Appendix D
Growth Balance Methods for Estimating Coverage of Adult Deaths

Brass (1975) proposed a method for assessing the coverage of death recording by comparing the age pattern of deaths with the age pattern of the population. In a stable population with no migration, the growth rate at each age is constant, so the difference between the entry rates and exit rates of successive age groups must be identical. A straight line fitted through the points has a slope determined by the reciprocal of death-reporting coverage and an intercept equal to the constant annual growth rate. This method has been applied to the 1988 adjusted population and 1988 deaths in the year before the census [18]. The results are not very encouraging: the points (see Figure D-1) do not lie on a straight line, the estimated growth rates are 3.5 percent per year for females and 3.8 percent for males, and the estimated coverage of deaths is in excess of 200 percent for both males and females.

The intercensal survival estimates of adult mortality have been seen to suggest very high levels of adult mortality, and one possible reason put forward to explain this is a change in census coverage between 1976 and 1988. The General Growth Balance method (Hill, 1987), developed for nonstable population applications from the Brass Growth Balance Method (Brass, 1975), provides a convenient way of assessing change in census coverage when the age pattern of adult mortality is reasonably well established.

In essence, the method compares two estimates of the death rate above a range of ages x—one estimate obtained from an age pattern of deaths, and



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Population Dynamics of Senegal Appendix D Growth Balance Methods for Estimating Coverage of Adult Deaths Brass (1975) proposed a method for assessing the coverage of death recording by comparing the age pattern of deaths with the age pattern of the population. In a stable population with no migration, the growth rate at each age is constant, so the difference between the entry rates and exit rates of successive age groups must be identical. A straight line fitted through the points has a slope determined by the reciprocal of death-reporting coverage and an intercept equal to the constant annual growth rate. This method has been applied to the 1988 adjusted population and 1988 deaths in the year before the census [18]. The results are not very encouraging: the points (see Figure D-1) do not lie on a straight line, the estimated growth rates are 3.5 percent per year for females and 3.8 percent for males, and the estimated coverage of deaths is in excess of 200 percent for both males and females. The intercensal survival estimates of adult mortality have been seen to suggest very high levels of adult mortality, and one possible reason put forward to explain this is a change in census coverage between 1976 and 1988. The General Growth Balance method (Hill, 1987), developed for nonstable population applications from the Brass Growth Balance Method (Brass, 1975), provides a convenient way of assessing change in census coverage when the age pattern of adult mortality is reasonably well established. In essence, the method compares two estimates of the death rate above a range of ages x—one estimate obtained from an age pattern of deaths, and

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Population Dynamics of Senegal FIGURE D-1 Brass growth balance method for estimating coverage of adult deaths, robust regression. SOURCE: Unpublished data, 1988 census. NOTE: Each point represents a particular age group (i.e., 0+, 5+, 10+). the other as the residual of the entry rate and population growth rate above age x. For the present application, the deaths in the 12 months before the 1988 census have been used with the 1976 and adjusted 1988 age distributions. Figure C-2 shows the plots of the application of the method. In terms of census coverage, the ratio of coverage in the 1976 census [17] to that in 1988 is 1.18 for males and 1.23 for females. As suggested earlier, either the 1976 census was a substantial overcount or the 1988 census was a substantial undercount. The estimates of coverage of deaths are less satisfactory: for males, relative to the coverage of the 1976 census, deaths were overreported by nearly 60 percent, whereas for females the corresponding figure is in excess of 170 percent. These estimates are most implausible. It is probably the case that the exaggeration of age in the census age distributions

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Population Dynamics of Senegal FIGURE D-2 General growth balance method for estimating coverage of adult deaths, robust regression. SOURCES: Unpublished data, 1976 and 1988 censuses. NOTE: Each point represents a particular age group (i.e., 0+, 5+, 10+). and deaths has greatly distorted the estimate of death coverage. As seen above, the age patterns of the adult mortality estimates based on deaths in 1987-1988 are very consistent with model patterns, and in the absence of any strong indication of systematic error, the data are accepted as being reasonably accurate.