Using census data to estimate old‐age mortality for developing countries

Thanks to substantial improvements in child and adult survival through most parts of the world in the last decades, old‐age mortality accounts now for large fractions of death. Yet for many developing countries, old‐age mortality is often only inferred by model life tables using mortality data at young ages, or sometimes at young and adult ages; and reliable estimates of old‐age mortality using data collected from old‐age population can hardly be found. Based on the fact that migration is rare and death risk is high at old ages, this paper proposes a new indirect method, namely the Census method, to estimate old‐ age mortality, using census data on old‐age population. This new indirect Census method aims to eliminate the effects of age‐reporting errors, and is composed of three models. The first model is the variable‐r method that converts the census populations into the person‐years of the underlying stationary population. The second is an adjustment model, which uses a common relationship between the survival ratios that is found in model life tables to eliminate the effects of age‐reporting errors in censuses. And the third is the extended Gompertz model, which estimates the number of survivors at exact ages of the underlying stationary population based on the most commonly observed mortality pattern. Examples are provided using census data from developing countries in Africa and Asia. Background Data on death collected from census or registration are less reliable in many developing countries. This reality leads to using survey data to measure mortality levels. Based on methods such as the children ever born and survival (Brass 1964; Brass and Coale 1968; United Nations 1983), young‐age (e.g., under the age of 1 or 5 years) mortality are estimated, for instance, in the World Fertility Surveys (see http://opr.princeton.edu/archive/wfs). Using these measures, and combining with reliable data from vital registration and census, the United Nations Population Division (United Nations 2013) and the United Nations Children’s Fund (UNICEF, http://www.childmortality.org ) has long been regularly publishing young‐age (under the age of 1 and/or 5 years) mortality for virtually all countries back to 1. Nan Li and Patrick Gerland, Population Division, United Nations. Correspondence to Nan Li, 2 UN Plaza‐DC2‐1906, New York, NY 10017, USA; Tel: (212)963‐7535; Fax: (212) 963‐2638; E‐mail: li32@un,org. 2. Views expressed in this paper are those of the authors and do not necessarily reflect those of the United Nations. The designations employed in this paper and the material presented in it do not imply the expression of any opinion whatsoever on the part of the Secretariat of the United Nations concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. Li‐Gerland (2013): Using census data to estimate old‐age mortality for developing countries XXVII IUSSP International Population Conference. Busan, Korea Session 17‐05: Indirect methods of mortality and fertility estimation: new techniques for new realities (Aug 27, 2013) 2 1970s or 1950s. Following the estimates of young‐age mortality, surveys such as the Demographic and Health Surveys (DHS, http://www.measuredhs.com) started to measure adult (e.g., between the age of 15 and 60 years) mortality for an increasing number of developing countries, based mainly on the data and method of sibling survival (United Nations 2002). Combining with census and vital registration data, Rajaratnam and colleagues (2010) estimated adult mortality for 187 countries from 1970 to 2010. Utilizing young‐age mortality and one‐dimension model life tables (e.g., inputting only infant mortality;Coale and Demeny (1966 and United Nations (1982), one may produce a life table, according to which mortality at any age can be inferred. Using young‐age and adult mortality and two‐dimension model life tables (e.g., inputting infant and adult mortality; see Murray et al. (2003;Wilmoth et al. (2011), one could do such inferences better. In fact, these measures, and together with reliable data from census and vital registration, are used by the World Health Organization (WHO, http://www.who.int/gho/countries/en/) to provided life tables for almost all the countries. These achievements significantly enriched our knowledge about the mortality of developing countries. While child and adult mortality of most countries are systematically studied, old‐age mortality has not held proper attention, although it is the elephant in the room. It would be mistaking to consider old‐age mortality is less important than at young‐age and at adulthood, especially in estimating the global burden of disease (Wang et al. 2012). This is because 55% of deaths worldwide in 2005‐2010 were estimated to be aged 60 years and older (United Nations 2013): 153 million out of a total of 277 million deaths occurred in 2005‐2010 in that age group (Figure 1) and more than half of all deaths occur at age 60 or higher in nearly all developing regions, except in sub‐ Saharan Africa where only one fourth or less happen at those ages. Figure 1. Number of deaths in 2005‐2010 by broad age groups age and development group 0 10 20 30 40 50 60 70 80 90 100 0-14 15-59 60+ (m ill io n) More developed regions Other less developed countries Least developed countries Source: United Nations (2013) Knowing young‐age and adult mortality, old‐age mortality could be inferred using model life tables. This is a progress from using only young‐age mortality and model life tables to infer old‐age mortality, but it is still not an estimation based on the data of old‐age population. How to systematically estimate old‐age mortality for developing countries, when the numbers of death of vital registration and census are unreliable, is perhaps still a field to be explored. In principle, old‐age mortality could be estimated using indirect methods such as orphanhood or widowhood methods (Timæus 2013a, 2013b; United Nations 1983, 2002), and using survey data if proper information were collected. For example, if information on the survival status of the parents of the respondents is collected in a census or survey, then old‐age mortality could be directly estimated based on these orphanhood data. Information collected by proxy respondents about their children, siblings and parents is indirect, but can efficiently enlarge the potential sample size to estimate deaths and other rare events. In practice, however, Li‐Gerland (2013): Using census data to estimate old‐age mortality for developing countries XXVII IUSSP International Population Conference. Busan, Korea Session 17‐05: Indirect methods of mortality and fertility estimation: new techniques for new realities (Aug 27, 2013) 3 indirect information about old‐age mortality has yet to be collected; and directly estimating old‐age mortality using deaths and exposure survey data (Bendavid, Seligman and Kubo 2011; INDEPTH Network 2002) is still unable to provide acceptable results, due mainly to sample size limitation or sample selection issues. On the other hand, this paper offers an approach to estimate indirectly old‐age mortality using data from population censuses and addressing issues related to errors of age reporting, assuming that the difference in completeness between successive censuses is negligible. For young age‐mortality, commonly used indicators are the infant mortality rate 0 1 q or the under‐five mortality rate 0 5 q , namely the probability of dying between ages 0 and 1 or 0 and 5, respectively. A common measure of adult mortality is the 15 45 q , which is the probability of dying between ages 15 and 60, where the 45 represents the years to reach 60 from age 15. While a standard measure of old‐age mortality still remains to emerge from future studies, this paper proposes to use 60 15 q as measure of old‐age mortality, namely the probability of dying between ages 60 and 75, or simply the old‐age mortality. The main reason to choose 60 as the lower bound is simply because it is a commonly used starting age for old‐age population, and the most commonly used statutory retirement age (United Nations 2012). The reason to choose 75 as the upper bound is that most developing countries have been tabulated census data with an open age group starting at this age, especially in earlier years when populations were smaller. In applying the variable‐r method, the general obstacle is its assumption of zero migration (Bennett and Horiuchi 1981), or its requirement on the accurate numbers of net migration (Preston and Coale 1982), which is more difficult to obtain than to estimate deaths. This obstacle should become trivial at ages of 60 years and old, when there are fewer migrants. Further, the increasing deaths at old ages would make the effect of the migration negligible. In applying variable‐r method to developing countries, however, the remaining difficulty is the age heaping and other errors in censuses, particularly at ages ending with 0. Based on the common age patterns of survival ratios, this paper proposes a procedure to correct the effects on old age mortality rates caused by age heaping and other reporting errors (e.g., misstatement, exaggeration) that are common in censuses of developing countries (Ewbank 1981; Preston, Elo and Stewart 1999). Another issue is that the variable‐r method produces only the person‐years for the underlying stationary population, while the number of survivor at exact ages are still unknown. These numbers are hard to estimate for developing countries, given the issue of age heaping and the lack of reliable population data between censuses. This issue is addressed here using an extended Gompertz model. Cautions must also be made, however, that the assumption of similar completeness of two successive censuses, which is required by the variable‐r method, is still necessary in this paper. Nonetheless, it can be assumed that old people are less mobile, and therefore are easier to count in censuses. Hence, this necessary assumption stands better in this study than in others focusing on younger ages. Nevertheless, under the assumption that census coverage improves over time, any improved completeness for the most recent census would lead to underestimation of old age mortality. In situations when the number of death by age between the censuses could be obtained from sources independent from the census population, the difference in completeness between two successive censuses could be estimated by the General Growth Balance method (Hill 1987), and its effect on estimating old‐age mortality could be adjusted. In cases when the post‐enumeration surveys are available and reliable for the censuses, the effect of the differential census coverage completeness between successive censuses could also be adjusted. In addition, instead of relying only on conventional intercensal periods analyzing two successive censuses, more robust results should also be obtained over longer intercensal period using multiple censuses. Evaluation of final old‐age mortality results by sex can Li‐Gerland (2013): Using census data to estimate old‐age mortality for developing countries XXVII IUSSP International Population Conference. Busan, Korea Session 17‐05: Indirect methods of mortality and fertility estimation: new techniques for new realities (Aug 27, 2013) 4 also reveal further insights about the plausibility of the underlying assumption about differential census coverage between censuses (e.g., male mortality substantially much lower than female old‐age mortality could be one of the symptoms). The Census method The method proposed here, namely the Census method, is composed of three parts: the variable‐r method, the adjustment of errors on age, and the extended Gompertz model. The variable‐r method The target of our estimation is the probability of dying between ages 60 and 75, 60 75 60 15 1 l l q   , (1) where x l represents the number of survivors at age x. Let p(x, t) be the observed number of population in age group [x,x+5) in a census at time t, where x=60, 65, 70. The growth rates at age x are computed as 70 , 65 , 60 ), /( ] ) , ( ) , ( [ ) ( 1 2 1 2    x t t t x p t x p Log x r . (2) And the accumulated growth rates are accordingly ). 70 ( 5 . 2 )] 65 ( ) 60 ( [ 5 ) 70 ( ), 65 ( 5 . 2 ) 60 ( 5 ) 65 ( ), 60 ( 5 . 2 ) 60 (