Simplified birth rate estimates under nonstable conditions

Coale's robust birth rate estimate, obtained by adjusting the birth rate of a stable population selected by matching the observed population of both sexes under the age of 15, C(15), and the probability of survival of births to age 5, l5, is shown to be equal to the birth rate obtainable by reverse surviving the proportion under the age of 15. Variations of matching the criterion of Coale's method to the rate of increase and C(15) or l5 are shown to lead to variants of Coale's birth rate estimate that are also nearly equal to the reverse survival birth rate based on C(15). A simplified birth rate estimate that does not require reference to models of life tables or stable populations is suggested and some of its applications are illustrated.     

Estimating infant and childhood mortality under conditions of changing mortality

Summary It is well known that estimates of infant mortality obtained using Brass's technique are very accurate. Biases are introduced, however, when one or more of the assumptions on which it relies are violated. Departures from the assumption of constant fertility may be handled by using a variant of the technique which depends on information on the age distribution of surviving children, rather than on indexes of the fertility function. Violations of the assumption of constant mortality - an increasingly common situation in most developing societies - produce upward biases in the estimates. The amount of bias is a function of the speed of mortality decline, the characteristics of the fertility pattern and, finally, of the age of the mother. This paper presents a simple technique which corrects these biases, and in addition, generates estimates of the parameters of the mortality trend. It differs from others in that it uses a cohort definition of mortality decline and relies on knowledge of the age structure of surviving children rather than on indexes of the fertility pattern.     

Applying Lee-Carter under conditions of variable mortality decline

The Lee-Carter method of mortality forecasting assumes an invariant age component and most applications have adopted a linear time component. The use of the method with Australian data is compromised by significant departures from linearity in the time component and changes over time in the age component. We modify the method to adjust the time component to reproduce the age distribution of deaths, rather than total deaths, and to determine the optimal fitting period in order to address non-linearity in the time component. In the Australian case the modification has the added advantage that the assumption of invariance is better met. For Australian data, the modifications result in higher forecast life expectancy than the original Lee-Carter method and official projections, and a 50 per cent reduction in forecast error. The model is also expanded to take account of age-time interactions by incorporating additional terms, but these are not readily incorporated into forecasts.     

Applying Lee-Carter under conditions of variable mortality decline

The Lee-Carter method of mortality forecasting assumes an invariant age component and most applications have adopted a linear time component. The use of the method with Australian data is compromised by significant departures from linearity in the time component and changes over time in the age component. We modify the method to adjust the time component to reproduce the age distribution of deaths, rather than total deaths, and to determine the optimal fitting period in order to address non-linearity in the time component. In the Australian case the modification has the added advantage that the assumption of invariance is better met. For Australian data, the modifications result in higher forecast life expectancy than the original Lee-Carter method and official projections, and a 50 per cent reduction in forecast error. The model is also expanded to take account of age-time interactions by incorporating additional terms, but these are not readily incorporated into forecasts.     

Comparing mortality estimates based on different administrative records

This study investigates how age and race are reported in interviews and on death certificates and how these demographic assignments affect life expectancy estimates for the total population, for males and females, and for blacks and whites. Differential reporting of demographic characteristics can produce different estimated life expectancies and thus differential assessments of the sex and race gaps in life expectancy. This difference underscores the need to define demographic characteristics carefully and to examine multivariate models and projections cautiously.     

An evaluation of the performance of kernel estimators for graduating mortality data

In the graduation of the age-specific mortality pattern, recent emphasis has been placed on the use of kernel regression estimators. Three such estimators are the Nadaraya-Watson, Gasser-Muller and kernel weighted local linear estimators. This paper discusses the theoretical background of each estimator and evaluates their accuracy in graduating age-specific mortality using data for France, Japan and Sweden. For comparison, we also fit the Heligman-Pollard model and its nine-parameter variant by Kostaki. The Gasser-Muller estimator is found to be superior to the two other kernel estimators in that it is both more stable and not influenced by boundary effects. Furthermore, compared with the two parametrric models, the Gasser-Muller estimator provides a more satisfactory graduation, especially at older adult ages, in terms both of smoothness and of fidelity between the observed and graduated rates.     

Migration bias in indirect estimates of regional childhood mortality levels

Demographers often use Brass‐style indirect methods to obtain childhood mortality estimates for regions within developing countries. Regional populations are not closed to migration, however, and mortality reports of women resident in a certain region on the survey date may contain information on events and exposure that occurred elsewhere as the mother migrated. Including this “imported”; mortality information may cause significant bias in regional estimates. In this paper the authors: (1) investigate the possible magnitude of migration bias using a multiregional simulation model, (2) propose a modification to standard methods which should reduce bias in many circumstances, and (3) apply the modified technique to data from Brazil's 1980 Census. We find that migration bias can indeed be significant, and that in the specific case of São Paulo state, imported mortality information may result in overestimates of local mortality levels of 10–15% when using Brass‐style methods.     

The use of hypothetical cohorts in estimating demographic parameters under conditions of changing fertility and mortality

The indirect methods of demographic estimation available to date are often inadequate to estimate levels in the presence of trends. The use of measures relative to hypothetical cohorts to minimize the effectsoftrends and estimate period levels is described. Procedures allowing the estimation of intersurvey levels of fertility, child mortality and adult mortality are illustrated using data from Thailand and Peru.     

A method for deriving mortality estimates from incomplete vital Statistics

Summary Although they are available in many developing countries vital registration records are very little used for mortality estimation which is still mainly based on census returns. However, defective death records may yield accurate estimations of mortality. This procedure requires few data only; a sex-age distribution of the population (preferably at the middle of a period) and a sexage distribution of deaths, either derived from vital records or from census returns to questions relating to deaths during the preceding twelve months. This method is based on the observation that for a fixed age structure of the population, there is a one-one relation between the age structure of deaths (measured by the proportion of deaths at older ages) and the level of mortality (measured by the death rate above a certain minimum age). It is assumed that at ages above this minimum the rate of underregistration of deaths does not vary significantly with age. Therefore, the age distribution of registered deaths makes it possible to estimate the true proportion of deaths at older ages. This in its turn will permit the estimation of the true level of mortality, because of the relation which exists between age structure of deaths and level of mortality. The true level is then compared with the observed, to estimate the rate of underregistration, and observed age-specific death rates can be adjusted in the light of this knowledge.     

A note on new estimates of the mortality of the extreme aged

This note reports on the utilization of the “extinct generation” method, a procedure that permits a reconstruction of “extinct” population cohorts from the death statistics for a series of years and provides alternative estimates of the mortality of the extreme aged population (persons 85 years of age and over) in the United States during the period 1951–1965. Remarkably close correspondence was found between the annual mortality rates thus derived and figures published by the National Center for Health Statistics. It was concluded that the quality of the mortality rates produced was superior to the official figures but not markedly so. An advantage of the method is the ability to produce rates in detail, such as for five-year age groups, not ordinarily published for the 85 and over population.     

The influence of social conditions on mortality rates

In this study the author examines the general problem of estimating the influence of social conditions on mortality rates and suggests that the methods of multiple regression analysis extensively used for this purpose cannot always be relied on to give the kind of results required. The argument is illustrated by reference to the work of Woolf and Waterhouse (J. Hyg., Camb., vol. XLIV, no. 2, 1945) on infant mortality in the county boroughs. The Confluence Analysis of Frisch, applied to their results suggests that the statistical series used by these authors are multicollinear, and use of Hotelling's method of Principal Components suggests that these five series represent not five but only two fundamental influences. One of these, almost equally strongly loaded in three of these series is identified with the ‘general social conditions'— a complex of bad housing and low money-incomes—which these and other writers have studied. This leads to the suggestion that the use of multiple regression analysis in attempts to estimate the separate influences of the individual constituents of this complex are likely to be unprofitable and misleading. It is suggested that the available information relating to social conditions in various districts can be most usefully employed in the form of a complex index which might be constructed by means of some form of Factor Analysis.     

Methods of adjusting the stable estimates of fertility for the effects of mortality decline

Summary The paper shows how stable population methods, based on the age structure and the rate of increase, may be used to estimate the demographic measures of a quasi-stable population. After a discussion of known methods for adjusting the stable estimates to allow for the effects of mortality decline two new methods are presented, the application of which requires less information. The first method does not need any supplementary information, and the second method requires an estimate of the difference between the last two five-year intercensal rates of increase, i.e. five times the annual change of the rate of increase during the last ten years. For these new methods we do not need to know the onset year of mortality decline as in the Coale-Demeny method, or a long series of rates of increase as in Zachariah's method.     

Data on survival of recent births as a source of child mortality estimates in the developing world: An assessment of census data

In many less developed countries, household surveys collect full and summary birth histories to provide estimates of child mortality. However, full birth histories are expensive to collect and cannot provide precise estimates for small areas, and summary birth histories only provide past child mortality trends. A simple method that provides estimates for the most recent past uses questions about the survival of recent births in censuses or large household surveys. This study examines such data collected by 45 censuses and shows that on average they tend to underestimate under-5 mortality in comparison with alternative estimates, albeit with wide variations. In addition, the high non-sampling uncertainty in this approach precludes its use in providing robust estimates of child mortality at the country level. Given these findings, we suggest that questions about the survival of recent births to collect data on child mortality not be included in census questionnaires.     

New estimates of fertility and child mortality in Africa, south of the Sahara

Summary Earlier work by Page and Coale has estimated demographic indices of fertility and mortality for parts of Africa using the Sullivan modification of Brass's technique. The present paper presents modified and more accurate estimates of fertility and child mortality, not only for the sub-national units covered by Page and Coale but also for areas not covered by them. The present analysis which employs Trussell's refinement of Brass and Sullivan's techniques also includes improvements overlooked in earlier estimates. The salient finding that emerges is that while the Brass mortality technique is very powerful, his equally ingenious fertility technique is very weak and should not be relied on for estimating fertility parameters.     

An analysis of indirect mortality estimation

Abstract In this paper the robustness of Brass's child-survivorship indirect mortality estimation technique is investigated. An analytical method is developed for studying the error or bias caused in indirect mortality estimates by poor data, badly chosen model functions, and specific demographic assumptions that are often violated in practice. The resulting analytical expressions give insight into the rationale of indirect methods, the conditions under which they are robust, and the magnitude of errors that occur when specific assumptions are violated.     

An analysis of indirect mortality estimation

In this paper the robustness of Brass's child-survivorship indirect mortality estimation technique is investigated. An analytical method is developed for studying the error or bias caused in indirect mortality estimates by poor data, badly chosen model functions, and specific demographic assumptions that are often violated in practice. The resulting analytical expressions give insight into the rationale of indirect methods, the conditions under which they are robust, and the magnitude of errors that occur when specific assumptions are violated.     

Follow-up surveys for census estimates of maternal mortality: experiences from Bolivia and Mozambique

Maternal mortality measurement through special census questions will be a common practice in the 2010 census round. To check this information or make it cause-specific, some countries have experimented with follow-up surveys containing verbal autopsies or triangulation with administrative data. However, follow-up studies can be costly and not without complications. In order to assess the benefits, two such experiences are discussed in detail (Bolivia, 2002; and Mozambique 2007–2008) and two others mentioned more briefly (Islamic Republic of Iran, 1996; and Democratic People’s Republic of Korea, 2008). In the former, several problems were apparent. In Mozambique, the follow-up survey used a cluster sample of 4.5% of deaths, from all causes. This design was adequate for the more common causes, but not for maternal mortality. Another problem was the large proportion of invalid cases (35.1%, plus 16% not verifiable) and the likelihood that there was a similar proportion of omitted deaths. The Bolivian census generated many invalid cases and missing ages, due in part to the flawed design of the questionnaire. This overburdened the follow-up, so that only 15% of the census deaths of women of reproductive age unrelated to pregnancy could be investigated. Once the false positives were eliminated, the results seem consistent with Growth Balance analyses, but the many classification errors compromise confidence in the results. Despite this mixed record of outcomes, it is believed that carrying out a limited number of similar studies in the current census round may be valuable, if appropriate lessons are learned from these experiences.