “Adjusted Death Rates and Other Indices of Mortality,” Chap. IV, Vital Statistics Rates in the United States, 1900–1940 (Washington, D. C.: Government Printing Office, 1959), pp. 60–91.

The Standardized Mortality Ratio expresses the relative mortality in administrative units as a percentage of the national rate, the national rate being set at 100. It uses an age-adjustment procedure identical to that of the indirect method and differs only in that the constant multiplier is 100 and not the crude death rate of the standard population.

6 Adjustments are sometimes made for differences in the sex composition of a population as well as for age differences. Age-sex-adjusted rates usually compute age-specific rates for males and females separately and use standard populations for each sex before summation to yield a single rate. Adjustment for sex differences in the United States total population is of lesser importance than adjustment for age and produces only slight change in rates. The rates calculated in this paper were adjusted for age only.

7 Mortality data were drawn from National Center for Health Statistics, Vital Statistics of the United States, 1959, 1960, 1961 (Washington, D. C.: Government Printing Office, 1962, 1963, 1964), and population data from, U. S. Bureau of the Census, U. S. Census of Population: 1960, General Population Characteristics, United States Summary, Final Report PC (1)-1B (Washington, D. C.: Government Printing Office, 1961). It is usual, with United States mortality data, to use the estimated population for July 1 as a population base for computing rates. Thus the Census, as taken in April, 1960, does not represent a midyear population, but in the case of a three year mortality study, 1959–1961, there are advantages in pivoting the rate calculation around the Census where data are presented in greater detail and coverage, and perhaps greater reliability.

8 Calculation of rates, including adjustment propcedures, the standard deviations and class intervals, was performed in a single operation using the IBM 7094 computing facility of the University of Illinois, Urbana, Illinois.

9 For a discussion of this question see J. Yerushalmy, “A Mortality Index for Use in Place of the Age-adjusted Death Rate,”American Journal of Public Health, Vol. 41 (1951), pp. 907 22.

10 The difference between the overall mean and the mean of the rate distribution is due to rounding error in the case of the crude rate computation; in the case of the age-adjusted rate it is due to both rounding error and the weightings of the procedure itself.