Mindel C. Sheps

Truncation Effect in Closed and Open Birth Interval Data

A numerical investigation using a flexible simulation model to establish interval analysis as an index for changing natality patterns. Such an index should reflect parity distribution, the age at which women start reproduction, and the spacing of their births. The simulated statistical results illustrate the truncation effect that reflects a negative correlation between parity and the length of closed and open intervals in a birth or marriage cohort. Truncation is related to the duration of marriage at survey, but this duration interacts with other assumptions. Holding duration constant does not ensure that the data on intervals will reflect postulated changes in the distributions. For complete birth orders, this analysis does reflect patterns of child spacing. However, it ignores changes in the parity distribution, whether produced by deliberate limitation of family size or by the onset of secondary sterility. This difficulty is not overcome by life table analysis except under highly restrictive assumptions. It is doubtful whether the current emphasis on securing such data is justified. Further investigation is needed to provide a better basis for the definition and analysis of interval data if they are to be used.

An analytic simulation model of human reproduction with demographic and biological components

Abstract This Monte Carlo model for simulating the reproductive history of a cohort of women is described in detail. The model provides for patterns of survival, sterility, formation and dissolution of sexual unions, fecundability, lactation, foetal wastage, family planning practices etc. Natality indices specific for marital status, for duration of marriage and for age, as well as analyses of birth spacing patterns are among the results that may be obtained. In the model, the experimental unit is an individual woman. The complete life history of a woman is generated and recorded before the history of the next woman is generated. The data for the whole cohort are analyzed at the end of the programme. The model includes two kinds of states into which a woman may pass, namely: (1) permanent changes of status such as death, sterility, or becoming a family planner, and (2) temporary states, each with a probability distribution of length of stay. The probabilities of the various events or changes of state may vary from age, parity, and other features of a womans status or history. Natural fecundability at any age may also vary from woman to woman. In this programme natality patterns and specific indices such as age-specific fertility rates are produced, in a quasi-realistic fashion, by the interplay of the demographic and biological parameters postulated for any cohort. Consequently, the effect of changes in anyone factor can be studied, as well as the interaction resulting from changes in several factors. The purposes and potentials of the model are both substantive and methodological. As an illustration, a series of computer runs attempting to simulate the reproductive patterns of Indian women is presented. These results, as well as some additional ones, indicate some effects of changes in marital patterns, levels of fecundability, duration of post-partum non-susceptibility, age incidence of sterility and foetal wastage. In the final section of the paper, the advantages and possible applications of the model are discussed together with the limitations encountered to date in the efforts to apply the model.

ESTIMATORS OF A TYPE I GEOMETRIC DISTRIBUTION FROM OBSERVATIONS ON CONCEPTION TIMES

In order to study distributions of fecundability, Potter and Parker fitted a Pearson Type I geometric distribution (with parametersa andb) to data from the Princeton Fertility Study. They, and subsequently other authors, estimateda andb from the observed moments of the month of first conception. A critical analysis of this method has shown that moment estimators ofa andb are moderately reliable only within a specified range of values ofa. Outside this range, either the estimators are extremely inefficient or their variances are not defined at all. Caution should therefore be taken in adopting this procedure. Furthermore, no moment estimate is defined whena is less than 2. It seems preferable to derive maximum likelihood estimates which have certain optimal properties and are defined for all permissible (i.e. positive) values ofa andb.For large samples, we here present: the covariance matrix (where defined) of the moment estimators, methods of obtaining maximum likelihood estimates and their covariance matrix, and the variances of estimates of specified moments of the fecundability of the sample. Results were obtained for three sets of data; in all cases, the maximum likelihood estimates fit the data better than do the moment estimates. Despite a substantial improvement, however, the fit is still poor for the two sets of data from the Princeton Fertility Study. Possible explanations are: a) that the departures from the assumption of constant fecundability for each couple are sufficient to produce the poor fit, b) that the data are inaccurate, or c) that the method of defining the sample of women from whom the data were obtained resulted in an over-representation of short conception times. The relative importance of these factors is difficult to establish.

Distribution of birth intervals according to the sampling frame

Abstract Observed distributions of the lengths of intervals between successive births (or of the open intervals since the most recent birth) are considerably affected by: (i) the sampling frame, which includes the method of ascertaining persons to be investigated and the kind of data obtained from each individual, (ii) the composition of the population sampled, and (iii) the effects of competing risks of such events as death, marriage, marital dissolution and the ending of previous intervals. Some of these factors also affect distributions of other duration variables such as age (at death or some point in time) marital duration, length of residence, etc. Estimates of birth intervals are complicated both by their dependence upon marital duration and survival and by the diversity of sampling frames which are realistically feasible or desirable.

Probability models for family building: An analytical review

Considerable literature now exists on stochastic models for the reproductive history of a cohort of couples. These models are of varying complexity and the relationships between separate treatments are not always clear. A classification system for such models is proposed, followed by a historical review of models for family building and for logically related processes. Models, differing only in treatment of time as discrete or continuous, are presented in detail for the simple case where the prob ability of conception is constant, and all conceptions lead to live births which are associated with a fixed nonsusceptible period. Analysis of different treatments is facilitated by introducing the notion of the time when a conception is recorded. Emphasis is placed on results for the probability of a recording at a specified time t, the probability of r recordings by time t, and the expected number of recordings in time t. Differences between the discrete and continuous time models are made explicit. It is shown that results for these models can be derived using renewal theory techniques, which are presented. More complex models based on renewal theory and allowing for several pregnancy outcomes or for variability in parameters are briefly described, followed by generalized models which allow parameters to vary with time. Applications of family building models are summarized.

A model for studying birth rates given time dependent changes in reproductive parameters.

If the reproductive behavior of a population changes radically, this change will be reflected in birth rates only after a time lag. In addition, however, an observed initial response to change (after a lag) is often followed by a partial regression toward the previous level. Is such a regression due to another change in the patterns of reproductive behavior, or may it be the built-in consequence of the original change in behavior, as the rates approach a new equilibrium? A time-dependent reproductive model, based on biological considerations, permits investigation of fluctuations in birth rates as a consequence of fluctuations in the probability of being able to conceive at any given point in time, i.e. of being susceptible to conception. Early effects of a change in behavior are likely to assume an extreme value that will not be seen again barring another change in behavior. Accordingly, differentials and trends in birth rates do not necessarily indicate corresponding relationships in the probability of conceiving or in abortion rates. Inferences from levels of birth rates about levels of these underlying biological factors should be made with caution. In particular, the built-in oscillations in the probability of being susceptible to conception, and the resulting oscillations in birth rates must be considered.

The Sampling Frame as a Determinant of Observed Distributions of Duration Variables

Publisher Summary This chapter discusses the sampling frame as a determinant of observed distributions of duration variables. A duration variable can be defined as the interval between the occurrences of two defined events. The observed distribution of a duration variable depends upon the sampling frame, according to which, measurements are made, and also upon competing risks because few sampling frames differentially omit individuals to whom the event, which ends the interval, occurred sometime prior to the survey can occur at some time after the signal event or can never occur because a competing event occurred first. By focusing upon the age specific risks, it is possible to estimate quantities relatively unaffected by these extraneous circumstances. Demographic and social science research frequently investigates characteristics of individuals who are in a specified category at a given point in time, for example, currently married women aged 35–39.

On Estimating the Risk of Conception from Censored Data

Publisher Summary This chapter discusses current issues in the estimation of the risk of conception from censored data. An important approach, to evaluate the effectiveness of contraceptive programs, is through estimation of the risk of conception of what are considered to be comparable groups, with and without the use of contraceptives. A fecund woman is at risk of conception either upon entering into a sexual union or upon resumption of ovulation, following the termination of a previous pregnancy. The waiting time, until she next conceives, is a segment of the interval between live births and is, therefore, an important determinant of the birth rate. Contraception exerts its effect on birth rates purely by changing the length of this interval. The waiting time to conception is determined by fecundability— the monthly probability of conceiving. The specific action of a contraceptive is to reduce fecundability. The chapter presents a few results for the special case, where fecundability is constant for each woman but varies between women according to a Beta distribution.

Attitudes toward family planning in Turrialba Costa Rica.

Family planning attitudes and practices in Turrialba a rural Costa Rican community during 1964-1965 were studied. 23 variables were investigated from which 16 hypothesized relationships were analyzed. Special attention was paid to: 1) aspirations for the children; 2) Catholic religiosity; and 3) awareness and knowledge of family planning. From a population of 2440 families which in the past 5 years had attended the Health Unit of Turrialba for prenatal care and child care up to the age of 6 a systematic sample was drawn to obtain 60 families in which the wifes age was 24-30 years and the husband and wife were living together. The questionnaire was administered and a nurse interviewed the wives and the author interviewed the husbands. 37% of subjects (two-thirds of these respondents were wives) indicated that the husbands alone should take the responsibility of deciding on family size or selecting birth control methods whereas only 8% felt that the wife alone should take this responsibility. Moreover 60% considered this a decision to be made by the husband alone or together with his wife and 31% felt it should be made by the wife alone or together with her husband. The husbands. however tended to pass this responsibility to the church. The average number of children in each household was 4 children per family. The womens age range was between 24 and 30 years 43% of them were 26 years or younger and 62% had 4 or more children. 4 children were the average desired a meaningful goal for family planning in Costa Rica where the actual average number of children per family remained around 7. Among 120 subjects contraceptive knowledge and method use respectively equalled 71% and 3% for condom; 45% and 5% for oral contraceptives; 29% and 7% for coitus interruptus; 16% and 0% for IUDs; 8.3% and 0% for sterilization; and 12.5% and 0.8% for spermicides jellies diaphragm and rhythm. Total contraceptive prevalence amounted to 16.6%.