Methodology and techniques compared

I apply and compare four techniques of estimating the level of completeness of death registration using the above data. These are Brass’s growth balance method (1975), Courbage and Fargues’s method (1979), Preston and Coale’s method (1980) and Gray’s method (1986). All four procedures require the same type of data: deaths and total population by five-year age groups and by sex. The Courbage and Fargues and Preston and Coale procedures have additional data requirements: a model age pattem of mortality and a provisional estimate of the rate of growth, respectively. Brass’s and Gray’s methods do not require knowledge of the growth rate. In fact, the rate of growth is one of their estimated outcomes. For instance, Gray’s approach makes full use of the implicit relationships between different sectional growth rates.

Table 3-2 presents a schematic summary of the other main features of each of these techniques, arranged chronologically. Appendix 3.1, Volume 2 discusses the technical aspects of each of these techniques in great detail.

Table 3-2: Schematic summary of other main features of four methods of estimating the level o f completeness of death

registration used in this thesis

Method

Features

Main parameter to Assumptions Strengths and

obtain the level weaknesses

of completeness of death coverage

Brass's Estimation of

partial death rate and birth rate at age a and above

Closed stable population Constant underregistration by age Courbage and

Fargues's Estimation of the true death rate at age one and above

Not very sensitive to age-misreporting but highly sensitive to departure from

population stability No age-misreporting assumption and

of age, either of constant underregis­ tration of deaths by age the population of deaths Model mortality pattern to represent mortality pattern of population in question 4- same as Brass's except closed stable population Preston Coale's and Estimation of the number of persons at exact age a in a stable population Same as Brass's Gray's Simultaneous estimation of growth rates and death correction factors for each age a

Fairly robust if assumed model morta­ lity pattern repre­ sents actual pattern of population in question, applicable to population great­ ly affected by mig­ ration but sensitive to age-misreporting and violation to constant

underregistration of deaths by age Fairly robust to vio­

lation of population stability assumption but not robust to age-misreporting and differential underregistration of deaths by age Non-stable Highly applicable to

closed population destabilized popula- + saune as Brass's tion and fairly except stable robust to age-misre- closed population reporting but

not robust to

differential under­ enumeration of deaths by age

The level o f completeness o f death registration (C) is mathematically derived by each procedure in a different way. C is drawn from partial birth and death rates at age a and above (Brass’s method); from the true death rate at age one year and above (Courbage and Fargues’s method); from estimated number of

persons at exact age a in a stable population (Preston and Coale’s method); and from estimated Cs with the simultaneous minimization of differences between sectional growth rates (Gray’s method).

As to their underlying assumptions, all four approaches have common assumptions of constant underregistration of deaths by age and accurate age-reporting. However, they have unique features; Gray’s procedure allows for non-stability of closed populations while Brass’s and Preston and Coale’s procedures require stable closed populations; Courbage and Fargues’s procedure does not assume a stable closed population; however, it assumes that the mortality pattern of the population analysed follows an assumed model pattern. The assumed model pattern in the application of this procedure in this chapter is the Coale and Demeny (1966) West model life system. This has been the model generally adopted in the analysis of Philippine mortality by the majority of Philippine researchers.

As they contain similarities and dissimilarities in the underlying assumptions, these four techniques also contain common and contrasting strengths and weaknesses. All four approaches are subject to inappropriate model specifications, which means their robustness is contingent upon the fulfilment of their underlying assumptions. The application of Brass’s approach to a population that experiences drastic decline in mortality but no change in fertility is an example of inappropriate model specification of his approach.

In reference to inappropriate model specifications, the relative variances of estimates of the correction factor calculated or implied at different ages in each of the Gray , Brass and Preston and Coale techniques are also estimated. These variances are indices of variation from the underlying assumptions of the model and are helpful for comparing their robustness (Gray, 1986:429-430). A similar index could not be estimated from the Courbage and Fargues technique because only one correction factor for all ages is yielded by each of the variants under consideration.

Although Brass’s and Preston and Coale’s techniques have identical assumptions, the former is less sensitive to age-misreporting but more sensitive to violation of the assumption of stable population. Martin (1980) empirically demonstrated that the Brass method overestimates the completeness of death registration when mortality is declining. On the other hand, the Preston and Coale method is fairly robust to departures from the population stability assumption but not robust when age-misreporting characterizes the data under investigation. Gray’s procedure is most applicable to a population experiencing different patterns of change in fertility and mortality; it is less sensitive to age-misreporting than Brass’s approach, but it is not robust to a departure from the assumption of constant underregistration of deaths by age, a fault which is in fact shared by each of the other three methods. Courbage and Fargues’s technique is highly useful in populations substantially influenced by migration but is subject to the choice of a model mortality pattern that represents the actual mortality pattem of the population in question; and sensitive to age- misreporting and differential underregistration of deaths by age.

Problems of age-misstatement could have been identified had the deaths and population data been subjected to various tests for the presence of this error and then adjusted if this error was seriously present, before performing the comparative analysis of the four techniques. Nevertheless, one advantage of not performing this data evaluation and adjustment if necessary, is the determination whether Philippine data are grossly deficient The underlying principle is that the methods would give good results only when the data are good and corresponding assumptions are not violated greatly. Hence, under this premise, the comparative analysis of the four techniques in this chapter proceeds directly without performing data evaluation; besides, Chapter 4 demonstrates that census age-reporting is more or less accurate in the Philippines.

Ideally, these methods are used to estimate mortality (at ages 5 years and over) because the extent of underreporting of childhood deaths is substantially different from that of the adult deaths. However, in certain cases where robust childhood mortality estimates could not be obtained independently, these methods can be applied to ages one year and over. The Courbage and Fargues and Gray methods actually allow estimation for ages one year and over; and Gray (1986:434) has argued that his ‘procedure is capable of picking up the variation of growth rate (r(a+)) values at low ages quite well.’ All relevant calculations of the four methods are performed using a FORTRAN program4.