An evaluation of brass mortality estimates under conditions of declining mortality

An evaluation of the Brass childhood mortality estimates under conditions of declining mortality shows them to overestimate current mortality. Error increases as the rate of mortality decline increases, as the childhood age up to which cumulative mortality is being estimated increases, and as age at onset of childbearing decreases. We use the results to develop a method for correcting the Brass estimates for the effects of quasistability. The method requires an estimate of the rate of mortality decline within the population in addition to information on the pattern of childbearing in the population.     

Mixed estimation of old‐age mortality

The estimation of the mortality of the “oldest old”; is subject to considerable random error, but important prior information exists that can be used to make the estimates more robust. Mixed estimation is a method of incorporating auxiliary information into the statistical estimation of linear models. We extend the method to cover general maximum likelihood estimation, and show that the mixed estimator can be represented approximately as a weighted average of the purely data based estimator and the auxiliary estimator. The methods can be applied to the analysis of the old‐age mortality via logistic and Poisson regression. A major advantage of the mixed estimator is the simplicity with which it can incorporate partial prior information. Moreover, no special software is needed in the fitting. We show how the targeting methods of Coale and Kisker can be represented as mixed estimation in a natural way that is more flexible than the original proposal. We also derive empirical estimates of the target information based on pooled data from several countries with high quality data. We consider the mortality of Finland at ages 80 +, study the reliability of the evidence of mortality crossover, and derive estimates of life expectancy at age 100.     

Orphanhood and adult mortality in the past: a critique of Latin American data and procedures

The author examines the applicability of indirect methods for estimating mortality from information about orphanhood based on methods developed by Brass and Hill using data from Latin America. The author concludes that the data sources available in the region may not be adequate for the application of such techniques.     

Comparison of Four Methods for Estimating Complete Life Tables from Abridged Life Tables Using Mortality Data Supplied to EUROCARE-3

ABSTRACT

To estimate mortality due to cancer, it is necessary to have mortality data by year of age in the population of cancer patients. When such data are not available, estimating one-year (complete) life tables from five-year (abridged) life tables is necessary. Four such methods—Elandt–Johnson, Kostaki, Brass logit, and Akima spline methods—are compared with respect to 782 empirical complete life tables pertaining to 19 European regions or countries, from 1954 to 2000. Abridged life tables are first derived from the empirical ones, then used to produce one-year-life tables by each of the four methods. These reconstituted complete life tables are then compared with the empirical complete life tables. Among the four methods, the Elandt–Johnson demographic method produces the best reconstitutions at adult ages, specifically those ages at which observed cancer survival needs to be corrected.     

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.     

Mortality and Attrition Processes in Longitudinal Studies in Africa: An Appraisal of the Iford Surveys

This paper considers the impact of sample-attrition through dropouts on mortality analyses, using the pioneering IFORD survey of Yaounde (Cameroon). The essential issue in the IFORD surveys is the possibility that mortality of members of the cohort may differentially select some children, with specific underlying characteristics. The paper implements a method to assess the following three distinct concerns that may arise in the analysis of the IFORD data: (a) the estimation of the relationship between the covariates and the rate of occurrence of mortality or attrition over time; (b) the study of the interrelation between processes under a specific set of conditions during intervals between rounds for those children still alive and in the survey at the beginning of each interval; and (c) the issue of whether mortality and mortality differentials are affected when attrition is ignored. This approach accounts for sample-selection bias that may have resulted in the attrition process. The analyses provide insights into the debate, which has been ongoing since the late 1970s among students of African demography, regarding the selection problem in the IFORD surveys. Based on a multinomial survival modelling and bivariate probit with sample-selection framework, the results substantiate the belief that average levels and differentials of mortality would not have been different for children who dropped out from the survey than for those who remained in the survey. This is evidence that mortality estimates are virtually unaffected if attrition is ignored.     

A flexible two-dimensional mortality model for use in indirect estimation

Mortality estimates for many populations are derived using model life tables, which describe typical age patterns of human mortality. We propose a new system of model life tables as a means of improving the quality and transparency of such estimates. A flexible two-dimensional model was fitted to a collection of life tables from the Human Mortality Database. The model can be used to estimate full life tables given one or two pieces of information: child mortality only, or child and adult mortality. Using life tables from a variety of sources, we have compared the performance of new and old methods. The new model outperforms the Coale-Demeny and UN model life tables. Estimation errors are similar to those produced by the modified Brass logit procedure. The proposed model is better suited to the practical needs of mortality estimation, since both input parameters are continuous yet the second one is optional.     

Model Migration Schedules: Three Alternative Linear Parameter Estimation Methods

ABSTRACT

Observed schedules of migration rates exhibit strong regularities in age patterns. These regularities may be captured and represented by a mathematical expression known as the multiexponential model migration schedule. Fitting this function to empirical data requires non-linear regression methods and often some experimentation with alternative initial estimates of the parameters. Simpler, linear methods of estimation are adequate for most applications. These may be carried out with hand calculators or simple spreadsheet-based calculations on the computer. Such methods are studied and appear to perform satisfactorily.     

The completeness of enumeration in the 1973 census of the population of Colombia

The effort is made to determine the true size and distribution by age and sex of the population of the Republic of Colombia in October 1973. After initially arriving at estimates of the levels of fertility and mortality during the intercensal period and then correcting the 1964 census population for age misreporting and selective undernumeration of males, a hypothetical populaiton corresponding to October 1973 is constructed. Comparing the constructed population with the population observed in the census yelds an estimate of completeness of enumeration in 1973 that is relative to the enumeration of females in 1964. This estimate is obtained under the assumption that net international migration during the period was of negligible importance. As there is reason to believe that this is not a valid assumption and upon examining the limited amount of evidence available, speculaitons are made concerning the amount of net out-migration to have occurred during the 1964-1973 period and the size of the coresponding modificaiton in the estimate of completeness of enumeration. After adjusting for underenumeration of males in 1964 and neglecting the impact of international migration, a theoretical 1973 census population of 23,201,000 was estimated. Apart from the total number of people enumerated, the information that was analyzed from the advance sample appears to be of good quality, at least in relation to prior censuses. The estimates of fertility and mortality reveal an important decline in Colombian fertility. By coming up with separate estimates of infant and childhood and adult mortality, it has been possible to shed new light on the shape and the level of mortality in Colombia. The new Brass method for estimating adult mortality provides reliable results even when mortality has been declining, and there are recognizable distortions in the distribution of the population by age.     

Child survivorship estimation: methods and data analysis

"The past 20 years have seen extensive elaboration, refinement, and application of the original Brass method for estimating infant and child mortality from child survivorship data. This experience has confirmed the overall usefulness of the methods beyond question, but it has also shown that...estimates must be analyzed in relation to other relevant information before useful conclusions about the level and trend of mortality can be drawn.... This article aims to illustrate the importance of data analysis through a series of examples, including data for the Eastern Malaysian state of Sarawak, Mexico, Thailand, and Indonesia. Specific maneuvers include plotting completed parity distributions and 'time-plotting' mean numbers of children ever born from successive censuses. A substantive conclusion of general interest is that data for older women are not so widely defective as generally supposed."     

Effect of aggregation on the estimation of trend in mortality

There are three approaches to analyzing and forecasting age‐specific mortality: (1) analyze age‐specific data directly, (2) analyze each cause‐specific mortality series separately and add the results, (3) analyze cause‐specific mortality series jointly and add the results. We show that if linear models are used for cause‐specific mortality, then the three approaches often give close results even when cause‐specific series are correlated. This result holds for cross‐correlations arising from random misclassification of deaths by cause, and also for certain patterns of systematic misclassification. It need not hold, if one or more causes serve as “leading indicators”; for the remaining causes, or if outside information is incorporated into forecasting either through expert judgment or formal statistical modeling. Under highly nonlinear models or in the presence of modeling error the result may also fail. The results are illustrated with U.S. age‐specific mortality data from 1968–1985. In some cases the aggregate forecasts appear to be the more credible ones.     

Infant mortality,birth order,and sibship size: The role of heterogeneous risk and the previous‐death effect

This paper derives an analytic model to study biases in infant mortality estimates by birth order and sibship size, which occur when the death of an infant tends to shorten the next birth interval and mortality risk varies among families. We find that order‐specific and sibship‐size‐specific estimates are biased by a selection for high‐risk women across birth orders, since women with higher risk will tend to have shorter intervals, and more births, within a given period of time. Sibship‐size‐specific estimates are, in addition, biased by a selection of women who have experienced deaths, even if there is no heterogeneity in risk. Numerical examples based on data from Matlab, Bangladesh, are used to illustrate the possible magnitude of these biases. The results resemble patterns of infant mortality by birth order and sibship size which are often observed empirically.     

A re-estimation of the multiplying factors for the Brass technique for determining childhood survivorship rates

Summary One of the truly significant contributions to practical demography is the procedure developed by William Brass for estimating life-table values from minimal data obtained in fertility surveys. Specifically, Brass designed a set of factors dependent on the shape of the fertility schedule, which convert proportions of children dead of women in standard age intervals into life table q(x)-values. Jeremiah Sullivan recently presented in this journal a method for simplifying the calculations involved in obtaining the multiplying factor in the Brass procedure. Both Brass and Sullivan employed restrictive fertility schedules to obtain their multiplying factors, and a rigorous test of either model has been hampered by the lack of numerous adequately recorded fertility schedules, especially those which begin early. Recently, a set of model fertility schedules which adequately duplicates empirical fertility schedules has been developed. These schedules were used to test the Brass and Sullivan procedures and to obtain new estimates of multiplying factors. Although the Brass and Sullivan procedures are shown to produce good estimators, new estimators, which prove superior to either, are developed and analysed.     

The Impact of Salmon Bias on the Hispanic Mortality Advantage: New Evidence from Social Security Data

A great deal of research has focused on factors that may contribute to the Hispanic mortality paradox in the United States. In this paper, we examine the role of the salmon bias hypothesis—the selective return of less-healthy Hispanics to their country of birth—on mortality at ages 65 and above. These analyses are based on data drawn from the Master Beneficiary Record and NUMIDENT data files of the Social Security Administration. These data provide the first direct evidence regarding the effect of salmon bias on the Hispanic mortality advantage. Although we confirm the existence of salmon bias, it is of too small a magnitude to be a primary explanation for the lower mortality of Hispanic than non-hispanic (NH)-White primary social security beneficiaries. Longitudinal surveys that follow individuals in and out of the United States are needed to further explore the role of migration in the health and mortality of foreign-born US residents and factors that contribute to the Hispanic mortality paradox.     

Parental survival data: Some results of the application of Ledermann's model life tables

Summary Ledermann's one- and two-parameter model life tables are used in order to summarize and compare adult mortality estimates derived from parental survival data, and also to link parental survival with child survival data. The Ledermann models provide an alternative to the logit model used by Brass and Hill. Examination of life tables derived from actual child and adult mortality estimates reveals that although the two types of models yield similar overall levels of mortality, they show marked differences in the estimated patterns by sex and age. It has not been possible to disentangle completely how much of this divergence is due to the models themselves and how much to inadequacies in the data available. Finally, we question whether it is always wise to establish a full life table from child and adult mortality estimates when these are based on data which refer to different periods of exposure to the risk of dying, without allowance for possible distortions resulting from mortality change.     

Adjustment for nonresponse with variables from different sources: Bias correction and precision loss,with application to the Swiss European Social Survey 2012

ABSTRACT

Adjustment for nonresponse should reduce the nonresponse bias without decreasing the precision of the estimates. Adjustment for nonresponses are commonly based on socio-demographic variables, although these variables may be poorly correlated with response propensities and with variables of interest. Such variables nevertheless have the advantage of being available for all sample units, whether or not they are participating in the survey. Alternatively, adjustment for nonresponse can be obtained from a follow-up survey aimed at sample units which did not participate in the survey and from which the variables are designed to be correlated with response propensities. However, information collected through these follow-up surveys is not available for people in the sample who participated neither in the survey nor in its nonresponse follow-up. These two sets of variables when used in a nonresponse model for the Swiss European Social Survey 2012 differ only slightly with regard to their effect on bias correction and on the precision of estimates. The variables from the follow-up are performing slightly better. In both cases, the adjustment for nonresponse performs poorly.     

The Movement Beyond (Lifestyle) Migration: Mobile Practices and the Constitution of a Better Way of Life

Abstract

This article revisits my ethnography of the British in rural France to question how mobility in post‐migration life was deemed intrinsic to the better way of life that they sought through their migration. Through the exploration of the migrants’ everyday lives, I reveal that the migrants’ mobile practices and their expectations of mobility contributed towards the perceived success of their new lives and were thus significant to the ongoing process getting to a better way of life. Beyond this example, the article also demonstrates how the findings of mobilities researchers may be mobilized in traditional anthropological fieldwork.     

Simultaneity bias in migration models: An empirical examination

A number of migration studies have attempted to explain migration that occurred over a given time interval by means of variables defined for the end of the period and/or variables relating to changes that occurred over the period. Since migration may influence end-of-period levels of explanatory variables by influencing the behavior of these variables over the period of migration, simultaneous-equations bias may be inherent in the parameter estimates of the many single-equation, multiple-regression analyses. This study constitutes an empirical examination of qualitative differences in the parameter estimates of five different types of migration models estimated for two different time periods, 1960 and 1970.     

Fertility and mortality estimation from the Panama Retrospective Demographic Survey, 1976

Summary Data from the Retrospective Demographic Survey of Panama offer a unique opportunity to test a wide range of methods for estimating indirectly basic demographic parameters from inaccurate and incomplete data. Our primary emphasis is to evaluate methods for estimating adult mortality from information on widowhood and orphanhood, though estimates of childhood mortality obtained from information on sibling and child survivorship are assessed as well. The results for most of the estimating procedures are consistent; this finding is encouraging because it lends support to the hypothesis that the techniques can provide good estimates of mortality. Methods which produce results which are inconsistent provide valuable lessons. In particular, methods for providing unconditional estimates of values ofl (x) for adults by combining directly information on childhood mortality and adult mortality are shown to produce estimates which predominantly reflect the level of childhood mortality employed. Furthermore, within-method consistency of estimates appears to be a very poor indicator of reliable performance of the estimating technique or quality of data, since most methods yielded estimates which were internally consistent, though estimates made by different methods could differ considerably. In summary, the analysis indicates a birth rate of around 35 per thousand, a death rate of around 7.5 per thousand, a total fertility ratio of about 4.8, and expectations of life at birth of approximately 59 and 64 years for men and women respectively.     

The Level and Age Pattern of Mortality in Bandafassi (Eastern Senegal): Results From a Small-Scale and Intensive Multi-Round Survey

The data collected in the Bandafassi demographic study in Eastern Senegal, a small-scale intensive and experimental follow-up survey of a population of about 7,000 in 1983, were analysed to derive an estimated life table. The use of multi-round surveys, combined with anthropological methods to estimate ages and collect genealogies, has resulted in unusually reliable data. Taking into account the uncertainty of the estimates due to the small size of the population, mortality was high, with life-expectancy at birth close to 31 years; a pattern of infant and child mortality close to that observed in other rural areas of Senegal, with a very high level or mortality between ages six months and three years; a seasonal pattern in child mortality with two high-risk periods, the rainy season and the end of the dry season; an adult mortality pattern similar to that described in model life tables for developed countries; no significant difference by sex or ethnic group. The Bandafassi population study and a few similar studies suggest that one possible way to improve demographic estimates in countries where vital registration systems are defective would be to set up a sample of population laboratories where intensive methods of data collection would continue for extended periods.