Fecundability, coital frequency and the viability of Ova

Summary An extension of Barrett and Marshall's model expressing fecundability as a function of coital pattern is proposed. In particular, this extension includes the probability that the ovum remains alive. The extended model has been applied to Barrett and Marshall's data, a series of cycles for which basal body temperature curves and the date of coitus have been recorded. It was thus possible to estimate the daily probabilities of fertilization and, under certain assumptions, the proportion of lost ova. This proportion was estimated to be above 50 per cent, and increases with age. The increase of fecundability with frequency of intercourse is more moderate than that predicted by Barrett and Marshall's model.     

Fecundability and the Frequency of Marital Intercourse: A Critique of Nine Models

The biological and demographic literature on the effects or frequency of intercourse on fecundability is reviewed in this paper. While empirical work and model-building results agree well on the effect of change from low to moderate coital frequencies, inconsistencies emerge when increase from moderate to high coital frequencies is considered. Of the models considered, it may be argued that the explicit provision for unfavourable cycles makes Schwartz's model an improvement over Barrett and Marshall's, Lachenbruch's and Trussell's. Moreover, even though he used a very different approach, Bongaarts obtained results that are much closer to those of Schwartz et al. than the others. Bongaarts's model is used as a starting point for new modelling, to be reported in the next issue, which deals with these inconsistencies by taking into account the ageing of gametes.     

Marshall on the population question. Part II

Marshall's treatment of the laws of returns, technical progress, capital formation, and international trade having been reviewed in Part II of this paper, included in the first instalment, his treatment of the genesis of living standards and of the circumstances whereon depend mortality, nuptiality, natality, and natural increase is examined in Part III, the first in the present instalment. Marshall's analysis of the behaviour of living standards reflects his “sociology” and helps to explain why he made no use of the optimum concept; it also reflects his conception of economic development. In Part IV his treatment of natural selection, competition, migration, location theory, and poverty and its cure is reviewed. It is concluded that Marshall's views respecting population represent both a continuation of those of his predecessors and a break therewith and serve nicely, in some instances, to bridge the gap between the demographic theories of the classical economists and those expressed in the second quarter of the present century.     

Marshall on the population question. I

English economic thought was dominated for close to a half century by the system of economic analysis developed by Alfred Marshall (1842–1924) whose views relating to population are examined. The demographic and economic changes taking place within Marshall's lifetime are briefly summarised in the Introduction. There follows in Part I a review of the opinions of Marshall's predecessors and contemporaries respecting both the behaviour of the laws of returns, technical progress, etc., and the circumstances on which population growth had depended or was likely to depend. The optimum is included among the concepts here treated. Reactions to the late nineteenth-century decline in natality are noted. In Part II Marshall's treatment of the laws of returns and of capital formation, together with their significance for the population question, is examined. His treatment of technological and organisational change and of international trade as counterbalances to population growth is considered. His failure to make use of the optimum concept is remarked as is the theory of economic growth that appears to underly his analysis of demographic development.     

A model for estimating fecundability of the currently married woman from the data on her susceptibility status—A cohort approach

A probability model to estimate fecundability of a married woman has been proposed under some mild assumptions. It utilises the knowledge on the susceptibility status of the married women (including menstruation, menopause, pregnancy and amenorrhea) and therefore sets another approach for estimating fecundability. In addition, it is capable of predicting the parity, proportion of foetal losses, fecundability and incidence of secondary sterility. The problem of finding out the consistent estimates of the parameters in the distribution is discussed in section 4. For illustra-tion, the model is applied to a set of simulated data after simplifying many assumptions of the model     

A non‐linear model of fecundability,postpartum amenorrhea,and sterility*

This paper proposes a convolution model of fecundability, controling for the effects of postpartum amenorrhea and unobserved heterogeneity in fecundability. Simulation analysis was used to assess the validity and reliability of estimates derived from the model. Analysis showed that the model captured the mean and standard deviation of age at the onset of sterility in simulated populations where sterility followed either a Gompertz, a gamma, or a lognormal distribution. The model performed well when sterility was specified by either a lognormal or a gamma distribution. The model also accurately estimated fecundability and postpartum amenorrhea. Next, the model was found to fit data from 17th and 18th century French Canadian birth histories. In this French Canadian sample the mean age at sterility was found to be 46.3 years using a gamma model. The decline in fecundability was almost linear after age 30. Thus, fecundability at age 40 had declined to about one‐third of that observed at age 30. Variability in individual fecundability was quite high. For example, women with fecundability one standard deviation above the mean had about 2.3 times as high fecundability as women one standard deviation below the mean.     

Socio-economic correlates of fecundability in a sample of taiwanese women

Estimates of fecundability (monthly probability of conception) in the absence of contraception are derived from the frequency distribution of conceptive delays immediately following marriage, reported by 2,443 married women aged 20 to 39 included in the Taichung (Taiwan) Intensive Fertility Survey of 1962. Average fecundability of women is positively associated with their socio-economic status. These differentials are not accounted for by differences among socio-economic groups with respect to memory and truncation biases (associated with the marriage duration), wife’s age at marriage, or unreported premarital conceptions. A Multiple Classification Analysis suggests that among the socio-economic characteristics, husband’s education, rural background, and modern family type are the more important predictors of fecundability. The importance of genetic factors as opposed to cultural factors in producing these socio-economic differences in fecundability can not be evaluated systematically. Moreover, the relation of a couple’s privacy, their attitude toward family building, and patterns of mate selection to their socioeconomic status would have to be taken into account before the differences in fecundability could be attributed to factors such as nutrition, health, or infections which might directly influence their physiological ability to conceive.     

Fecundability and its relation to age in a sample of Taiwanese women

Abstract In this paper reliable estimates of mean fecundability at marriage for a sample of heterogeneous Taiwanese women are obtained by using a set of data collected retrospectively. The effects of 'truncation bias' and 'memory bias' are estimated by studying the relationships between mean fecundability and the duration of marriage. Then the variations in fecundabilities by age at marriage are studied. The data are taken from an intensive fertility survey of married women between the ages of 20 and 39 conducted in Taichung city of Taiwan towards the end of 1962 prior to a year-long family planning action programme. Fecundability, the probability of conception in the absence of contraception, is estimated by using a Type I geometric model and is estimated from the observed distribution of first pregnancy intervals-the period between the onset of marriage and the beginning of first conception. The estimated fecundability level relatively free from truncation and memory bias is 195±3 per 1.000 women. The fecundability level increases with wife's age at marriage (up to 25) independently of its association with the duration of marriage.     

A Model of Age-specific Fecundability

A new model of the behavioural and physiological causes of age-specific variation in marital fecundability is presented. Total fecundability is decomposed into a series of susceptibility factors (the length of ovarian cycles, the length of the fertile period within each cycle, the probability that a cycle is ovulatory, and the likelihood that an act of unprotected intercourse within the fertile period results in conception) and an exposure factor reflecting the effect of duration of marriage on coital frequency. The impact of intra-uterine mortality on effective fecundability is also modelled. Data on western women, from which standard age curves of fecundability are estimated, suggest that any decline in fecundity between ages 30 and 40 is attributable to changes, not in the ability to conceive, but in the capacity to carry a pregnancy to term. Sensitivity tests suggest that the most important potential sources of inter-population variation in fecundability are intra-uterine death and the incidence of anovulatory cycles.     

A method for the estimation of fecundability

A new method for the estimation of the mean and variance of fecundability is described. The data input required for this procedure is the distribution of the interval from marriage to first birth, or from the resumption of the conception risk after contraction to the subsequent birth. The estimates of the mean and variance of fecundability are obtained by fitting a model to the observed interval distribution. To test the method, it is applied to data from five historical populations. The fecundability means in these populations ranged from 0.18 to 0.31 while the co-efficients of variation all had values near 0.56. A short method for the estimation of the mean of fecundability based on the same model, but not requiring a computer, is also presented.     

Modeling Seasonality in Fecundability,Conceptions, and Births

This paper develops a model of seasonal fluctuations in fecundability, conceptions, and births. We begin with a model of individual fecundability that combines behavioral and biological components, with particular attention to the roles of coital frequency, sperm concentration, fetal loss, and contraception. The individual-level model is then expanded into a model of seasonal fluctuations in births at the population level, which accounts explicitly for seasonal fluctuations in the size of the susceptible population. We illustrate the use of the model by analyzing proposed explanations of birth seasonality that rely on extreme summer heat.     

Findings and implications of a correlation analysis of the closed and the open birth intervals

A correlation analysis of data on four fertility variables viz. closed birth interval, open birth interval, age and parity, collected in a survey of about 2,000 married women in the reproductive ages in rural India, is carried out in order to study the interrelationships among these variables. Two hypotheses are formulated governing the relationship of the closed and open birth intervals with the fecundability distribution of fertile women, and Parity Progression Ratios which are largely influenced by the proportion of women becoming sterile after each parity. The data lend support to the hypothesis that while the closed intervals are influenced mainly by the distribution of fecundability of women of non-zero fecundability, the open birth intervals are influenced mainly by Parity Progression Ratios or the proportion of women becoming secondarily sterile after each parity. The analysis suggests that we can use the mean open intervals of women classified by parity as indices of fertility, and such an index is comparable to the index of average age of women of given parity. In areas where it is difficult to ascertain the correct age of women this might be of practical value.     

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.     

Hutterite fecundability by age and parity: Strategies for frailty modeling of event histories

Effective fecundability declines with age and parity. Furthermore, women differ in their effective fecundability: some women have persistently low or high monthly chances of live-birth conception. Estimates are presented concerning the magnitude of these effects in a natural-fertility population: 406 Hutterite women in North America who had 3,206 births, largely in the 1940s and 1950s. The estimates are based on models that incorporate the effects of persistent heterogeneity and that use the full information provided by multiple-spell duration data. In addition, hazards rather than probabilities are modeled, piecewise linear hazard functions are used, and age and parity effects are decomposed systematically. These methods permit the development of more elaborate models of changing fecundability and of heterogeneity in postpartum amenorrhea.     

The Effects of Breastfeeding and Nutrition on Fecundability in Rural Bangladesh: A Hazards-Model Analysis

Data taken from the ‘Determinants of Natural Fertility’ study, Bangladesh, are used with multivariate hazard models to study variations in fecundability between women, especially the relationship between nutritional status, breastfeeding practices, and the monthly probability of conceiving. It is found that fecundability varies both between women of a given age and, for a particular woman, by age. The variation is related to four variables: separation, which affects coital frequency; age, which represents biological changes; lactation practices; and the duration of amenorrhoea. Nutrition above famine or starvation levels is not a significant determinant of fecundability. The most surprising finding is the effect of the pattern of breastfeeding on fecundability: as a menstruating woman begins to wean her child, her probability of conceiving increases as her serum prolactin, which inhibits ovulation, decreases. Thus, those menstruating women who are most likely to conceive are those who have completely weaned their infants in the very recent past.     

A Multistate model of fecundability and sterility

This paper develops a multistate hazards model for estimating fecundability and sterility from data on waiting times to conception. Important features of the model include separate sterile and nonsterile states, a distinction between preexisting sterility and sterility that begins after initiation of exposure, and log-normally distributed fecundability among nonsterile couples. Application of the model to data on first birth intervals from Taiwan, Sri Lanka, and the Amish shows that heterogeneity in fecundability is statistically significant at most ages, but that preexisting sterility and new sterility are unimportant before age 40. These results suggest that sterility may not be an important determinant of natural fertility until later reproductive ages.     

Effects of various factors on selection for family planning status and natural fecundability: A simulation study

The effect of various factors on selection for family planning status and for natural fecund ability is studied in a simulation that incorporates a beta distribution of fecundability among women. The mean fecundabilities of current spacers, current limiters, current nonusers, and pregnant women are compared. These ratios are influenced by duration of marriage and by desired number of children. Effects of different levels of contraception are measured. Another strategy, spacing the last two wanted births, is also studied. It is found that breast-feeding status has little effect on fecundability selection. The women usually found to have greatest fecundability are not those recently pregnant at durations of marriage five and ten years, unless they wanted fewer than two children, but rather those who are using contraception to limit the number of children.     

Distribution of Closed Birth Intervals in a Heterogeneous Population

The probability distribution of parity-specific closed birth intervals in a heterogeneous population of women is obtained from Biswas' (1980) concept of gradually decreasing fecundabilities. The distribution of parity-specific last closed birth intervals and its moments of various orders are derived for a heterogeneous female population. Simulations are used to compare with models for a homogeneous female population with constant fecundability. The consideration of heterogeneity allows a better fit for empirical closed birth intervals.     

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.      

Family planning in Taiwan, Republic of China: Progress and prospects

Abstract The family planning programme in Taiwan is considered to have been most successful and has been systematically evaluated. In the light of some expressed scepticism, however, its impact on fertility will have to be carefully reviewed. The present article discusses six specific problems : How many women have accepted the Lippes loops or pills offered in the programme ? How long will the loop stay in utero ? What proportion of married women is currently wearing the loops ? What changes have occurred in the knowledge-attitude-practice (KAP) of family planning among the target population ? How many births have been prevented by the IUD programme ? And finally, How much has fertility declined ? The fertility decline in Taiwan has been accelerating since the programme started in 1964. Approximately 40% of the decline in the birth rate, from 36.3 in 1963 to 27.7 in 1969, or 8.5 points per 1,000 in six years, however, was due to changes in age structure and delayed marriage. An increasing proportion of girls of marriageable age and a possible increase in the fecundability of the population will work against the programme's objective. Concerted efforts and heavier investment are essential for the final success of the programme.