The Menstrual Cycle Fecundability Study

The Menstrual Cycle Fecundability Study (MCFS) was a multinational longitudinal study conducted to determine the daily probability of conception relative to ovulation (Colombo & Masarotto, Reference Colombo and Masarotto2000). From 1992 to 1996, healthy women were recruited from seven European centres (Milan, Verona, Lugano, Paris, Dusseldorf, London and Brussels) providing services on fertility awareness and natural family planning to participate in the study. The entry criteria for women were: experienced in the use of a natural family planning method of contraception; married or in a stable relationship; between 18 and 40 years old at entry into the study; had at least one menses since last breast-feeding or delivery; and did not currently use hormonal treatment, or another treatment with effects on fecundability. Neither partner could be permanently infertile and both had to be free from any illness that might cause sub-fertility. The protocol also required that couples did not mix incidences of unprotected and protected intercourse, e.g. use of barrier methods or withdrawal, in a given cycle.

While the MCFS is rich in information about the timing and frequency of intercourse and cycle characteristics, there is only limited information about the characteristics of couples enrolled in the study. At entry, information was collected on: the month and year of birth of the woman and her partner; the number of previous pregnancies, if any; the date of her last delivery (or miscarriage) and of the end of breast-feeding, if relevant; and the date of last oral contraceptive pill taken, if any. After entry, date of marriage was collected from married couples.

During the study, for each menstrual cycle, various characteristics of the cycle (basal body temperature, cervical mucus quality) were recorded daily, together with information on menstrual bleeding for each day. Women were asked to record every episode of sexual intercourse, specifying if it was unprotected intercourse or protected. Cycles in which even a single act of protected intercourse or simple genital contact occurred were excluded from the MCFS dataset used for the analysis. The reliability of the information recorded on acts of intercourse was checked by the natural family planning teacher, in discussion with the subjects at the end of each menstrual cycle. The importance of continuing to keep the record chart when subjects were trying to conceive was emphasized. Further details on the research protocol, study methods and participants can be found in Colombo & Masarotto (Reference Colombo and Masarotto2000), along with an example of a completed menstrual cycle record chart.

Information on both reproductive physiology and sexual behaviour was collected for 881 women, 7017 menstrual cycles and 575 pregnancies. The number of subjects and contributed cycles varied markedly between study centres. Most women (93.7%) contributed fewer than twelve cycles of exposure. Although the Lugano centre enrolled mostly couples planning a pregnancy, most couples were trying to avoid pregnancy initially (although intentions can and did change during follow-up). The average age of women in the study population was close to 29 years and was relatively similar at each study centre. The median number of recorded acts of intercourse was six in the conception cycles and four in the non-conception cycles. Other descriptive statistics, such as the intercourse pattern by age, can be found in Colombo & Masarotto (Reference Colombo and Masarotto2000), but note that these statistics are for all couples, not just nulliparous women.

In this study, only menstrual cycles with peak mucus day identified are considered. This conventional marker of ovulation was identified locally in each study centre from daily records of cervical mucus symptoms in each cycle and the timing of intercourse is relative to this surrogate marker of ovulation, which is referred to as day 0 (mucus reference day).

The first five cycles just after stopping the contraceptive pill were excluded due to concerns that recent previous pill use may result in a short-term reduction in fecundability (the number of such cycles excluded was small as only 6.7% of the participants were pill users before entry into the study). The data used were limited to European centres participating in the MCFS, excluding data from New Zealand (two women with two pregnancies). In order to try to answer the question ‘Can women wait until their early thirties to try for a first birth?’, only waiting times to conception for nulliparous women between 20 and 36 years of age, whose husband/partner is aged less than 40 was studied, because there were too few first pregnancies after age 36. Only menstrual cycles with at least one intercourse in the 12-day interval (−8, 3) were used in the analysis. This interval of potential fertility was chosen so as to include the fertile window, i.e. those days during which intercourse has a non-zero probability of resulting in conception. Note that no pregnancies occurred when intercourse only occurred outside of this 12-day interval. Further details on how this 12-day interval of potential fertility was chosen are given in Colombo & Masarotto (Reference Colombo and Masarotto2000, Section 2.5, second paragraph).

Table 1 presents the number of couples, menstrual cycles and pregnancies after applying the successive selection criteria used. The last row is the analytic sample. It consists of 342 nulliparous women, 1595 menstrual cycles and 210 women (61.4%) who obtained a first pregnancy during the study (uncensored observations on time to first pregnancy and non-sterile couples) and 132 women who did not conceive (censored observations on time to first pregnancy and some of these couples may be sterile). Note that for many couples the number of cycles was often too small to provide much information about the probability that the couple was sterile. This is not a problem for the modelling approach chosen, but would be a problem for analysts trying to exclude sterile couples from the dataset analysed.

Table 1.

Number of couples, menstrual cycles and pregnancies after applying successive selection criteria

The last row is the analytic sample.

^a Woman's age at first entry and first observed cycle.

^b Partner's age at woman's first entry and first observed cycle.

^c Only cycles with at least one intercourse in the 12-day interval (−8, 3).

Table 2 presents the estimated probability of conception for women aged <24, 24–27, 28–31 and 32+, where each woman contributes at least one cycle in the age group and age is age at the beginning of the cycle. A traditional estimate of fecundability is based on observation done on a population during a fixed period of time. The MCFS is a mixture of observations done on subjects remaining under observation for variable periods of time. And there are further complications, since there are re-entries and, besides that, each entry is sometimes made of pieces of information given by the same unit (as happens when the sequence of cycles is interrupted because of exclusion of cycles, or simply when charts are missing informing on cycles, as it happens when one of the partners is away from home). For these reasons, a simple table of fecundability by age estimated in traditional fashion is not provided. Instead, this estimated probability of conception as a crude measure of fecundability is provided.

Table 2.

Probability of conception by age of woman

^a Age at the first day of the menstrual cycle.

^b Thirty-two women are counted more than once because of their having cycles in more than one age group; as a consequence, the total of column 2 differs from the figure of 342 couples given in the last row of Table 1.

^c At least one menstrual cycle in the age group.

Mixture model for waiting time to conception with long-term survivors

The analysis is based on a two-population (fecund, sterile) mixture model that combines a discrete-time survival model incorporating unobserved heterogeneity in the risk of first conception for those fecund with a logistic regression model for the probability of being in the sterile subpopulation. The use of a survival model with long-term survivors (sterile subpopulation) explicitly allows for the possibility that some women have zero risk of conception.

The analysis is based on a ‘sterility/conditional fecundability’ mixture model that simultaneously combines a discrete-time hazard model for the cycle-specific probability of first conception with a logistic regression model for primary sterility (McDonald & Rosina, Reference McDonald and Rosina2001). The discrete-time survival model is used to model the sequence of menstrual cycles for each woman, where there is a positive probability of conception (non-sterile couple exposed to the risk of pregnancy in that cycle, i.e. at least one intercourse in the interval (−8, 3) relative to mucus reference day 0). Each cycle with positive exposure to the risk of conception is considered a discrete-time point. This may be conceptualized as the waiting time to conception for cycles with a positive probability of conception. The event of interest for each cycle is first conception, i.e. first clinical pregnancy.

In this study, the effect of age of woman on conditional fecundability is investigated, while simultaneously controlling for the effect of primary sterility, coital pattern and age of the male partner. Primary interest is in estimating the effect of age of woman, net of the coital pattern, rather than modelling the day-specific pregnancy probabilities and how these depend on the coital pattern. Therefore, the model used specified the effects of the coital pattern on the probability of conception differently from Dunson et al. (Reference Dunson, Colombo and Baird2002, Reference Dunson, Baird and Colombo2004) by defining three windows relative to day 0 and the presence or absence of intercourse on a day in each window.

The effect of age of woman is modelled using a cubic spline, in order to model the age pattern of fecundability in a smooth flexible non-parametric manner. Cubic splines do have a drawback in that they can behave poorly in the tails, i.e. before the first knot and after the last knot, especially when there are few observations in the tails. To avoid artificial end effects, constraints on the behaviour of the spline in thetails are added, e.g. one common constraint is that all the fitted values before the first knot and after the last knot are linear. With these constraints, one has restricted cubic splines (also termed natural splines), which constrain the function to be linear in the tails (for further details, see Harrell, Reference Harrell2001, pp. 20–24). As the ages of the couple are strongly correlated, to minimize potential multicollinearity problems, the effect of age of the man is simply specified with a dummy variable: <35 and 35+. Parameters for study centre are included in the model (the reference category is Verona). The ‘coital pattern and frequency’ is modelled by defining high (A), medium (B) and low (C) risk windows in the 12-day period of potential fertility and five categories, where ‘yes’ and ‘no’ refer to the presence or absence of intercourse on a day in the window: (1) 2+ acts of intercourse in A (reference category); (2) only one act of intercourse in A; (3) A no, B yes, C yes; (4) A no, B yes, C no; and (5) A no, B no, C yes. The classification of the 12-day interval of potential fertility into three windows relative to the conventional marker of ovulation (day 0): A (−2, −1, 0), B (−4, −3, 1) and C (−8, −7, −6, −5, 2, 3) was done using the daily fecundability estimates (with mucus reference day) presented in Colombo & Masarotto (Reference Colombo and Masarotto2000, Table 10). The 12 days were grouped into contiguous days on either side of window A on the basis of the estimated level of fecundability for each day based on the Schwartz et al. (Reference Schwartz, MacDonald and Heuchel1980) model.

Many couples were avoiding pregnancy, i.e. avoiders, in most cycles as in almost 50% of the cycles there were no acts of intercourse in the 12-day window of potential fertility. Fertility intentions of couples could and do change during the study (most couples don't want to remain childless their whole lives). In the dataset analysed, only cycles with at least one act of intercourse in the fertile window (−8, 3) were used. Many of the cycles in this study correspond to cycles where the couple are presumably trying to achieve pregnancy, i.e. achievers (plus some risky avoiders), given the concentration of intercourse near ovulation. Table 3 presents the percentage distribution of coital patterns for women of all ages, as well as those aged <24, 24–27, 28–31 and 32+. Table 3 shows that in almost 50% of the cycles there was at least one act of intercourse in window A, the 3-day period with the highest risk of conception, and the proportion of couples concentrating their intercourse near ovulation increases with age. Presumably older women concentrate more acts of intercourse in window A than younger women due to a desire to have a child.

Table 3.

Percentage distribution of coital patterns by age of woman^a

^a Age at the first day of the menstrual cycle.

^b Window A includes days (−2, −1, 0), window B includes days (−4, −3, 1) and window C includes days (−8, −7, −6, −5, 2, 3) relative to day 0 (mucus reference day).

Model for the waiting time to conception

Let T denote the waiting time to first conception for fecund couples, i.e. the number of menstrual cycles until first conception (for cycles with intercourse in the fertile window). The geometric distribution results when the discrete-time hazard, pr(T=t|T≥t), is constant over time. Fitting a constant hazard model, with possibly censored data, by maximum likelihood estimation is straightforward using software for fitting logistic regression models to binomial distributed data. Letting the constant hazard vary from individual to individual on the basis of observed heterogeneity (covariate information) is also straightforward (McDonald & Rosina, Reference McDonald and Rosina2001). One approach to incorporating unobserved heterogeneity in this time-constant discrete-time hazard model is by using a logistic-normal-geometric model for survival times. The logistic-normal-geometric model is a ‘mixed-geometric’ random effects model which allows for unobserved heterogeneity in the hazard across the population. It uses a logit link relating the hazard to explanatory variables and includes a normally distributed random effect term, which incorporates unobserved heterogeneity into the survival model. For details, see McDonald & Rosina (Reference McDonald and Rosina2001).

The survival component of the mixture model uses a logistic-normal-geometric model for the waiting time to first conception. Time starts at entry into the MCFS study. The survival model includes a restricted cubic spline of age, s(age), and other covariates, X, and regression effects, γ, and a random effect, Zσ, representing unobserved heterogeneity in the risk of conception, i.e.:

where Z ∼ N(0, 1). The effect of age of woman is modelled by using a restricted cubic spline with knots at ages 24, 28 and 32 years. For standard hypothesis testing, the number and location of the knots must be specified in advance. Stone (Reference Stone1986) found that in a restricted cubic spline model: (1) the location of the knots is not very crucial in most situations and (2) more than five knots are seldom required. So the decision in practice is between using three, four or five knots. For most purposes, Durrleman & Simon (Reference Durrleman and Simon1989) recommended using three knots. The spline used included three equally spaced knots for simplicity and the belief that such a restricted cubic spline could model any curvilinear effects of age of woman on fecundability with sufficient flexibility over an age range of less than 20 years. This spline is a linear polynomial before age 24, a cubic polynomial between ages 24 and 28, a cubic polynomial between ages 28 and 32 and a linear polynomial after age 32, where all polynomials are joined smoothly. A restricted cubic spline with knots at ages 24, 28 and 32 years can be written as:

where δ( ) is an indicator function, equal to 1 if the argument is positive and 0 otherwise, and k ₁, k ₂, k ₃ are the spline knot parameters at ages 24, 28 and 32 respectively. A restricted cubic spline can be represented in many forms and this truncated power basis form of the restricted cubic spline hides the fact that linear, quadratic and cubic functions of age are used between adjacent knots. This restricted cubic spline allows us to model non-linear relationships between age of woman and the logit of the hazard between ages 24 and 32 without specifying a given functional form.

Model for primary sterility

The analysis is based on a two-population (fecund, sterile) mixture model. Let Y=1 indicate a couple who would eventually conceive (those fecund) and Y=0 indicate a long-term survivor (those sterile). Note that Y is partly observable; the value of Y is known to equal 1 if a conception occurred, but the value of Y is unknown (missing) if a conception has not yet occurred, i.e. for right-censored observations.

For a couple with column vector F of explanatory variables, the distribution of Y can be modelled by a logistic regression model:

where α is a column vector of regression parameters to be estimated. Hence, the sterility component of the mixture model is a logistic model for primary sterility with covariates, F, and regression effects, α.

Model fitting using Gibbs sampling

Bayesian estimation of the regression parameters and unobserved heterogeneity parameter was carried out using the free software package BUGS, an acronym for ‘Bayesian inference Using Gibbs Sampling’, which is described by Thomas et al. (Reference Thomas, Spiegelhalter, Gilks, Bernardo, Berger, Dawid and Smith1992), because of its flexibility in fitting complex models. The BUGS code used to specify the model is available from the authors. The Gibbs sampler is a general purpose Monte Carlo method for generating random variables from a target distribution of interest indirectly, in this case, a multivariate posterior distribution. A burn-in of 5000 iterations was used and inference based on a sample of 50,000 observations from the posterior distribution. Inferences are based on numerical summaries of the univariate marginals of the posterior distribution; here the posterior mean and median are used as measures of location and 95% credible intervals defined by the 2.5% and 97.5% points of the univariate marginal posterior distribution are used as the measure of precision.

The non-informative priors used for the regression parameters were independent N(0, 0.0001) distributions, where the second parameter of the normal distribution is the precision, i.e. the reciprocal of the variance. A N(0, 1) prior for the unobserved Z and a mildly informative uniform prior of σ ∼ U[0, 5] was used. An informative beta prior was used for the proportion fecund, i.e. f ∼ beta(367.68, 15.32), which corresponds to a mean of 0.96 and 95% credible interval between 0.94 and 0.98. Note that for many couples the number of ‘unsuccessful’ cycles was often too small to provide much information about the probability that the couple was sterile. The beta prior was chosen as the proportion of couples with primary sterility has been estimated to be around 3% to 4%. Therefore, a 95% credible interval between 2% and 6% for the percentage sterile was used.