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.     

Death by survey: Estimating adult mortality without selection bias from sibling survival data

The widely used methods for estimating adult mortality rates from sample survey responses about the survival of siblings, parents, spouses, and others depend crucially on an assumption that, as we demonstrate, does not hold in real data. We show that when this assumption is violated so that the mortality rate varies with sibship size, mortality estimates can be massively biased. By using insights from work on the statistical analysis of selection bias, survey weighting, and extrapolation problems, we propose a new and relatively simple method of recovering the mortality rate with both greatly reduced potential for bias and increased clarity about the source of necessary assumptions.     

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.     

Contribution of mortality decline to longer working life: The case of indonesian males 1980–1995

The length of working life of Indonesian males has been estimated for 1980 and 1995. Data on age specific labour force participation rates are obtained from the 1980 census and the 1995 intercensal population survey. Data on agespecific mortality have been adopted from appropriate model life tables based on indirect estimates of child mortality in the absence of any direct information about mortality. The contribution of declining mortality to the lengthening of working life has been greater than the contribution of higher labour force participation rates. Reductions in mortality at ages before entry into the labour force have increased the potential for added and improved education and training needed for the work force, which is also a contribution of reduced mortality to human capital development. The findings have implications for policy and future employment plans.     

Methods For Comparing The Mortality Experience of Heterogeneous Populations

Methods are presented which produce Maximum Likelihood Estimates (MLE) of the degree of heterogeneity in individual mortality risks under a variety of assumptions about the age trajectory of those mortality risks. With these estimates of the degree of population heterogeneity it is possible to adjust comparisons of mortality risks across populations for the effects of population heterogeneity, differential mortality selection, and different age trajectories of the force of mortality. These methods are demonstrated by applying a variety of standard assumptions about the age trajectory of the force of mortality to the analysis of a broad range of cohort mortality data for the U.S. and Swedish populations. The estimates of the degree of heterogeneity, produced under all of the selected force of mortality models, consistently indicated a considerable degree of heterogeneity in mortality risks.     

Are Cohort Mortality Rates Autocorrelated?

In this paper the author examines the proposition that heterogeneity in individual frailty leads to autocorrelation in cohort mortality rates. A simple model is used to construct analytic expressions for the covariance of cohort mortality rates at different ages under a number of alternative assumptions about the stochastic process generating shocks in mortality. The model then is used to construct a procedure that uses correlations in cohort mortality rates to estimate the extent of heterogeneity in a population without relying on strong assumptions about the distribution of frailty or the shape of the underlying hazard. The procedure then is used to show that cohort mortality data from France are consistent with a generalized random-effects model in which frailty is gamma-distributed.     

Effects of targets and aggregation on the propagation of error in mortality forecasts

Official forecasts of mortality depend on assumptions about target values for the future rates of decline in mortality rates. Smooth functions connect the jump‐off (base‐year) mortality to the level implied by the targets. Three alternative sets of targets are assumed, leading to high, middle, and low forecasts. We show that this process can be closely modeled using simple linear statistical models. These explicit models allow us to analyze the error structure of the forecasts. We show that the current assumption of perfect correlation between errors in different ages, at different forecast years, and for different causes of death, is erroneous. An alternative correlation structure is suggested, and we show how its parameters can be estimated from the past data.

The effect of the level of aggregation on the accuracy of mortality forecasts is considered. It is not clear whether or not age‐ and cause‐specific analyses have been more accurate in the past than analyses based on age‐specific mortality alone would have been. The major contribution of forecasting mortality by cause appears to have been in allowing for easier incorporation of expert opinion rather than in making the. data analysis more accurate or the statistical models less biased.     

Estimation of a structural model of the determinants of neonatal mortality in Hungary, 1984-88 and 1994-98

We developed and evaluated a structural model of the determinants of neonatal mortality in Hungary that embodies the causal mechanisms by which its proximate and indirect determinants--socio-economic, behavioural, and biological--are related. The statistical model used distinguishes between endogenous and exogenous variables and allows the causal effect of each to be correctly estimated. Unobserved variables are integrated into the model, which was tested using Hungarian data for the periods 1984-88 and 1994-98. The principal findings are as follows: weight at birth and duration of gestation are the most important of the (direct) causal determinants of neonatal mortality. Mother's age has an indirect and detrimental effect: when mothers are older than 30 years of age, the risk of lower birth weight or multiple births and, in consequence, neonatal mortality is increased. Father's age has no direct or indirect causal effect on neonatal mortality.     

Measurement of adult mortality in less developed countries: a comparative review

"This paper compares the direct and indirect methods used to measure adult mortality in the developing world. No other approach can substitute fully for accurate and complete vital registration, but in many countries it is unrealistic to expect the registration system to cover the majority of the population in the foreseeable future.... The difficulties involved in measuring adult mortality using surveys and other ad hoc inquiries are discussed.... While the choice of methods must depend on each country's situation, direct questions require very large samples and are unreliable in single-round inquiries. On the other hand, although indirect methods provide less detailed and up-to-date information than is ideal, they are adequate for many practical purposes. In particular, the experience of the 1980s suggests that questions about orphanhood perform better than earlier assessments indicated, and recent methodological developments have circumvented some of the limitations of the indirect approach."     

Infant mortality in the Marshall Islands

Levy and Booth present previously unpublished infant mortality rates for the Marshall Islands. They use an indirect method to estimate infant mortality from the 1973 and 1980 censuses, then apply indirect and direct methods of estimation to data from the Marshall Islands Women's Health Survey of 1985. Comparing the results with estimates of infant mortality obtained from vital registration data enables them to estimate the extent of underregistration of infant deaths. The authors conclude that 1973 census appears to be the most valid information source. Direct estimates from the Women's Health Survey data suggest that infant mortality has increased since 1970-1974, whereas the indirect estimates indicate a decreasing trend in infant mortality rates, converging with the direct estimates in more recent years. In view of increased efforts to improve maternal and child health in the mid-1970s, the decreasing trend is plausible. It is impossible to estimate accurately infant mortality in the Marshall Islands during 1980-1984 from the available data. Estimates based on registration data for 1975-1979 are at least 40% too low. The authors speculate that the estimate of 33 deaths per 1000 live births obtained from registration data for 1984 is 40-50% too low. In round figures, a value of 60 deaths per 1000 may be taken as the final estimate for 1980-1984.     

Teaching population dynamics with a simulation exercise

Because many students learn general points best by an empirical demonstration rather than by a purely analytical approach, most of the mysteries of the formation and the evolution of a population under the action of mortality and fertility can be conveniently demonstrated on a computer in the form of population projections under various assumptions. Such an exercise can be simple and yet constitute a powerful teaching tool. Not only will it enable the student to observe the effects of central demographic processes but also it will serve to integrate through concrete applications many of the more technical concepts usually covered in an introductory population course, but rarely made meaningful to average beginning students. An easily administrable exercise along these lines is described in hopes that other instructors in population courses will find it as useful a teaching device as we did.     

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.     

A new technique to estimate infant mortality with an application for El Salvador and Colombia

The paper presents new estimates of infant mortality for Colombia and El Salvador for the years 1950--1970. These estimates are obtained by using a technique which improves on Brass's method in that it suppresses the assumption of constant mortality and introduces instead assumptions about linear and nonlinear changes in mortality risks affecting various cohorts of individuals.     

Optimizing the Lee-Carter Approach in the Presence of Structural Changes in Time and Age Patterns of Mortality Improvements

Researchers using the Lee-Carter approach have often assumed that the time-varying index evolves linearly and that the parameters describing the age pattern of mortality decline are time-invariant. However, as several empirical studies suggest, the two assumptions do not seem to hold when the calibration window begins too early. This problem gives rise to the question of identifying the longest calibration window for which the two assumptions hold true. To address this question, we contribute a likelihood ratio–based sequential test to jointly test whether the two assumptions are satisfied. Consistent with the mortality structural changes observed in previous studies, our testing procedure indicates that the starting points of the optimal calibration windows for most populations fall between 1960 and 1990. Using an out-of-sample analysis, we demonstrate that in most cases, models that are estimated to the optimized calibration windows result in more accurate forecasts than models that are fitted to all available data or data beyond 1950. We further apply the proposed testing procedure to data over different age ranges. We find that the optimal calibration windows for age group 0–49 are generally shorter than those for age group 50–89, indicating that mortality at younger ages might have undergone (another) structural change in recent years.     

The impact of induced abortion on black and white birth outcomes in the United States

This paper examines the impact of induced abortion on birth outcomes by treating abortion as an endogenous input into the production of infant health. To gauge the direct and indirect effects of abortion, three measures of infant health are considered simultaneously: the neonatal mortality rate, the percentage of low-weight births, and the percentage of preterm births. All three are race specific and all pertain to large counties in the United States in 1977. The results suggest that by preventing unwanted births, abortion enhances the survivability of newborns of a given birth weight and improves the distribution of births among high-risk groups.     

Estimating the Effect of Smoking on Slowdowns in Mortality Declines in Developed Countries

Declines in mortality rates for females at older ages in some developed countries, including the United States, have slowed in recent decades even as decreases have steadily continued in some other countries. This study presents a modified version of the indirect Peto-Lopez method, which uses lung cancer mortality rates as a proxy for smoking exposure, to analyze this trend. The modified method estimates smoking-attributable mortality for more-specific age groups than does the Peto-Lopez method. An adjustment factor is also introduced to account for low mortality in the indirect method’s study population. These modifications are shown to be useful specifically in the estimation of deaths attributable to smoking for females at older ages, and in the estimation of smoking-attributable mortality more generally. In a comparison made between the United States and France with the modified method, smoking is found to be responsible for approximately one-half the difference in life expectancy for females at age 65.     

Estimating Mortality Differences in Developed Countries From Survey Information on Maternal and Paternal Orphanhood

In general, the use of indirect methods is limited to developing countries. Developed countries are usually assumed to have no need to apply such methods because detailed demographic data exist. However, the potentialities of demographic analysis with direct methods are limited to the characteristics of available macro data on births, deaths, and migration. For instance, in many Western countries, official population statistics do not permit the estimation of mortality by socioeconomic status (SES) or migration background, or for estimating the relationship between parity and mortality. In order to overcome these shortcomings, I modify and extend the so-called orphanhood method for indirect estimation of adult mortality from survey information on maternal and paternal survival to allow its application to populations of developed countries. The method is demonstrated and tested with data from two independent Italian cross-sectional surveys by estimating overall and SES-specific life expectancy. The empirical applications reveal that the proposed method can be used successfully for estimating levels and trends of mortality differences in developed countries and thus offers new prospects for the analysis of mortality.     

The Courbage-Fargues method of indirect measurement of mortality: adequacy and inadequacy of the case of Togo in 1971

This study tests the validity of an indirect method of estimating mortality from inaccurate data from demographic investigations conducted in Togo in 1971. The method yields good results for Togo where life expectancy at birth is estimated at 40.51 years for males and 43.12 years for females. The article responds to the request of participants of the Colloquim of Abidjan and then corrects the mortality level of Togo in 1971 derived from the biased demographic investigation in Togo in 1971. OCDE tables were used to support estimates of mortality. A hypothesis of the method was that the deaths of the last 12 months are underreported in a constant proportion. A 2nd hypothesis was that the mortality of the country is related to a mortality pattern according to age. This method of Courbage-Fargues has produced satisfactory results. Certain demographers believe that the undercount rates are probably differentials according to age, particularly among those who die in the 1st few years of life. Others believe that knowledge of deaths that occur in the later years lacks certainty. Mortality data in Africa are not adequate enough to utilize as bases for estimates. For Togo, in particular, the application of other indirect measures of mortality is hoped for to allow comparisons.     

Maternal Education, Birth Weight, and Infant Mortality in the United States

This research determines whether the observed decline in infant mortality with socioeconomic level, operationalized as maternal education (dichotomized as college or more, versus high school or less), is due to its “indirect” effect (operating through birth weight) and/or to its “direct” effect (independent of birth weight). The data used are the 2001 U.S. national African American, Mexican American, and European American birth cohorts by sex. The analysis explores the birth outcomes of infants undergoing normal and compromised fetal development separately by using covariate density defined mixture of logistic regressions (CDDmlr). Among normal births, mean birth weight increases significantly (by 27–108 g) with higher maternal education. Mortality declines significantly (by a factor of 0.40–0.96) through the direct effect of education. The indirect effect of education among normal births is small but significant in three cohorts. Furthermore, the indirect effect of maternal education tends to increase mortality despite improved birth weight. Among compromised births, education has small and inconsistent effects on birth weight and infant mortality. Overall, our results are consistent with the view that the decrease in infant death by socioeconomic level is not mediated by improved birth weight. Interventions targeting birth weight may not result in lower infant mortality.     

The variance of population characteristics in stable populations, with applications to the distribution of income

Summary Stable population theory has recently been used to analyse the effects of changes in fertility and mortality on economic variables such as income per head. In this paper more general results are derived to describe the effects of changing vital rates on the variance and higher moments of the distribution of some age-dependent variable. Simple analytical expressions are derived which decompose the effects of changes in age structure into the effects on inter-cohort and intra-cohort variance. The results are easily applied to standard measures of the distribution of income. By combining the analytical results with actual age profiles of income and income variance from the United States and Brazil it is observed that both the magnitude and direction of the effects of population growth on measured inequality are sensitive to the specific age profiles used. The most surprising result is that the Brazilian age profiles suggest that higher growth rates may actually reduce measured inequality, although the effect is relatively small.