Some further results from a stochastic fertility model for women

Any realistic model of human fertility should encompass the distributions and interactions of three time intervals a fecund married woman may experience repeatedly in her childbearing period: (1) waiting time for a conception, (2) gestation period, and (3) period of postpartum amenorrhea. Perrin & Sheps (1964) presented a model in which human reproduction is viewed as a Markov renewal process with a finite number of states. Das Gupta (1973b) presented a general probability model of fertility along the lines suggested by Perrin & Sheps which removes two limitations of their model. First, it does not assume that the distributions of durations of stay in the fertility states are independent of each other. Second, it allows us to study the effect of breast-feeding on demographic characteristics, such as interval between live births or birth rate. Results derived in Das Gupta (1973b) include the distributions of time intervals and the exact probabilities of different states at a particular time. The present paper includes additional results pertaining to the same general model, such as the distribution of number of conceptions in a fixed period of time, the distribution of time needed for a fixed number of conceptions, pregnancy rate and fertility rate, and the distribution of the time elapsed since last live birth. The general results are applied to specific models to obtain some known results.     

Flux induced biochemical differentiation.

Any realistic model of human fertility should encompass the distributions and interactions of three time intervals a fecund married woman may experience repeatedly in her childbearing period: (1) waiting time for a conception, (2) gestation period, and (3) period of postpartum amenorrhea. Perrin &; Sheps (1964) presented a model in which human reproduction is viewed as a Markov renewal process with a finite number of states. Das Gupta (1973b) presented a general probability model of fertility along the lines suggested by Perrin &; Sheps which removes two limitations of their model. First, it does not assume that the distributions of durations of stay in the fertility states are independent of each other. Second, it allows us to study the effect of breast-feeding on demographic characteristics, such as interval between live births or birth rate. Results derived in Das Gupta (1973b) include the distributions of time intervals and the exact probabilities of different states at a particular time. The present paper includes additional results pertaining to the same general model, such as the distribution of number of conceptions in a fixed period of time, the distribution of time needed for a fixed number of conceptions, pregnancy rate and fertility rate, and the distribution of the time elapsed since last live birth. The general results are applied to specific models to obtain some known results.     

The frequency of lysosomal storage diseases in The Netherlands

We have calculated the relative frequency and the birth prevalence of lysosomal storage diseases (LSDs) in The Netherlands based on all 963 enzymatically confirmed cases diagnosed during the period 1970–1996. The combined birth prevalence for all LSDs is 14 per 100,000 live births. Glycogenosis type II is the most frequent LSD with a birth prevalence of 2.0 per 100,000 live births, representing 17% of all diagnosed cases. Within the group of lipidoses, metachromatic leukodystrophy (MLD) is the most frequent LSD. MLD was diagnosed in 24% of lipidoses and the calculated birth prevalence was 1.42 per 100,000 for all types combined. Krabbe disease, diagnosed in 17% of cases, also belongs to the more frequent lipid storage diseases in The Netherlands with a birth prevalence of 1.35 per 100,000. The birth prevalence of Gaucher disease, commonly regarded as the most frequent lipid storage disease is 1.16 per 100,000 for all types combined. The combined birth prevalence for all lipid storage diseases is 6.2 per 100,000 live births. Within the group of mucopolysaccharidoses (MPSs), MPS I has the highest calculated birth prevalence of 1.19 per 100,000 (25% of all cases of MPS diagnosed), which is slightly more frequent than MPS IIIA with an estimated birth prevalence of 1.16 per 100,000. As a group, MPS III comprises 47% of all MPS cases diagnosed and the combined birth prevalence is 1.89 per 100,000 live births. The birth prevalence of MPS II is 0.67 per 100,000 (1.30 per 100,000 male live births). All other MPSs are rare. The combined birth prevalence for all MPSs is 4.5 per 100,000 live births. Mucolipidoses and oligosaccharidoses are very rare with birth prevalences between 0.04 and 0.20 for individual diseases. Only 49 cases were diagnosed between 1970 and 1996. Their combined birth prevalence is 1.0 per 100,000 live births.     

The two-sex multiethnic stable population model

A two-sex multiethnic stable population is a model with fixed mortality and fertility parameters that explicitly recognizes the behavior of males and females in at least two distinct ethnic groups. The presence of intergroup fertility may allow the different ethnic groups to grow at a constant rate in a population with a fixed sex-ethnic composition. The present paper considers a variety of rules for determining the ethnicity of intergroup births based on the ethnicities of the mother and father, and examines the mathematical models implied by those rules. Numerical examples are presented for a two-ethnic-group population in cases where intergroup births are shared equally by the two groups, are all considered members of one particular group, and are all members of the father's group. A special case of a more general model, where sons become members of the father's group and daughters become members of the mother's group, is also considered. The results suggest that when intergroup fertility is not uncommon, how ethnicity is determined can substantially influence the ethnic composition of the population.     

Demography of the human sex ratio in some Latin American countries, 1967-1986.

A sample based on hospital births recorded for the Latin American Collaborative Study on Congenital Malformations (ECLAMC) program was used in the present study to determine sex ratios for live births and for stillbirths. Sixty-four cities and 147 hospitals in 11 countries (Uruguay, Chile, Argentina, Brazil, Bolivia, Peru, Paraguay, Ecuador, Venezuela, Colombia, and Costa Rica) were included in the present analyses. The number of live births was 1,886,653 in the period 1967-1986, and the number of stillbirths was 24,818 in the period 1978-1986. The sex ratio for the total sample was 0.5112 for live births and 0.5477 for stillbirths. The sex ratio as a whole is decreasing with time in a parabolic fashion. Each country in our study behaved differently. Except for Peru and Uruguay, the countries experienced a significant decrease in the sex ratio after 1978 for live births; only Brazil did not show a temporal trend for the sex ratio for stillbirths.     

Spina bifida and hydrocephalus: a population study over a 35-year period.

The records of the B.C. Health Surveillance Registry were used to analyze all live births with spina bifida and hydrocephalus (SBHC) in British Columbia between 1952 and 1986 inclusive. A total of 479 cases (218 males and 261 females) occurred during this period in 1,298,267 consecutive live births, for an incidence of 3.7/10,000. There were more females, with the sex ratio being significantly different from that of the general population born over this period. No significant seasonal differences were observed over the time period. A comparison of life expectancy for individuals born 1962-1970 and 1970-1986 showed significant improvement in the probability of surviving to the age of 1 year for the latter group. There was also a small but statistically significant increased chance of surviving to age 7 years in the latter group but no difference in the probability of surviving from 7 years to 16 years. Life expectancy figures are shown in a format practical for counseling with regard to prognosis for affected individuals. Additional malformations not attributable to SBHC were observed in 6% (27 cases). These included renal anomalies, cleft lip and/or palate, tracheoesophageal fistula, and diaphragmatic hernia. The incidence of each defect was significantly greater than in the general population of births.     

Birth seasonally among peasant cultivators: The interrelationship of workload,diet, and fertility

The monthly distribution of live births was analyzed over a 51-year period, 1926–1976, for a rural Taiwan fishing community. Unlike previous studies of birth seasonality, monthly distributions of births did not deviate from what would be expected by chance. This new case is shown to be consistent with the suggestion, developed by Pasternak during a study of birth seasonality in two Taiwan farming communities, that for peasant cultivators the annual cycle of production exerts a more decisive influence on birth seasonality than time of marriage or attributes of temperature, rainfall, or workload. An hypothesis that links the productive cycle to conceptions through the intervening variable of diet is presented and successfully tested using several sets of data on monthly births. A direct effect of nutrition on human fertility, suggested by recent studies of reproductive performance under conditions of nutritional stress, may largely explain seasonality of conceptions and births in populations that experience significant seasonal variation in diet.The Cross Harbor data presented in this paper were collected as part of an ongoing investigation of the comparative demography and social structure of fishing, farming, and market town communities located within a particular Chinese regional system. The support of the National Science Foundation during the period of fieldwork is gratefully acknowledged. I wish to thank G. William Skinner, William H. Durham, Greg Acciaioli, Steven Sangren, Chuang Miao-huei, Harumi Befu, and Philip L. Ritter for their comments on earlier drafts of the present article. I owe a special debt of gratitude to Burton Pasternak (City University of New York), who intellectually inspired and personally encouraged the writing of this paper.     

Epidemiology of Down syndrome (Trisomy 21), Hawaii, 1986-97

BACKGROUND: The live birth prevalence of Down syndrome is approximately 10 per 10,000 live births in the United States. Down syndrome prevalence has been reported to change over time and to vary by selected demographic factors. METHODS: Data from a population-based birth defects registry in Hawaii involving 363 Down syndrome cases delivered during 1986-97 were used to calculate overall prevalence and to investigate secular trends and differences by selected demographic factors. RESULTS: The total (live birth, fetal death, and elective termination) prevalence was 14.74 per 10,000 live births and fetal deaths. The unadjusted live birth prevalence was 8.67 per 10,000 live births. The adjusted live birth (live births and proportion of elective terminations expected to have resulted in live births) prevalence was 12.59 per 10,000 live births. No significant secular trends were observed for either total prevalence (P = 0.688) or adjusted live birth prevalence (P = 0.604). The total Down syndrome prevalence per 10,000 live births was highest for Far East Asians (22.01), followed by whites (17.06), Filipinos (15.94), and Pacific Islanders (9.21). Prevalence per 10,000 births was higher in metropolitan Honolulu (18.57) than in the rest of Hawaii (14.15). After adjusting for maternal age, however, the differences within the demographic groups were not statistically significant. CONCLUSIONS: The live birth prevalence of Down syndrome in Hawaii during 1986-97 was lower than reported in the literature. Prevalence did not change significantly over time. Any differences in prevalence by maternal race/ethnicity and place of residence appeared to result from differences in maternal age distribution.     

Seasonality of births in South-Eastern Nigeria.

A study of seasonal pattern of births in Nigeria was conducted using data on live births for the period 1971-76 from 4 climatically similar southeastern states (Anambra, Imo, Cross River and Rivers State). After pooling the data, the monthly distribution for different years was calculated. The resulting time series was graphically compared with temperature levels during time of conception, or nine months back. Data analysis revealed a seasonal pattern in the monthly distribution of births, with the peak period observed during April-June, and a trough during November-January. Counting 9 months back, the conceptions were calculated as occuring during July, August, or September of the previous year. In terms of the annual agricultural cycle of the southeastern states, July-September corresponded with the period of light farm work or relative idleness for men (main activity during this period is weeding and tending the crops, tasks primarily done by women and children); this is also a period of abundance of fruits, vegetables and palm wine, and rains after dusk, conditions conducive to mating.     

Incidence rates for cleft lip and palate in British Columbia 1952-71 for North American Indian, Japanese, Chinese and total populations: secular trends over twenty years

The incidence of cleft lip and/or cleft palate was examined for the 1952-71 period for the Province of British Columbia. Although there were some fluctuations, some of which were significant, there was no general trend which indicated that the rates were either increasing or decreasing. These rates are important for a background calculation when investigating new invironment teratogens. The total rate of 1.97 per 1,000 live birth is comparable with other Caucasian populations where there is good ascertainment and adequate follow-up period. This study also confirmed the previously reported high rate for North American Indians in British Columbia (3.74 per 1,000 live births) and established rates for the Japanese (3.36 per 1,000 live births) and Chinese (1.76 per 1,000 live births) of British Columbia. Since these three sub-populations are relatively small in relation to the total population, they do not influence the overall total rate to any great extent.     

Epidemiology of Down syndrome in South Australia, 1960-89.

During 1960-89 687 Down syndrome live births and 46 Down syndrome pregnancy terminations were identified in South Australia. Ascertainment was estimated to be virtually complete. The sex distribution of Down syndrome live births was found to be statistically different from the non-Down syndrome live-birth sex distribution (P less than .01). Smoothed maternal age-specific incidence was derived using both maternal age calculated to the nearest month and a discontinuous-slope regression model. The incidence of Down syndrome at birth for the study period was estimated to be 1.186 Down syndrome births/1,000 live births. Annual population incidence was shown to be correlated with trends in the maternal age distribution of confinements. If current trends in the maternal age distribution of confinements continue, the population incidence of Down syndrome in South Australia is predicted to exceed 1.5 Down syndrome births/1,000 live births during the 1990-94 quinquennium.     

Applications of terminating nonhomogeneous renewal processes in family planning evaluation

A terminating nonhomogeneous renewal process is formulated and studied in relation to the development of quantitative methods in family planning evaluation. The motivation underlying the results presented here was to satisfy a need, which arose during computer studies, to complete and extend a stochastic model of human reproduction reported previously. The paper is divided into seven sections detailing the nature of changes made in previous work. Two novel developments in the paper are the formulation of the waiting time between live births in terms of an absorbing semi-Markov process and the waiting time to conception in populations utilizing several methods of contraception as an absorbing Markov chain. These formulations not only permit the accommodation of many family planning variables but also lead to greater conceptual simplification than formulations used in previous work.     

Rates of trisomies 21, 18, 13 and other chromosome abnormalities in about 20 000 prenatal studies compared with estimated rates in live births

Summary Data were analyzed on the results of 19675 prenatal cytogenetic diagnoses reported to two chromosome registries on women aged 35 or over for whom there was no known cytogenetic risk for a chromosome abnormality except parental age. The expected rates at amniocentesis of 47,+21; 47,+18; 47,+13; XXX; XXY; XYY; and other clinically significant cytogenetic defects by maternal age were obtained from a regression analysis on the observed rates, using a first degree exponential model. After an adjustment for maternal age, these rates were compared with previously estimated rates by maternal age in live births. The rates of 47,+21 at amniocentesis and live birth are approximately parallel, with the latter about 80% of the amniocentesis rates. The rates of 47,+18 at amniocentesis and live birth are approximately parallel, with the live birth rates about 30% of the amniocentesis rates, consistent with high fetal mortality of 47,+18 after amniocentesis. The rates of 47,+13 at amniocentesis indicate an increase in maternal age that is not as marked as thar previously estimated in live births. The rates at amniocentesis for XXX and XXY increase with maternal age, with the rates of XXY almost identical to those estimated previously in live births, suggesting no late fetal mortality of XXY. The rates of XYY show a slight decrease with maternal age also consistent with little late fetal mortality of XYY. No consistent trend with age is seen for the pooled group of other clinically significant defects.     

A statistical analysis of the effect of warfare on the human secondary sex ratio

Many factors have been hypothesized to affect the human secondary sex ratio (the annual percentage of males among all live births), among them race, parental ages, and birth order. Some authors have even proposed warfare as a factor influencing live birth sex ratios. The hypothesis that during and shortly after periods of war the human secondary sex ratio is higher has received little statistical treatment. In this paper we evaluate the war hypothesis using 3 statistical methods: linear regression, randomization, and time-series analysis. Live birth data from 10 different countries were included. Although we cannot speak of a general phenomenon, statistical evidence for an association between warfare and live birth sex ratio was found for several countries. Regression and randomization test results were in agreement. Time-series analysis showed that most human sex-ratio time series can be described by a common model. The results obtained using intervention models differed somewhat from results obtained by regression methods.     

An epidemiologic study of congenital malformations of the anterior abdominal wall in more than half a million consecutive live births.

The records of an ongoing health surveillance registry that utilizes multiple sources of ascertainment were used to study the incidence rate of congenital malformations of the anterior abdominal wall in live-born children in British Columbia during the period 1964--1978 inclusive. No overall increase in incidence rate of these anomalies was detected during the study period. The estimated live-born incidence rates were: one in 4,175 live births for omphalocoele, one in 12,328 live births for gastroschisis, and one in 29,231 live births for prune belly. The data were analyzed with regard to sex and associated anomalies. Some practical implications regarding assessment of these infants are discussed.     

Incidence of the mucopolysaccharidoses in Northern Ireland

An epidemiological study of the mucopolysaccharidoses (MPS) in Northern Ireland using multiple ascertainment sources was carried out and the incidence rate for the period 1958–1985 was estimated. An incidence of approximately 1 in 76 000 live births was obtained for MPS 1H (Hurler phenotype); 1 in 280 000 for MPS 1 H/S (Hurler/Scheie phenotype); 1 in 140 000 live births (1 in 72 000 male live births) for MPS II (Hunter syndrome); 1 in 280 000 for MPS III (Sanfilippo syndrome) and 1 in 76 000 for MPS IV A (Morquio syndrome type A). No cases of MPS IS (Scheie phenotype), MPS IV B (Morquio syndrome type B) or MPS VI (Maroteaux–Lamy syndrome) were ascertained during the study period. Three cases of non-immune hydrops fetalis born to consanguineous parents were thought to be due to β-glucuronidase deficiency (MPS VII) on the basis of placental histology and enzyme studies on both parents but no living cases of MPS VII were ascertained. The overall incidence for all types of mucopolysaccharidosis was approximately 1 in 25 000 live births. A comparison is made with incidence estimates obtained from other published studies. Received: 25 May 1997 / Accepted: 22 August 1997     

Twinning rates in Ghana.

The incidence of twin births in Accra and Kumasi, the two major cities in Ghana, was investigated. In Accra, data were collected from the Korle-Bu Teaching Hospital while data were collected and analyzed from the Komfo Anokye Teaching Hospital in Kumasi. Both hospitals are the leading teaching hospitals in Ghana. The data consisted mainly of single and twin births recorded in the hospitals over a period of 12 years in Accra (1988-1999) and 15 years in Kumasi (1985-1999). The study revealed an incidence of 33.4 twin births per thousand live births for Accra and 26.6 twin births per thousand live births for Kumasi. Though these values are not as high as those reported among the Yoruba tribe of southwest Nigeria, who are reported to have the highest twin birth rates in the world, the present values still rank among the highest recorded twin birth rates.     

Parents' age at birth of their offspring and child survival

This study presents some new results on parental age as a risk factor for child survival. The study is based on individual registration forms for live births and infant deaths collected in Hungary from 1984 to 1988. Logistic regression models have been fitted for early neonatal and neonatal mortality on the one hand, and post-neonatal mortality on the other hand. Children of older males and females have significantly higher early neonatal and neonatal mortality rates compared to those of younger males and females. The impact of age of both parents remains, however, slighter than that of other biological characteristics such as previous number of fetal deaths, induced abortions, or live births. The authors discuss possible biological explanations.