Individual-level sterility: A new method of estimation with application to sub-saharan Africa

This paper extends work on measures of population proportions sterile to propose a new estimator of an individual woman's age at sterility and consequently her sterility status at given ages. Accuracy and reliability, examined in a simulation study, appear satisfactory. From World Fertility Survey data for five African countries, the proportions sterile by age estimated by the individual measure and by the population estimator are almost identical. Cameroon and Kenya show substantial variation in prevalence and incidence of sterility across ethnic groups and by number of marriages. Unexpectedly, the evidence suggests that sterility increased from 1960 on in Kenya and remained unchanged in Cameroon.     

Extrapolation of IUD continuation curves

Summary Calculation of the number of contraceptive acceptors needed to register predesignated effects on birth or growth rates presupposes that it is known for how long couples practise each contraceptive method. Life table techniques may be used to estimate proportions continuing with a given method: but most follow-up studies yield data for durations no longer than from two to three years. To estimate continuation rates for the longer durations relevant to a five-or ten-year target period, the curve of continuation must be extrapolated. Four functions, including the one most commonly used and three new ones, are compared on the basis of data from the Taichung IUD Follow-up Study that commands an effective observation period of eight years. This unusual length makes it possible to perform the experiment of pretending that observation length is only one, two, … five years and then compare results based on these varyingly abbreviated spans with those based on the full observation period. No one of the four functions is found to be ideal under all circumstances. A strategy for choosing among the functions is suggested.     

Labor force status life tables for the United States, 1972

As an ordinary life table follows a closed group from birth to the death of its last member, a labor force status life table follows a closed group through life and through the statuses “in the labor force” and “not in the labor force.” Using data from the January 1972 and January 1973 Current Population Surveys, two types of labor force status life tables were calculated for the United States, 1972. One type was a conventional working life table (for males) which started with an ordinary life table and partitioned the life table population into labor force statuses using age-specific proportions in the labor force. The other type was an increment-decrement table, prepared for both males and females, which was calculated so as to be consistent with the rates of labor force accession and separation implied by the data. Increment-decrement labor force status life tables are generally preferable to conventional working life tables. They reflect the implications of a clearly specified set of behavioral rates, provide detailed measures of the flows between labor force statuses, do not introduce seriously biasing approximations into the calculation of summary measures of labor force experience, and can be applied to female data as easily as male data. In practice, incrementdecrement labor force status life tables can be calculated from current and retrospective data generated by a single labor force survey. The increment-decrement labor force status life tables for the United States, 1972 reflected the extent to which the labor force participation of males exceeded that of females, but indicated that, on the average, half a woman’s lifetime between the ages of 16 and 65 was spent in the labor force. There were marked differences in the proportions, by age, of males and females in the labor force, with the male pattern rising to a single, flat peak and the female pattern being bimodal. Nonetheless, the two sexes shared similar age patterns in the proportions changing, or not changing, their labor force status.     

Application of life table techniques to measurement of contraceptive effectiveness

Two problems are associated with the analysis of use-effectiveness of contraception. First, couples belonging to a sample of contraceptors typically vary in their monthly chances of contraceptive failure. Second, one does not observe for many, and perhaps a majority of the couples, how long they can remain protected with the contraceptive, because either they are stopping contraception to plan a pregnancy or else observation of them is being interrrupted by lost contact, by discontinuation of contraception for other reasons, or by the end of the study. It is argued that because of these two problems-namely, sample heterogeneity and incomplete histories-the Pearl pregnancy rate, which has been traditionally used to measure contraceptive effectiveness, is inadequate.A life table method is described that permits one to combine incomplete histories with complete ones for purposes of estimating the proportions of the sample that might have remained protected for specified periods if all members had remained under observation for these periods. The versatility of the techniques is illustrated in relation toa retrospective survey. A detailed account of procedure is given. Finally, it is shown that only under specialized conditions that are rarely met in practice is it possible to estimate the results of the new technique from knowledge of Pearl pregnancy rates alone.     

Analyzing fertility histories: Do restrictions bias results?

The straightforward tests we have conducted lead to two major conclusions. First, parameter estimates, such as the proportions that practice contraception or that breastfeed, can be biased in data restricted to the last closed and open interval. This is particularly true the further back in time one goes. However, the second conclusion is that these restrictions do not bias estimates of the structure of the relationships predicting fertility. This may seem surprising, and perhaps even magical. The reason is that multivariate life table techniques allow one to reach the same conclusion even if the proportions in various categories are altered by a criterion such as limiting the analysis to intervals begun by the last and next-to-last live births. Limiting the analysis in this way means that there are fewer short intervals and thus fewer cases of intervals with characteristics associated with short intervals (e.g., no contraceptive use, no breastfeeding, or infant mortality). As long as the model specified in the multivariate life table is an appropriate one, that is, it is not misspecified, and as long as the skew produced by the WFS restriction is not too extreme, then the multivariate life table procedures can produce unbiased estimates of the structure of the relationships predicting birth interval dynamics. Thus even though the WFS data are in fact inappropriate for some simple parameter estimation procedures, they appear to be adequate for the more complex multivariate procedures of the sort used here. Several caveats must be added to the foregoing results. First, we have performed this test in only one country, Korea; it is possible that the same results might not be obtained in other countries. We expect, however, that they would. Second, our procedure only looks at the first 40 months of experience in the birth interval. A procedure that incorporates the long tails of the birth interval distribution may obtain different results. In fact, we caution against analyzing the tail of the distributions using data from the normal WFS sample, since these would be most affected by the restriction to last closed and open intervals. Third, the extent to which these results are generalizable to other types of substantive problems is unknown at present. We suspect, however, that examining the determinants of lengths of breastfeeding will produce similar results. Finally, even with multivariate procedures, it would be highly misleading to impose the WFS restrictions and then examine trends in the length of birth intervals.(ABSTRACT TRUNCATED AT 400 WORDS)     

Shift in life-history strategy from reproduction to defense with colony age in the galling aphidHemipodaphis persimilis producing defensive first-instar larvae

Summary Colony defense in some aphids is performed by sterile soldiers but in others by monomorphic larvae of a specific instar stage. This paper, focusing on a galling aphidHemipodaphis persimilis with monomorphic defensive first instars, examined the mechanism by which the proportion of defenders is regulated in the colonies. Demographic analyses showed that the ratios of first instars (defenders) were kept constantly high (58% on average) from mid June to late September. High proportions of first instars could be explained by consistently high birth rates (birth rate hypothesis) or by a prolonged duration of the first instar stage (instar span hypothesis). With the progress of colony age, the mature-embryo content of apterous adults, used as an index of the birth rate, decreased and the proportions of advanced instars increased. These results did not support the birth rate hypothesis. By contrast, calculation of a newly proposed index, the molting rate, showed that the duration of the first-instar stage was short in incipient galls but became longer with colony age. The duration of other instar stages was always kept short. These results corroborate the instar span hypothesis and suggest that the prolongation of the first-instar stage is an adaptive mechanism by which the defender ratio is kept high in mature colonies where the birth rate is declining. The frequency of aggressive behavior in first instars increased from incipient to mature galls. Seasonal changes in the instar span and aggressiveness of first instars suggest that inH. persimilis colonies there is a strategic shift from the reproductive to defensive phase with colony age.     

Age structure,growth, attrition and accession: A new synthesis

This paper shows that each equation describing relationships among demographic parameters in a stable population is a special case of a similar and equally simple equation that applies to any closed population and demonstrates some implications of these new equations for demographic theory and practice. Much of formal demography deals with functions that pertain to individuals passing through life, or to a stationary population in which births of individuals are evenly distributed over time. These functions include life expectancy, probabilities of survival, net and gross reproduction rates, expected years spent in various states and the probability that certain events will occur in the course of life. The stable population model permits the translation of population structure or processes in a more general type of population, with constant growth rates, back into equivalent populations for a stationary population. The method for translation developed in this paper, requiring only a set of age-specific growth rates is even more general, applying to any population. Age specific growth rates may also be useful for performing reverse translations, between a population's life table and its birth rate or its age distribution. Tables of numbers of females by single years of age in Sweden are used to illustrate applications. Tables summarize the basic relations among certain functions in a stationary population, a stable population and any population. Applications of new equations, particularly to demographic estimation of mortality, fertility and migration, from incomplete data, are described. Some other applications include; the 2 sex problem, increment decrement tables, convergence of population to its stable form, and cyclical changes in vital rates. Stable population models will continue to demonstrate long term implications of changes in mortality and fertility. However, in demographic estimation and measurement, new procedures will support most of those based on stable assumptions.     

Formal models and methods for the analysis of kinship and household organization

This paper discusses the use of formal models for analyzing kin-group and household organization. The authors begin by presenting a conceptual framework that relates the supply of kin to rules of household formation, demographic constraints, and observed household structure. This framework is used to evaluate an array of techniques and models of kinship and households. Kin relations and household structures can be described using a unifying model designed to identify the dynamic of a system of states out of and into which the units of analysis can move. The behavior of the system is identified through knowledge of transition rates. It is then possible to link such transition rates to coarse indicators of the system, such as proportions occupying a state and distribution of the units by state. Analytic, macro-, and microsimulation models are just alternative ways of linking a state-space and measures of transition rates to final indicators or outcomes. No model can avoid addressing the independence, homogeneity, and time-invariance assumptions, or the 2-sex problem.     

Bias in graduated life table functions

Survival proportions and expectations of life estimated directly from observed crude mortality rates are usually unbiased. Estimates of survival proportions and expectations of life obtained from graduated mortality rates at individual ages tend to be positively biased, although the actual bias is small for reasonably large experiences.     

Land use and first birth timing in an agricultural setting

The dramatic changes in the earth’s landscape have prompted increased interest in the links between population, land use, and land cover. Previous research emphasized the notion of population pressure (population pressure increases demands on natural resources causing changes in land use), overlooking the potentially important effects of changes in land use on humans. Using multiple data sets from the Chitwan Valley Family Study in Nepal, we test competing hypotheses about the impact of land use on first birth timing. We argue that while agricultural land should encourage early childbearing, land area devoted to public infrastructure should discourage it. The results show that individuals from neighborhoods with larger proportions of land under agriculture experienced first birth at rates higher than those from neighborhoods with smaller proportions. On the other hand, individuals from neighborhoods with larger proportions of land under public infrastructure experienced first birth at rates lower than those from neighborhoods with smaller proportions. However, the effects of public infrastructure are not as strong as the land area devoted to agriculture.

Heterogeneity,dependence among causes of death and Gompertz

Heterogeneity in a population with respect to mortality, or variation in “frailty”; among members of that population, which has been discussed extensively in the literature over the last decade and a half is essential to any realistic model of dependence among causes of death. The main problem then is the development of a mortality model incorporating heterogeneity and cause of death which is both realistic and of manageable proportions.

In a recent paper (J. H. Pollard, 1991), it has been shown that many life table results are remarkably insensitive to the strict shape of the mortality curve, at least for more developed populations, and that accurate approximations can in many cases be obtained knowing only the mortality rates at two representative ages (e.g. 50 and 70). These results and the Gompertz “law”; of mortality can be used to develop manageable approximate formulae for the expectation of life under heterogeneity and correlation among the causes of death. The formulae are confirmed by simulation.

Numerical results indicate, somewhat surprisingly, that the effects of correlation among causes of death, even at quite high levels, on expectation of life and changes on expectation of life when particular causes of death are reduced or eliminated are relatively minor.     

Estimating internal migration from incomplete data using model multiregional life tables

A principal feature of current methods of estimating demographic measures from incomplete data is the use of model life tables that approximate the mortality of a region for which reliable mortality data are unavailable. Observed decennial rates of survivorship may be used to identify out of a set of such model life tables one that best matches the observed data. This paper introduces the concept of a modelmultiregional life table and outlines a procedure for selecting an appropriate one using place-of-birth-by-residence data.     

The multistate life table with duration‐dependence

A method for generalizing the multistate, or increment‐decrement, life table to include rates which depend upon duration of exposure to risk, as well as upon age, is proposed. The method is built upon the linear approximation, called the linear integration hypothesis, developed mainly by Rogers and his colleagues. Although the use of rates indexed by duration categories leads to a substantial increase in the state space of the model, it is possible to arrange the rates in such a way that matrices to be inverted are no larger than those encountered in the usual multistate life table. In the more general approach it is possible to derive several new summary indices of the life‐table cohort's history, such as the mean and median time in current status, at any age. The method is illustrated using a simple four‐state marital‐status model which has appeared often in the literature; here, rates of divorce and widowhood vary by duration of marriage as well as age.     

Estimating African-American mortality from inaccurate data

This paper evaluates the quality of vital statistics and census data for estimating African-American mortality over a period of six decades. The authors employ intercensal cohort comparisons and extinct generation estimates to demonstrate that conventionally constructed African-American death rates may be seriously flawed as early as age 50. Using the crude death rate at ages 50+ for 1978-1982 in conjunction with estimated growth rates and two model life table systems, the authors estimate black age-specific death rates in 1978–1982. These results suggest that if a racial crossover in death rates occurs, the age pattern of mortality among African-Americans must be far outside the range observed in populations with more accurate data.     

Estimating adult mortality levels from information on widowhood

Summary A range of indirect techniques has been developed for mortality estimation in societies lacking adequate vital registration records. Information on orphanhood has been widely used as an estimator of adult mortality, with generally plausible results. Doubts have remained, however, about potential biases, and the method is less satisfactory for the estimation of male mortality. Information on widowhood, or more strictly the survival of first spouse, has several possible advantages over information on orphanhood. Model first marriage functions and model life tables are used to calculate proportions widowed of first spouse, for both females and males, by marital duration and by age. These proportions widowed are then related to life table survivorship probabilities to provide weighting factors for the conversion of observed proportions widowed into estimates of survivorship probabilities. The application of the method is illustrated with data collected by the 1974 post-enumeration survey of Bangladesh, with apparently encouraging results.     

Contraceptive sterilization in the U. S.: 1965 and 1970

There was an impressive increase between 1965 and 1970 in the prevalence of contraceptive sterilization, an increase that accelerated in the later years of the period and was shared in by virtually all subgroups considered. Among couples in 1970 for whom sterilization had been an option (recognizing that it is a terminal method), about one of every five had chosen this method of contraception. About half of all sterilizations were vasectomies, though vasectomies have outnumbered tubal ligations in recent years. Differentials in prevalence and in increases during 1965–1970 are reported for a number of life-cycle and social variables. In addition, a profile of the contraceptive sterile is presented for recent sterilizations. Significant proportions are relatively young and of low parity at the time of sterilization. In the context of the continued diffusion of the pill and IUD and increases in legal abortion, the net demographic effect of increasing sterilization is regarded as low, though sterilization is an important component of an effective fertility control regime.     

Analysis of oral contraceptive use through multiple decrement life table techniques

Multiple decrement life table technique is used to analyze the oral contraceptive use in a sample of once married women in Metropolitan Toronto. The overall pattern in the Canadian data is found to be essentially similar to that found in the U. S. Continuation rates show differences by cause of decrement. Two types of rates, net and absolute, are presented, and the relationship between single decrement continuation rates and total continuation rates is examined. Some problems of clinical versus retrospective sample survey data in studies of contraceptive effectiveness are commented on.     

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.     

Some determinants of the migration of professional manpower

Determinants of migration of professional manpower are investigated using data from a 1970 survey of immigrants to the United States. From a respondent's stated "intent to stay" in the United States and five other characteristics a six-dimensional contingency table is formed. We find a well-fitting log-linear model for this table. Thus, we establish the importance of selected determinants of migration and present a table of predicted rates of intent to stay in the United States.     

Developing strategies for deriving small population fertility rates

Many agencies require population estimates and projections by ethnic group. These projections need ethnic-specific, age-specific fertility rates (ASFRs) but their inclusion is challenging since ethnicity is not recorded at birth registration. In this paper maternity data are used in a case study of electoral wards in Bradford, West Yorkshire, to develop fertility rates for small populations for a 1991 based projection. The challenge is to capture local variations in fertility by ethnic group when data are sparse. Small areas were grouped together using cluster analysis to define combinations with similar sociodemographic and fertility experiences so that sparse data could be aggregated to estimate reliable ethnic-specific fertility rates. For comparison, the data were aggregated into the 1991 Office for National Statistics area type classification. Fertility rates by single year of age for all area types were smoothed using the Hadwiger function. For the White ethnic group there were sufficient births to create ethnic-specific, ward-level ASFRs. For other ethnicities grouping of areas was necessary. The accuracy of the ASFRs in predicting births was assessed using mean absolute percentage error. Results show that for some minority groups district-level ethnic-specific fertility rates produced the most accurate birth estimates even though they were based on a larger area. This implies that rates created may be informative about the local area for White ethnic type but not in the same way for smaller ethnic groups. In terms of grouping strategies we recommend that existing classifications are assessed to determine how well variations in rates are stratified before embarking on a custom scheme. Where population sub-groups are small in some areas, it may be more reliable to use rates derived for larger areas and apply these to local populations. Inevitably, the rates used in a projection are a compromise but hopefully will still capture important dimensions of population change.