Regression-like analysis of birth interval sequences

Employing a family of generalized linear models for the gamma distribution, the structure of birth interval data derived from three historical populations is examined. The relative importance of such factors as current age, parity of the mother, and duration of marriage in determining the length of succeeding intervals is investigated. The results suggest that the three data sets have a common, rather simple structure and various applications of such empirical models are considered.     

On some probability distributions for forward birth interval

Parents’ decisions to have children are modeled by a simple stopping rule that describes the probability of having another child as a function of the number of boys and girls already born to the parents. Because the stopping rule depends on the sex of the offspring, the rule may introduce a correlation between sex of offspring and the number of siblings the offspring has. When this is coupled with a correlation between number of siblings and well‐being, a correlation between sex and well‐being may emerge despite equal treatment of the two sexes within each family. The author provides sufficient conditions on a stopping rule for it to be sexist in the sense that the average well‐being of one sex is higher than that of the other sex.     

On some probability distributions for forward birth interval

Statisticians from Varanasi, India have proposed 2 mathematical models for forward birth interval which are more realistic than past models. For example, past models have assumed fecundability to be constant throughout a woman's reproductive life. On the other hand, the proposed models assume fecundability changes with parity. Further the statisticians use all types of marital durations making their models usable even for short marriage durations. The 1st model uses a parity specific model to develop a model for forward birth interval regarless of parity. The statisticians also include moments of the 1st and 2nd models as expressed for the rth order raw movement of these models to estimate some of their parameters. These models can be used to conduct prospective surveys of family planning programs since birth intervals can best evaluate the effect of these programs. These models have not yet been advanced enough to follow women over a fixed period, however. They only observe women until the last woman conceives. The statisticians do not apply the models to parity specific data because they were not available. Yet they do run the models with parities 0 and 1. The models reveal that the mean length of forward birth interval is strongly influenced by the conception rate which the woman has at the time of the survey. Thus, if women with a certain parity in a community begin an effective family planning method on the survey day, which in effect would reduce the prevailing conception rate, that method would significantly postpone the next live birth.     

A three parameter model for birth projections

The approach underlying the model proposed in this article constitutes a considerable departure from the conventional methods used for the projection of birth series. Instead of following the customary procedure of directly projecting the age-specific fertility rates, they can be derived with this model from only three relatively simple fertility measures, namely, total fertility rate, mean age of fertility, and modal age of fertility. The reduction of the number of fertility parameters offers appreciable operational and analytical advantages. Among these, the most significant is the fact that statistical manipulation is confined to only three fertility measures, all of which are particularly appropriate for the in-depth analysis which is required to provide a rationale for assumptions of future fertility.     

A three parameter model for birth projections

Abstract The approach underlying the model proposed in this article constitutes a considerable departure from the conventional methods used for the projection of birth series. Instead of following the customary procedure of directly projecting the age-specific fertility rates, they can be derived with this model from only three relatively simple fertility measures, namely, total fertility rate, mean age of fertility, and modal age of fertility. The reduction of the number of fertility parameters offers appreciable operational and analytical advantages. Among these, the most significant is the fact that statistical manipulation is confined to only three fertility measures, all of which are particularly appropriate for the in-depth analysis which is required to provide a rationale for assumptions of future fertility.     

Analysing open birth interval distributions

Summary This paper began with the recognition that open birth interval distributions are analogous to age distributions. It then became clear that closed birth interval distributions are, somewhat more loosely, analogous to mortality schedules, and that the relationship between open and closed birth interval distributions could be explored by imitating the formal demography of mortality and age distribution. Pursuing this programme, we develop the formal demography of open and closed birth interval distributions and show that under certain assumptions open interval distributions may be used to estimate closed interval distributions, just as age distributions may be used to estimate mortality. An illustrative application to Indonesian data is given.     

Parity patterns of birth interval distribution

A simplified model is presented for the measurement of inter-live birth interval distributions. Comparative analyses of "effective fecundability," the mean length and variation of postpartum infecundity, and the parity progression ratio based on this measurement model are presented using data from U.S. marriage cohorts and from an Indian sample. Parity differentials in these reproduction parameters are investigated, and the ramifications for fertility estimate and projection discussed.     

Prospective study of birth interval dynamics in rural Bangladesh

A group of 209 married, fecund women in rural Bangladesh were studied prospectively for 24 months from 1969 to 1971 to define some of the biological and sociological factors relating to fertility performance. These women were selected from a larger study population of 112,000 that had been followed with a daily house-to-house vital registration programme since 1966. The selected women were interviewed bi-weekly and were asked questions about menstruation, pregnancy, lactation, husband's occupational absences, and monthly urine tests for pregnancy were taken. The results for 193 non-contracepting women revealed that the seasonal pattern of births previously observed in this population could be associated with a corresponding seasonal pattern of conceptions and that this was due to a seasonal trend in fecundability. The highest conception rates were in the coolest months of the year. Post-partum lactational amenorrhoea was very prolonged, averaging 17 months for women with a surviving child. The appearance of the first post-partum menstrual flow (onset of ovulation) also had a seasonal trend which could not be adequately explained. The median waiting time to conception, once menstruation had resumed was eight months. This interval was influenced by seasonal fluctuations, as well as by the age of women and by husbands' absences. The foetal wastage rate was 15·0 per 100 conceptions, with 62 per cent of the foetal losses occurring during the second month of gestation. Overall, the average birth interval was 33 months, with the prolonged lactational amenorrhoea accounting for almost 45 per cent of this interval.      

Prospective study of birth interval dynamics in rural Bangladesh

Abstract A group of 209 married, fecund women in rural Bangladesh were studied prospectively for 24 months from 1969 to 1971 to define some of the biological and sociological factors relating to fertility performance. These women were selected from a larger study population of 112,000 that had been followed with a daily house-to-house vital registration programme since 1966. The selected women were interviewed bi-weekly and were asked questions about menstruation, pregnancy, lactation, husband's occupational absences, and monthly urine tests for pregnancy were taken. The results for 193 non-contracepting women revealed that the seasonal pattern of births previously observed in this population could be associated with a corresponding seasonal pattern of conceptions and that this was due to a seasonal trend in fecundability. The highest conception rates were in the coolest months of the year. Post-partum lactational amenorrhoea was very prolonged, averaging 17 months for women with a surviving child. The appearance of the first post-partum menstrual flow (onset of ovulation) also had a seasonal trend which could not be adequately explained. The median waiting time to conception, once menstruation had resumed was eight months. This interval was influenced by seasonal fluctuations, as well as by the age of women and by husbands' absences. The foetal wastage rate was 15·0 per 100 conceptions, with 62 per cent of the foetal losses occurring during the second month of gestation. Overall, the average birth interval was 33 months, with the prolonged lactational amenorrhoea accounting for almost 45 per cent of this interval. From the Department of Population Dynamics, Johns Hopkins University, School of Hygiene and Public Health, Baltimore, Maryland 21205.     

Bayesian analysis of an econometric model of birth inputs and outputs

This study offers a simultaneous equations model of the birth process with seven endogenous variables: four birth inputs (maternal smoking, maternal drinking, first trimester prenatal care, and maternal weight gain) and three birth outputs (gestational age, birth length, and birth weight). The data are taken from the National Longitudinal Survey of Youth. Our analysis conditions on twenty-nine exogenous variables including four racial dummies to account for the widely cited racial differences in birth outputs. We find that there is sizeable correlation between the disturbances in the four input and three output equations and among output disturbances, and that results from our simultaneous equations model are substantially different from those using the single-equation approach. It appears that the High/Low Risk Birth Weight Puzzle remains unresolved under our modeling framework.All correspondence to Kai Li. The authors gratefully acknowledge the research support of the Social Sciences and Humanities Research Council of Canada, and helpful comments on an earlier draft by the editor (Junsen Zhang), two anonymous referees, Sid Chib, Kei Hirano, John Geweke, Gary Koop, seminar participants at the University of Alberta, the University of California at Irvine, University of Kansas, University of Minnesota, Queen Mary College of University of London, Washington University at St. Louis, and participants of the 2001 Winter Meetings of the Econometric Society in New Orleans. We are solely responsible for any errors contained herein. Responsible editor: Junsen Zhang.     

The determinants of effective fecundability based on the first birth interval

There are substantial differences in fecundability among nine developing countries in different parts of the world. In addition, within countries, later age at marriage has a clear, positive, nonlinear effect on fecundability. Women with higher education and those with more educated husbands have higher fecundability. Urban residents have higher fecundability than rural. The higher fecundability of more recent cohorts is the most consistent observation. Since those variables most frequently shown to have inverse relationships to fertility show direct relationships to fecundability within populations, the role of fecundability as a proximate variable in models of the determinants of fertility requires further specification.     

A Relational Gompertz Model of Male Fertility: Development and Assessment

Brass has proposed a relational Gompertz model of female fertility which, in combination with the standard fertility distribution developed by Booth, has proved useful in a range of applications, such as indirect estimation, demographic modelling, and population projections. This paper develops a standard distribution of male fertility for use in conjunction with the relational Gompertz model. The derivation of the standard takes advantage of the similarity between the shape of male and female fertility distributions. It entails ‘stretching’ the female standard, so that it extends to age 80, and then transforming it, using the Gompertz model into a pattern which is more typical of male fertility distributions in the developing world. An assessment of this new standard by fitting the relational Gompertz model based on it to a series of male fertility distributions from diverse populations, suggests that it performs very well.     

A Gompertz fit that fits: Applications to canadian fertility patterns

In this paper an attempt is made to refine the method of fitting the Gompertz function to the cumulative fertility rates by using iterative techniques. The method is tested with the historical data series for the Canadian population. The demographic implication of the parameters of the Gompertz function as fitted to the fertility distribution is examined, and the usefulness of the method in projecting future fertility trends is studied. The Makeham function is also fitted to the fertility distribution by the same iterative technique, and the relative efficiency of this function is compared with that of the Gompertz.     

A critical analysis of Australian policies and guidelines for water immersion during labour and birth

Background

Accessibility of water immersion for labour and/or birth is often dependent on the care provider and also the policies/guidelines that underpin practice. With little high quality research about the safety and practicality of water immersion, particularly for birth, policies/guidelines informing the practice may lack the evidence necessary to ensure practitioner confidence surrounding the option thereby limiting accessibility and women’s autonomy.

A preliminary analysis of the high birth rate in India]

The author first provides some basic demographic data for India and points out that the current annual rate of population growth of 2.45 percent is slightly higher than the annual increase in food production. Problems in the areas of employment, education, housing, and transportation, as well as the general problem of poverty, are seen as a consequence of this imbalance. The lack of success of the national family planning program is attributed primarily to the failure to achieve a satisfactory rate of economic growth. Contributory factors include early marriage, the low status of women, the desire for large families, and administrative problems associated with the family planning program.     

[An inquiry concerning the birth model].]

The author modifies the parity progression model of fertility by using the parity progression ratio as a control indicator of fertility. A regression equation is used to calculate the total fertility rate for China at parity one.     

Pitfalls in benefit-cost analysis of birth prevention

Abstract The paper summarizes the procedure usually employed by Enke, Meier and others to estimate the benefit-cost ratio of a prevented birth. Some possible deficiencies in the formulation, the possible lack of relevance of the resulting computations, are considered. For example, since the benefit-cost ratios are exceptionally high they would imply unusually high rates of investment for family planning. The results would also apply for the birth prevention of not only high parity births, but also for first and second children. Some arguments are presented which suggest the possibility that the income distribution might be worsened as a consequence of the application of a family planning programme based on these principles - especially those which employ subsidies to induce the practice of family limitation. In addition it is also argued that the average economic quality of the population may be lower than otherwise as a consequence of such programmes, and that the consequences of such events are not taken into account in the usual formulation. Also the usual estimates of costs of such programmes are questioned since the relation between acceptances and births prevented are unknown given the lack of knowledge about the substitution between the proposed methods of family limitation and other means of population control. Finally, we present a model based on reasonable but different assumptions than the formulation popularized by Enke and others, and show that on the basis of this model it is possible to obtain results which are the exact opposite of the Enke model. Also it is argued that the model presented is much more sensitive to actual data than the usual formulation.     

A cohort analysis of the timing of first birth and fertility in Ghana

This paper examines the nature of the inverse association between age at first birth and fertility across successive generations of Ghanaian women. Within the context of enhanced non-marital opportunities for contemporary women and declining fertility, we develop a rationale for and test the hypothesis that in a medium fertility environment as currently found in Ghana, the effect of age at first birth on fertility becomes more important than ever before. Five birth cohorts were identified (1938–1944; 1945–1949;1950–1954; 1955–1959; 1960–1964)from a merged file of the 1988, 1993 and 1998 Ghana Demographic and Health Surveys. The analyses were restricted to women over 35 years old at the time of the surveys, which allowed us to use current parity as a reasonable proxy for completed fertility. Preliminary results suggest that women who had first births early tend to have a higher number of births than those whose first births occur late, regardless of birth cohort. In multivariate analyses, the effect of age at first birth as a determinant of fertility was found to be more substantial among later cohorts. The implications of the findings are discussed.     

A model with long-term survivors for the analysis of current-status nuptiality data

The model proposed in this paper combines a logistic regression model and a Weibull regression model for the analysis of current-status data. This joint model allows a simultaneous estimation of two sets of effects on the covariates: one on the probability that the event occurs (also known as quantum) and the other on the timing of the event. Thus, the model can be seen either as an extension of a survival-analysis model for use with current-status data where a survival fraction is added in order explicitly to take into account the possibility that the event may never occur, or as an extension of survival analysis with long-term survivors to the analysis of current-status data. As an illustrative application we apply our model to a study of nuptiality in seventeenth-century Italy.     

A model with long-term survivors for the analysis of current-status nuptiality data

The model proposed in this paper combines a logistic regression model and a Weibull regression model for the analysis of current-status data. This joint model allows a simultaneous estimation of two sets of effects on the covariates: one on the probability that the event occurs (also known as quantum) and the other on the timing of the event. Thus, the model can be seen either as an extension of a survival-analysis model for use with current-status data where a survival fraction is added in order explicitly to take into account the possibility that the event may never occur, or as an extension of survival analysis with long-term survivors to the analysis of current-status data. As an illustrative application we apply our model to a study of nuptiality in seventeenth-century Italy.