Estimating Completeness of Death Registration
Direct Approaches
There are two broad approaches to estimating completeness of death registration: direct and indirect. In the direct approach, the true level of mortality is independently estimated and compared with the level reported in the registration system.
Household surveys of child survival, often performed in conjunction with census enumeration, are examples of the direct approach, but few such surveys are available for the pre-World War ∏ era. Of more interest to social scientists are “matching” studies, in which deaths appearing in one tabulation (e.g., a parish register) are matched with deaths tabulated in the civil registration system during the same period (Marks, Seltzer, and Krotki 1974). It can be shown that, if inclusion in the civil registration system and inclusion in the alternative tabulation are statistically independent, then completeness of civil registration, say C, is equal to the ratio of deaths recorded in both systems, say D(Both), to deaths recorded in the alternative system, say D(Alt):C = D(Both)∕D)Alt). (1)
It is important to note that, given statistical independence, it is unnecessary to assume that the alternative recording system is complete. The main advantage of matching studies, which have had extensive historical application (e.g., Crimmins 1980), is their conceptual simplicity. They are also well suited to the study ofhighly disaggregated mortality data, such as deaths in a given city from a given cause among a given segment of the population. The main difficulties, in addition to violations of the independence assumption, are empirical, particularly in deciding what constitutes a true match. It should be added that the matching-study approach is inherently labor intensive.
Indirect Approaches
Most indirect approaches to estimating completeness of civil registration are of comparatively recent development.
The basic data requirement for all such methods is a reported age distribution of deaths in a given year. Other requirements, depending on the method employed, include population by age in the study year and age-specific population growth rates (calculated from two censuses, neither of which need have been taken during the study year). Most indirect methods require either the assumption of a stable population (i.e., one that is closed to migration and in which rates of birth and death have been constant for a long period of time) or, at a minimum, the assumption of no migration. In some cases, the methods are fairly robust to violations of these assumptions.Some notion of the indirect approach can be gained by looking briefly at one of the earliest and simplest of these methods developed by William Brass. (The present section is based on the discussion in MacKellar 1987.) The Brass method is based on the fundamental population change accounting identity:
r(x+) = δ(x+) - d(x+) + ∕n(x+). (2)
Here r(x+) is the actual growth rate of the population aged over x, and δ(x+) is the actual birthrate of the population aged over x; that is, the number ofxth birthdays celebrated in a given year divided by the number of person-years lived in a state of being aged over x in that year, d(x+) is the actual death rate of the population aged over x, analogously defined; and m(x+) is the actual net migration rate of the population aged over x, analogously defined.
Setting x equal to zero, we find that (2) reduces to the familiar identity whereby the growth rate of the total population equals the crude birthrate minus the crude death rate plus the crude rate of net migration.
The population is assumed to be stable, and since the age distribution of a stable population is invariant, r(x+) is constant for all x. Let this constant growth rate be r. Since there is, by assumption, no net migration, we have m(x+) = 0 for all x. The completeness of death registration is assumed to be constant with age over age x.
Let the proportion of actual deaths enumerated be C. Then (2) can be rearranged to yield the following:δ(x+) = r + (1/C) d'(x+), (3)
where d'(x+) is the recorded death rate over age x.
If N(x+) is the recorded population aged over x and N(x, x + n) is defined as the population aged between x and x + n, δ(x+) can be estimated by a statistic such as the following:
δ(x+) = (N(x — n, x) + N(x, x + n))∕2nN(x+'>. (4)
Thus, given a set of observed age-specific death rates and a single population census for the calculation of δ(x+), linear regression or any other curvefitting procedure can be used to estimate the population growth rate and the completeness of death registration (see United Nations 1983 for a discussion of estimation issues).
The primary advantages of indirect approaches are, first, that their data requirements are modest, and second, that as a result, they are much less labor intensive than direct methods. However, indirect methods are applicable almost exclusively to national-level populations and allow no disaggregation by cause of death, residence, socioeconomic status, and so on.