Revised Fixed-base Model for Estimation of Adult Mortality in Developing Countries

This paper presents a revised Fixed-base model (RFBM) for the estimation of adult mortality in developing countries. The RFBM also derives estimates of adult mortality from the age distributions of two censuses by 5-year age-groups. Unlike the original version, RFBM does not depend on person – years lived between exact ages 0 and 5 years ( 5 0 L ) and the mid-point population of those aged 0 – 4 years ( 5 0 N ). Both 5 0 L and 5 0 N are known to be affected by under-reporting in most developing countries. The estimates of the RFBM appear to have improved and compare favourably with estimates from other methods. We recommend the use of the model, especially when there is insufficient data for direct estimation of adult mortality in developing countries, among others.


Introduction
Mortality serves as a gauge of a nation's extent of socio-economic and health development. As the level of demographic parameters (especially mortality) of a country improves; the ranking of the country on health issues increases among the committee of nations. Among the components of population change, mortality stands out because it affects some age distributions directly and others indirectly Nwogu and Okoro [1]. The focus of this present study is on mortality at age five years and above (denoted as adult mortality in most intercensal methods).
The direct estimation of adult mortality in many developing countries is difficult due to unreliable or incomplete civil registration systems. In most developing countries, because of the limitations of civil registration systems, demographic parameters are derived from censuses and survey data ─ these two sources are often defective, Nwogu and Okoro, [1]; Okoro [2]; Okoro and Nwogu [3]. Hence, the dependence on indirect techniques for the estimation of adult mortality in developing countries.
Derivation of adult mortality from two census age distributions is an alternative means explored by most developing countries to overcome or augment her ineffective civil registration systems. The intercensal survival methods still relevant are those that assume arbitrary intercensal period such as Preston integrated method [4], Preston-Bennett method [5], United Nations Synthetic Survival Ratio [6], Fixed-base model proposed by Nwogu and Okoro [1], etc. The Fixed-base model and Preston-Bennett method [5] are similar and do not make reference to life tables.
The Fixed-base model is considered for revision because it adopted a more conservative approach in the estimation of person-years lived ( ) x n L and expectation of life at age x ( ) x e but not without a limitation. The probability of surviving to exact age one ( 1 l ) an index for infant mortality is known to produce poor results according to many authors (UN [7]; kpedekpo [8]; Nwogu [9]; Okoro et al. [10]). In deriving 0 5 L used in the estimation of x n L , 1 l is one of the components used. However, it has been shown that 1 l is affected by under reporting. If it is possible to obtain an estimate that does not depend on both There are six sections to the paper. The first section contains an introduction; the second section contains a review of the Fixed-base model; the third section contains the derivation of the revised Fixed-base model; the fourth section contains empirical examples; the fifth section contains discussion; and the final section contains the conclusion.

Fixed-base Model
Nwogu and Okoro [1] proposed a Fixed-base model for estimation of adult mortality in developing countries based on the concept of variable-r method. The model proposed by Nwogu and Okoro [1] for estimation of expectation of life at age x ( is the total of person-years lived between exact ages 0 and 5 years, and is the mid-point population, and is the age-specific growth rate, Ln is log base e . For the open age interval (   ), Nwogu and Okoro [1] applied an expression by Kpedekpo [8] for the estimate of the number of person-years lived from  years and where, 9 0 l is the radix (equal to one) while 5 l and 10 l are the probabilities of surviving to exact ages 5 and 10 respectively, and other elements are as defined in the original Fixed-base model.

Estimation of open ended interval life table function (
For the open age interval (   ) in this revised version, we adopted an approach by Preston-Bennett [5] for the estimate of the number of person-years lived from  years and above )]

Algorithm for estimation of adult mortality using the revised fixed-base model
The measure of adult mortality adopted in this study is the expectation of life at age x ) ( x e for ...
is the 5-year age distribution derived from the two census

Empirical Examples
The revised model with other related models were applied to selected developing countries in this section.

Application to Nigeria female populations: 1991 -2006
The revised model was applied to census age distributions of the Nigerian female populations, from 1991 to 2006. Equations (3.6) through (3.11) were applied to the female populations to obtain the expectation of life at age x.

Application to Zambia female populations: 2000 -2010
The revised model was also applied to Zambia Female Populations, 2000 -2010.

Discussion
The RFBM was applied to census Okoro and Nwogu [15]. The data used in preparing or simulating such life tables are not from developing countries. They are mere interpolated values that put question marks on such estimates.
For Zambia, the age-specific estimates of the expectation of life of the RFBM appear very consistent with the WHO estimates from ages 5 to 20. Then, from age 35 and above, the WHO and Preston-Bennett method estimates were consistently higher than the RFBM estimates. The observed differences among the methods may be due to reasons mentioned above. It may also be that both the World Health Organization and Preston-Bennett method overestimated the life expectancy for that age range. Even at that, WHO estimates are interpolated values from existing model life tables which makes it susceptible to errors while the RFBM, FBM, and Preston-Bennett method derive their estimates directly from reported census data which may be affected by agemisreporting. Just like other inter-censal survival methods, the RFBM may be biased by net-migration, completeness of the two censuses, etc., UN [6]; UN [7]; ECA [16].

Conclusion
This paper revised the Fixed-base model for the estimation of adult mortality in developing countries. The model can derive estimates of adult mortality from the age distributions of two censuses. The estimates from the RFBM compared favourably well with estimates from other methods. World Health Organization estimates are used for assessment in this study not as a direct comparison of results because the data sources and methodology are not the same. The RFBM appear more consistent with the original version and the WHO estimates. The RFBM is a good alternative for the estimation of adult mortality in developing countries. The use of indirect techniques for estimation of most demographic parameters and socio-economic indicators should not obstruct the need to improve the civil registration systems so that mortality estimates can be derived directly from death records without going through the rigorous processes of indirect techniques.

APPENDIX
Appendix A

Peer-review history:
The peer review history for this paper can be accessed here (Please copy paste the total link in your browser address bar) https://www.sdiarticle5.com/review-history/88889