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.     

Estimating the Reliability of Single-Item Life Satisfaction Measures: Results from Four National Panel Studies

Life satisfaction is often assessed using single-item measures. However, estimating the reliability of these measures can be difficult because internal consistency coefficients cannot be calculated. Existing approaches use longitudinal data to isolate occasion-specific variance from variance that is either completely stable or variance that changes systematically over time. In these approaches, reliable occasion-specific variance is typically treated as measurement error, which would negatively bias reliability estimates. In the current studies, panel data and multivariate latent state-trait models are used to isolate reliable occasion-specific variance from random error and to estimate reliability for scores from single-item life satisfaction measures. Across four nationally representative panel studies with a combined sample size of over 68,000, reliability estimates increased by an average of 16% when the multivariate model was used instead of the more standard univariate longitudinal model.     

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.     

Validity and Reliability of Subjective Social Indicators: The effect of different measures of association

In an international research project, a meta analysis of multitrait-multimethod matrices was used to evaluate the effects of characteristics of survey measurement instruments on the quality of survey data. The analyses in this project were done on the basis of polychoric/polyserial correlations. The result of such a study can be used to correct for measurement errors if the correlation in the substantive study is also a polychoric/polyserial correlation. It is, however, doubtful if these quality estimates of survey measurement instruments are appropriate for studies based on the most frequently used Pearson correlations. In this paper, the general approach will be discussed first. After that, the results with respect to validity and reliability estimates, obtained using two different measures of association, will be compared: the polychoric/polyserial correlations and the Pearson correlations. This study suggests that the differences between estimates of the reliability for scales with different numbers of categories are quite large, while all other effects remain approximately the same. The reasons for the differences will also be given. All the results are based on experiments containing questions with respect to satisfaction with life and aspects of life. Thus the study provides estimates of validity and reliability on measures of satisfaction with life and aspects of life which can be used in practice for the prediction and optimization of data quality and for correction of the data with regard to measurement error.     

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.     

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.     

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.     

Child mortality in rural India

This paper focuses on infant and child mortality in rural areas of India. We construct a flexible duration model, which allows for frailty at multiple levels and interactions between the child’s age and individual, socioeconomic, and environmental characteristics. The model is estimated using the Indian National Family and Health Survey 1998/1999. The estimation results show that socioeconomic and environmental characteristics have significantly different impacts on mortality rates at different ages. These are particularly important immediately after birth. The parameter estimates indicate that child mortality can be reduced substantially, particularly by improving the education of women, providing safe water, and reducing indoor air pollution caused by dirty cooking fuels. Finally, we still found substantial differences in mortality rates between states, which are associated with differences in schooling expenditures, female immunization, and poverty rates.     

Multidimensional Life Table Estimation of the Total Fertility Rate and Its Components

Using discrete-time survival models of parity progression and illustrative data from the Philippines, this article develops a multivariate multidimensional life table of nuptiality and fertility, the dimensions of which are age, parity, and duration in parity. The measures calculated from this life table include total fertility rate (TRF), total marital fertility rate (TMFR), parity progression ratios (PPR), age-specific fertility rates, mean and median ages at first marriage, mean and median closed birth intervals, and mean and median ages at childbearing by child’s birth order and for all birth orders combined. These measures are referred to collectively as “TFR and its components.” Because the multidimensional life table is multivariate, all measures derived from it are also multivariate in the sense that they can be tabulated by categories or selected values of one socioeconomic variable while controlling for other socioeconomic variables. The methodology is applied to birth history data, in the form of actual birth histories from a fertility survey or reconstructed birth histories derived from a census or household survey. The methodology yields period estimates as well as cohort estimates of the aforementioned measures.     

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.     

Socio-economic Differentials in Infant and Child Mortality during Mortality Decline: England and Wales, 1890–1911

In this paper data from the 1911 Census of the Fertility of Marriage of England and Wales are used to study patterns of mortality decline by socio-economic characteristics, principally the occupation of husband. That census reported data on number of wives, children ever born, and children dead by marriage-duration cohorts for 190 non-overlapping occupations of husband. These results, along with those on number of rooms in the dwelling of the family are used to make indirect estimates of childhood mortality using the techniques described in United Nations, Manual X. These procedures produce values of q(a), the probability of dying before reaching some exact age ‘a’. Estimates for q(2), q(3), q(5), q(10), q(15), and q(20) are derived from data on women married 0–4, 5–9, 10–14, 15–19, 20–24, and 25–29 years, respectively. These estimates can also be dated to a point in the past. These values can also be converted to a corresponding level of a Model West life table, which describes the ‘average’ mortality regime which the children of those women experienced. This furnishes a basis to look at mortality decline for various social classes and occupational groups. Ordinary least squares regressions of the levels of Model West life tables implied by the 1(a) values on time give one measure of mortality decline. Another is the absolute amount of the increase in the level of the Model West life tables from marriage-duration cohort 20–24 years to 0–4 years. The aggregate results indicate that social class in England and Wales during the 1890s and 1900s tended to be related to the speed of mortality decline: childhood mortality declined more rapidly in the higher and more privileged social class groups. But the results were neither nearly as strong nor as regular as those which predicted the level of mortality within any marriage-duration cohort. These outcomes are not particularly sensitive to the three different social-class stratification schemes used: the 1911 English Registrar General's classification; the 1951 English Registrar General's classification; and the 1950 U.S. Census classification. There was also a fairly regular and predictable gradient for the number of rooms in the home: child mortality was higher in families who lived in larger dwellings. Analysis of 190 detailed male occupational groups revealed that considerably more of the variation in mortality levels than of trends could be explained by social-class categories. Between 20 and 40 per cent of variation in mortality trend could be accounted for by social class alone, as opposed to 50 to 80 per cent of mortality levels for different marriage-duration cohorts. Results for a more restricted sample of 116 occupations for which income estimates could be made revealed a similar pattern. In addition, income was virtually unrelated to the pattern of mortality decline, and improvement was more rapid in groups who were more urban. This reflects the role of rapidly improving urban sanitation in the late nineteenth and early twentieth centuries in England. In contrast, income was significantly related to childhood morality levels for various marriage-duration cohorts (with higher income associated with lower mortality), while urbanization was inversely correlated with mortality levels (more urban groups experienced higher mortality). Overall, social class (or occupation group), income, and urbanization were more successful in explaining mortality levels than time trends across occupations, although social class and the extent of urbanization did reasonably well in accounting for trends. Over a longer period, the transition in child mortality was under way by the 1890s, but its pace and timing varied in different occupations and social class groupings. Although absolute differences in infant mortality were reduced after about 1911, relative inequality persisted even as infant and child survival improved for all groups.     

Assessing Asset Indices

The use of asset indices in welfare analysis and poverty targeting is increasing, especially in cases in which data on expenditures are unavailable or hard to collect. We compare alternative approaches to welfare measurement. Our analysis shows that inferences about inequalities in education, health care use, fertility, and child mortality, as well as labor market outcomes, are quite robust to the economic status measure used. Different measures—most significantly per capita expenditures versus the class of asset indices—do not, however, yield identical household rankings. Two factors stand out in predicting the degree of congruence in rankings. First is the extent to which expenditures can be explained by observed household and community characteristics. Rankings are most similar in settings with small transitory shocks to expenditure or with little random measurement error in expenditure. Second is the extent to which expenditures are dominated by individually consumed goods, such as food. Asset indices are typically derived from indicators of goods that are effectively public at the household level, while expenditures are often dominated by food, an almost exclusively private good. In settings in which individually consumed goods are the main component of expenditures, asset indices and per capita consumption yield the least similar results.     

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.     

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."     

Maternal mortality in South Africa: lessons from a case study in the use of deaths reported by households in censuses and surveys

South Africa is unique in being a developing country which has asked questions on pregnancy-related deaths in both its 2001 census and 2007 household survey, and monitors maternal and pregnancy-related mortality through vital registration and a confidential enquiry into maternal deaths. These sources of data provide a wide range of estimates of maternal mortality for the country. This paper examines these estimates to assess to what extent the differences between them are due to data deficiencies, methodological deficiencies or definitional differences. The results show that since maternal deaths are relatively rare it is fairly difficult to establish the maternal mortality rate with a great degree of accuracy in a setting where data are less than perfect. They also show that to some extent the differences are due to differences and errors in processing of data but that pregnancy-related mortality should not be treated as synonymous with maternal mortality. However, after adjustment, pregnancy-related mortality from vital registration was comparable with the level that may be expected using several alternative approaches, while the rate reported by households in census and surveys was about double that from vital registration. Nonetheless, all the data indicate an upward trend in maternal mortality that is in keeping with the impact of the HIV/AIDS epidemic, which is likely to have contributed to the discrepancies.     

Welfare measurement in labour supply models with nonlinear budget constraints

This paper is concerned with the measurement of individual welfare in labour supply models which allow for the impact of income taxation and income support schemes on labour supply decisions. The paper is motivated by the concern over the need to have measures which can be interpreted easily, which can be compared with net income, and which can be meaningfully aggregated. To illustrate the issues we use estimates of a discrete choice model of labour supply for United Kingdom lone mothers to compute alternative welfare measures which might be considered as having intuitive appeal to policy-makers. We compute welfare change based on these measures arising from a recent reform of the child support payments system. Received: 25 February 1997/Accepted: 12 March 1998     

The geometric mean of the age-specific death rates as a summary index of mortality

Even though a single summary index of mortality can never replace the set of age-specific death rates, it has been found to be extremely useful for a wide variety of purposes. Such indexes are generally one of two types: aggregative indexes, such as directly standardized rates which reflect absolute differences between corresponding age-specific mortality rates; and average of relatives indexes which reflect proportional differences between those rates. The choice of index depends upon the purposes for which it is to be used, and is important as different indexes can produce very different results. While directly standardized rates are widely used, they depend upon the selection of an appropriate standard population and give disproportionately heavy weight to the high ages. Average of relatives indexes give equal weight to all ages, but are infrequently used as no index of that type has gained wide acceptability. This paper recommends the use of the geometric mean of the age-specific mortality rates as such an index, and shows that this index is readily calculable, unbiased, needs no standard population, is directly comparable to all other indexes so calculated, and accurately reflects exponential mortality patterns.     

The sources of error in Brass's method for estimating child survival: the case of Bangladesh

Abstract Brass's method for estimating child mortality is based on an ingeniously simplified model. However, it frequently leads to values of q(x) that are not consistent with each other. This is most obvious for estimates of q(1). This paper examines the extent to which such inconsistencies are caused by simplifications in the model. Three assumptions are relaxed by adjusting for differences in infant mortality by birth order, taking account of annual fluctuations in mortality, and using a different age pattern of fertility for each cohort. These adjustments are applied to data from the 1974 Bangladesh Retrospective Survey of Fertility and Mortality and the 1975 Bangladesh Fertility Survey in which additional data from the Cholera Research Laboratory are used. The resulting estimates are more consistent both internally and with estimates from other surveys and by other procedures.     

Measuring fertility demand

We propose a multidimensional conceptualization of fertility demand and evaluate potential measures of each dimension, using data from a telephone survey of Wisconsin residents age 18-34. Most of the measures met tests for interval-level measurement; all produced high estimates of test-retest reliability. We found support for only two dimensions of demand, intensity and certainty; potential measures of centrality had relatively low associations with any of the latent dimensions. Demand certainty improved prediction of fertility expectations beyond a trichotomous (yes, no, don’t know) measure, but demand intensity did not. We found mixed evidence for the conceptualization of fertility demand as a single continuum on which desire to avoid pregnancy is the opposite of desire to have a child.