Modelling digit preference in fecundability studies.

Retrospective studies of fecundability, in which women are asked how many cycles they required to become pregnant, are often affected by problems of digit preference. A probability model for such digit preference is proposed in which misreporting favours 6 or 12 (and possibly also 3) cycles. It is assumed that in the absence of misreporting the number of cycles follows a beta-geometric distribution. The model is applied to two data sets, with clear-cut results: The inclusion of additional parameters to model the misreporting can lead to substantial improvements in fit, but causes little change to the estimated parameters of the underlying beta-geometric distribution. In some cases misreporting parameters may be regarded as nuisance parameters, while in others they may be of interest. We have found estimates of these parameters to vary between different categories of women in an interpretable manner. The models may also be used to estimate the percentage of couples in any study that misreport their conception waiting time.     

Maximum likelihood estimation of the parameters of the prior distributions of three variables that strongly influence reproductive performance in cows

Ovulation detection rate, pregnancy rate, and embryo loss rate greatly affect the reproductive performance of cows. A previous model described the separate effects of these variables on the resulting calving patterns and assumed that the variables have the same value for all cows belonging to the same herd. This is not a realistic biological assumption, so the beta distribution is used to introduce "between-cow" variation in the three variables. Two approaches are used to find maximum likelihood estimates of the parameters of these prior beta distributions. The first considers sequences of ovulations, artificial inseminations, and pregnancies, separately. For both ovulation detection rate and pregnancy rate this approach considers the number of "successes" of each event for a particular cow (e.g., in the case of an ovulation, a success is a detection), and conditions on the total number of occurrences of that event in the cow, so that beta-binomial distributions are considered. However, for embryo loss rate the number of pregnancies required until a particular cow calves is considered, so that a beta-geometric distribution results. If the cow is removed before she calves, a censored sequence will result. The second approach considers the sequences of ovulations, artificial inseminations, pregnancies, and embryo losses, together, which will stop only when the cow calves. Otherwise, if she is removed before that time, a censored sequence will result. In this case, a joint distribution, with three independent prior beta distributions, is considered. The results of the analysis of data from 22 herds are discussed.     

Studies of fertility and fecundity: comparative approaches from demography and epidemiology

The approaches used by demographers and by epidemiologists for studying the fecundity of couples (i.e. their ability to conceive) have converged, whereas they were historically divergent. Demography traditionally focused on fertility - the circumstances in which livebirths occur - with the aim of predicting population changes, in particular. Demographers also rapidly became interested in fecundity, developing concepts such as fecundability and definitive sterility. The measurement of fecundability is based on determination of the time to pregnancy (TTP), the basic tool of the epidemiologist. However, while demographers were developing methods for estimating the distribution of fecundability among couples based on TTP, epidemiologists turned to methods for analysing the role of diverse factors potentially influencing fecundity at the individual level.     

Bayesian inferences on predictors of conception probabilities

Reproductive scientists and couples attempting pregnancy are interested in identifying predictors of the day-specific probabilities of conception in relation to the timing of a single intercourse act. Because most menstrual cycles have multiple days of intercourse, the occurrence of conception represents the aggregation across Bernoulli trials for each intercourse day. Because of this data structure and dependency among the multiple cycles from a woman, implementing analyses has proven challenging. This article proposes a Bayesian approach based on a generalization of the Barrett and Marshall model to incorporate a woman-specific frailty and day-specific covariates. The model results in a simple closed form expression for the marginal probability of conception, and has an auxiliary variables formulation that facilitates efficient posterior computation. Although motivated by fecundability studies, the approach can be used for efficient variable selection and model averaging in general applications with categorical or discrete event time data.     

Modeling human fertility in the presence of measurement error

The probability of conception in a given menstrual cycle is closely related to the timing of intercourse relative to ovulation. Although commonly used markers of time of ovulation are known to be error prone, most fertility models assume the day of ovulation is measured without error. We develop a mixture model that allows the day to be misspecified. We assume that the measurement errors are i.i.d. across menstrual cycles. Heterogeneity among couples in the per cycle likelihood of conception is accounted for using a beta mixture model. Bayesian estimation is straightforward using Markov chain Monte Carlo techniques. The methods are applied to a prospective study of couples at risk of pregnancy. In the absence of validation data or multiple independent markers of ovulation, the identifiability of the measurement error distribution depends on the assumed model. Thus, the results of studies relating the timing of intercourse to the probability of conception should be interpreted cautiously.     

Therapeutic donor insemination with frozen semen.

Although it is now accepted that cryopreserved semen must, on ethical and medicolegal grounds, be used for donor insemination many clinicians still believe that it has an unacceptably reduced fecundability rate as compared with fresh semen. We studied the outcome of 81 recipients who started therapeutic donor insemination (TDI) treatment during 1986 in a program that used exclusively cryopreserved semen; 55 had never undergone TDI and were receiving the first series (six cycles), 6 were receiving the second series (also six cycles), and 20 had achieved pregnancy through TDI previously and were starting the treatment again. Insemination with semen stored in 0.5-ml French straws was performed daily during the periovulatory period while the modified Insler score was 10 or greater out of 15. A total of 42 (52%) of the recipients became pregnant within six TDI cycles; 4 (10%) had a spontaneous abortion. An average of 4.8 straws were used per cycle among those who became pregnant and 5.1 per cycle among those who did not. On average 2.6 cycles were required to achieve pregnancy. The overall fecundability rate was 14.6%. We conclude that a TDI program involving exclusively frozen semen can be operated with a success rate comparable to rates achieved with fresh semen if a simple, established cryopreservation method and an uncomplicated clinical management protocol are used.     

A comparison of the beta-geometric model with landmarking for dynamic prediction of time to pregnancy

We conducted a simulation study to compare two methods that have been recently used in clinical literature for the dynamic prediction of time to pregnancy. The first is landmarking, a semi-parametric method where predictions are updated as time progresses using the patient subset still at risk at that time point. The second is the beta-geometric model that updates predictions over time from a parametric model estimated on all data and is specific to applications with a discrete time to event outcome. The beta-geometric model introduces unobserved heterogeneity by modelling the chance of an event per discrete time unit according to a beta distribution. Due to selection of patients with lower chances as time progresses, the predicted probability of an event decreases over time. Both methods were recently used to develop models predicting the chance to conceive naturally. The advantages, disadvantages and accuracy of these two methods are unknown. We simulated time-to-pregnancy data according to different scenarios. We then compared the two methods by the following out-of-sample metrics: bias and root mean squared error in the average prediction, root mean squared error in individual predictions, Brier score and c statistic. We consider different scenarios including data-generating mechanisms for which the models are misspecified. We applied the two methods on a clinical dataset comprising 4999 couples. Finally, we discuss the pros and cons of the two methods based on our results and present recommendations for use of either of the methods in different settings and (effective) sample sizes.     

Measuring potential fertility through null segments: An exploratory analysis

Abstract

Procedures are presented for estimating from null segments the natural fecundability of couples who may be practicing contraception. The procedures include an assessment of bias. Also presented is a new measure designed to bring out the implications for residual fertility of the pregnancy outcome probabilities and fecundability functions recorded for given five‐year age classes of respondents. Application is made to two Taiwan samples featuring segment coded data.     

Bayesian Modeling of the Level and Duration of Fertility in the Menstrual Cycle

Time to pregnancy studies that identify ovulation days and collect daily intercourse data can be used to estimate the day-specific probabilities of conception given intercourse on a single day relative to ovulation. In this article, a Bayesian semiparametric model is described for flexibly characterizing covariate effects and heterogeneity among couples in daily fecundability. The proposed model is characterized by the timing of the most fertile day of the cycle relative to ovulation, by the probability of conception due to intercourse on the most fertile day, and by the ratios of the daily conception probabilities for other days of the cycle relative to this peak probability. The ratios are assumed to be increasing in time to the peak and decreasing thereafter. Generalized linear mixed models are used to incorporate covariate and couple-specific effects on the peak probability and on the day-specific ratios. A Markov chain Monte Carlo algorithm is described for posterior estimation, and the methods are illustrated through application to caffeine data from a North Carolina pregnancy study.     

Distributions of coital rates and of fecundability

Abstract

Attempts have been made to fit distributions of conception waits on the assumption that fecundability is distributed as a Pearson Type I beta distribution. Since the fits were unsatisfactory (Majumdar and Sheps, 1970), the question arises whether fecundability is distributed as a Type III. If it were, then the probability of coitus should also be distributed as a Type III, and distributions of coital rates should be better fitted by the negative binomial than by Skellam's distribution. The data available for such fits have been briefly reviewed here and fits attempted. There is some slight evidence in favor of the hypothesis, but more data are needed before the question can be decisively answered.     

Fertility of couples following cessation of contraception

A retrospective study of the delay in conception after stopping different methods of contraception is undertaken among 5108 pregnant women residing in a departement in the Paris region. Particular attention is paid to the delay that sometimes separates the cessation of contraception and the beginning of intercourse without precautions. The counfounding factors considered are: the observation of a waiting period following cessation of contraception; the existence of a strategy, i.e., a coital pattern adopted by certain couples who have intercourse more often during the middle of the cycle, hoping to conceive more rapidly; the regularity of the menstrual cycle and the woman's age at the beginning of unprotected intercourse. The statistical techniques include chi-square analysis, analysis of variance correlation, partial multiple regression and actuarial rates of infecundity. The mean age of women at their last period was 26.3 years; 37.6% were primagravida; 87.3% worked outside the home and 36.6% were smokers. 72% of the women used oral contraceptives; 14% the IUD, and 14% other methods. Among all factors studied, 4 are strongly related both to fertility and to mode of contraception: the waiting period, coital strategy, regularity of the menstrual cycle and the woman's age. Shorter average time required to conceive (TRC) and greater fecundability are associated with the observation of a waiting period, no coital strategy, and regular cycles. The woman's age at the time of unprotected intercourse shows no correlation with TRC; it does, however, show a correlation with fecundability, which increases with age to reach a maximum in the age group 25-29 and then decreases progressively. These 4 factors are also related to the mode of contraception. Those using hormonal contraception were more likely to observe a waiting period. However, they report a coital strategy less frequently, their usual cycle is more often irregular and they are younger than IUD or other method users. Results demonstrate a decreased fertility for couples after the pill and, to a lesser degree, after IUD use, but only among those who did not take other precautions (waiting period). For couples observing a waiting period, there is no decrease of fertility following the initial exposure to the risk of conception. This comparison of return of fertility following cessation of different contraceptive methods shows that raw data must be interpreted with caution. It is essential to take into account the possibility of delay in becoming exposed to the risk of conception while various confounding factors must also be considerd.     

Decreased fecundability in Hutterite couples sharing HLA-DR.

To study the effects of parental HLA sharing on pregnancy outcome, we initiated population-based studies in the Hutterites. We previously reported longer intervals from marriage to each birth among couples sharing HLA, particularly HLA-DR. In the present report, we present the results of a prospective, 5-year study of fecundability and fetal loss rates in this population. Between April 1986 and April 1991, 154 pregnancies were observed in 104 couples. The median number of months of unprotected intercourse to a positive pregnancy test was significantly longer among couples sharing HLA-DR who stopped nursing prior to the first menses as compared with couples not sharing HLA-DR who stopped nursing prior to the first menses (5.1 vs. 2.0 mo, respectively; P = .016). Fetal loss rates were increased among couples sharing HLA-B as compared with couples not sharing HLA-B (.23 vs. .12, respectively; P = .041, adjusted for age, gravidity, and kinship). These data suggest that our earlier observations of increased birth interval lengths among Hutterite couples sharing HLA were predominantly due to longer intervals until a clinical pregnancy among couples sharing HLA-DR and, to a lesser degree, were due to increased fetal loss rates among couples sharing HLA-B.     

Quasi-likelihood estimation for relative risk regression models

For a prospective randomized clinical trial with two groups, the relative risk can be used as a measure of treatment effect and is directly interpretable as the ratio of success probabilities in the new treatment group versus the placebo group. For a prospective study with many covariates and a binary outcome (success or failure), relative risk regression may be of interest. If we model the log of the success probability as a linear function of covariates, the regression coefficients are log-relative risks. However, using such a log-linear model with a Bernoulli likelihood can lead to convergence problems in the Newton-Raphson algorithm. This is likely to occur when the success probabilities are close to one. A constrained likelihood method proposed by Wacholder (1986, American Journal of Epidemiology 123, 174-184), also has convergence problems. We propose a quasi-likelihood method of moments technique in which we naively assume the Bernoulli outcome is Poisson, with the mean (success probability) following a log-linear model. We use the Poisson maximum likelihood equations to estimate the regression coefficients without constraints. Using method of moment ideas, one can show that the estimates using the Poisson likelihood will be consistent and asymptotically normal. We apply these methods to a double-blinded randomized trial in primary biliary cirrhosis of the liver (Markus et al., 1989, New England Journal of Medicine 320, 1709-1713).     

Estimation of the parameters of a type I geometric distribution from truncated observations on conception delays

In connection with the estimation of the average fecundability of a group of women, it has been assumed in the past that the waiting time for a conception follows a type I geometric distribution, and its two parameters have been estimated by the method of moments and the method of maximum likelihood. In a follow-up study, starting with a group of women, there is always the possibility that some women will remain nonpregnant in the limited period of time they are observed, and the problem arises as to how to estimate the same parameters if the follow-up experiment is terminated after a fixed period of time. The present paper deals with this truncation problem, and provides three different methods for estimating the parameters, which are applied to data from the Menstrual and Reproductive History Study at the University of Minnesota. In the last section, an extended model is presented which incorporates the possibility of dropout cases.     

Modeling the dependence between number of trials and success probability in beta-binomial-Poisson mixture distributions

Beta-binomial models are widely used for overdispersed binomial data, with the binomial success probability modeled as following a beta distribution. The number of binary trials in each binomial is assumed to be nonrandom and unrelated to the success probability. In many behavioral studies, however, binomial observations demonstrate more complex structures. In this article, a general beta-binomial-Poisson mixture model is developed, to allow for a relation between the number of trials and the success probability for overdispersed binomial data. An EM algorithm is implemented to compute both the maximum likelihood estimates of the model parameters and the corresponding standard errors. For illustration, the methodology is applied to study the feeding behavior of green-backed herons in two southeastern Missouri streams.     

A Scoring Tool to Identify East African HIV-1 Serodiscordant Partnerships with a High Likelihood of Pregnancy

Introduction

HIV-1 prevention programs targeting HIV-1 serodiscordant couples need to identify couples that are likely to become pregnant to facilitate discussions about methods to minimize HIV-1 risk during pregnancy attempts (i.e. safer conception) or effective contraception when pregnancy is unintended. A clinical prediction tool could be used to identify HIV-1 serodiscordant couples with a high likelihood of pregnancy within one year.

Methods

Using standardized clinical prediction methods, we developed and validated a tool to identify heterosexual East African HIV-1 serodiscordant couples with an increased likelihood of becoming pregnant in the next year. Datasets were from three prospectively followed cohorts, including nearly 7,000 couples from Kenya and Uganda participating in HIV-1 prevention trials and delivery projects.

Results

The final score encompassed the age of the woman, woman’s number of children living, partnership duration, having had condomless sex in the past month, and non-use of an effective contraceptive. The area under the curve (AUC) for the probability of the score to correctly predict pregnancy was 0.74 (95% CI 0.72–0.76). Scores ≥7 predicted a pregnancy incidence of >17% per year and captured 78% of the pregnancies. Internal and external validation confirmed the predictive ability of the score.

Discussion

A pregnancy likelihood score encompassing basic demographic, clinical and behavioral factors defined African HIV-1 serodiscordant couples with high one-year pregnancy incidence rates. This tool could be used to engage African HIV-1 serodiscordant couples in counseling discussions about fertility intentions in order to offer services for safer conception or contraception that align with their reproductive goals.     

Canine and feline abortion diagnostics

Knowledge of the causes of canine or feline pregnancy loss is limited and the success rate for making a definitive diagnosis is disappointingly low. Although these facts are discouraging, there are some things that can be done to improve success rates. This paper will address limitations and explore ways for improvement. For abortions caused by microbial infections, there are many reasons why it may not possible to identify the agents. "Non-infectious" causes are much more difficult to diagnose, and their relative importance is unknown. These include endocrine failure, underlying endometrial disease, genetic abnormalities, nutritional deficiencies, and toxicosis from drugs or environmental sources. Genetic abnormalities are a major cause of human pregnancy loss, yet we have little specific information about genetic diseases leading to abortion in animals. This paper addresses ways clinicians and diagnosticians can work together to improve diagnostic success. Necropsy techniques for fetal and placental examination and sampling are briefly reviewed. It is hoped that this series of papers will stimulate discussion on the causes and pathogenesis of pregnancy failure, and focus attention on areas where abortion diagnostics can be improved.     

Demographic correlates of paternity confidence and pregnancy outcomes among Albuquerque men

We examine the demographic correlates of paternity confidence, or men's assessment of the likelihood that they are the genetic father of a particular child. Evolutionary theory predicts that men will provide less parental investment for putative genetic offspring who are unlikely to be their actual offspring, but confidence of paternity has not been as extensively examined as its importance would merit. Using self-reported data on paternity confidence in 3,360 pregnancies reported by men living in Albuquerque, New Mexico, we find that low paternity confidence is more common among unmarried couples and for unplanned pregnancies. We also find that men are more likely not to state paternity confidence (i.e., they refuse to answer the question) if a pregnancy is unplanned. We additionally examine the pregnancy outcomes associated with confidence of paternity. We find that low paternity confidence pregnancies are significantly more likely to be aborted, and pregnancies for which paternity confidence is unstated are more likely to be aborted or to miscarry. Both abortion and miscarriage are associated with unmarried couples, with unplanned pregnancies, and with couples who have fewer children together.     

The laws of Taharat HaMishpacha: potential effects on fertility

The laws of Taharat HaMishpacha (Family purity), which regulate coital activity among Orthodox Jews according to menstrual cycle phase in a population that generally does not use contraception, have potentially important effects on fertility. Analysis of these effects based on menstrual cycle and ovulatory phase lengths for women in the childbearing years shows that the majority of cycles are potentially exposed to coital activity during a fertile period and the increased likelihood of coitus following abstinence has a potentially fertility-enhancing effects. Since most Orthodox Jewish women complete the period of tumah (ritual impurity) and attend the mikveh (a ritual water immersion which marks the end of the cycle) on or before day 14 of the postmenstrual phase, only 22% of cycles are potential sources of diminished fertility as a result of restricted coitus. Any delay in the resumption of sexual relations would result in reduced fecundability for a much larger proportion of cycles. For example, if sexual relations are not resumed until day 15, the proportion of cycles wherein coitus is restricted to the postovulatory phase increases from a maximum of 30% to 41%. Observance of the laws do not greatly diminish the overall fertility of the population assuming that 1) the majority of tumah intervals do not extend beyond 14 days, and 2) coital activity is resumed immediately following return from mikveh. For the individual woman with a predominance of short cycles, delays in conception are probable.     

Peut-on optimiser la congélation des spermatozoïdes testiculaires? L’expérience du Centre Hospitalier de Poissy Saint-Germain

50% or more of non-obstructive azoospermic men have no spermatozoa in their testicular tissue, and no non-invasive predictor of spermatogenesis is yet available. For this reason, we therefore performed all TESE (74 TESE for non-obstructive azoospermia and 37 TESE for obstructive azoospermia) prior to initiating ovarian stimulation. 34% (25/74) of TESE performed for non-obstructive azoospermia were successful. Spermatozoa were retrieved in 100% of cases of obstructive azoospermia. When TESE were positive, spermatozoa were frozen in 25–50 μl micro-droplets (several straws). 60 ICSI cycles (25 couples) were treated for non obstructive azoospermia. The clinical pregnancy rate per ICSI cycle was 18%, and the implantation rate per embryo transferred was 9.2%. 81 ICSI cycles (37 couples) were treated for obstructive azoospermia. The fertilization rate was 54%, and embryo transfer was performed in 89% (72/81) of cycles. The clinical pregnancy rate per embryo ICSI cycle was 26%, and the implantation rate per embryo transferred was 16%. This management of azoospermic patients, including TESE and multiple testicular tissue freezing in micro-droplets prior to ovarian stimulation, avoids ova pick-up cancellation and multiple TESE, as several ICSI can be performed after a single TESE. Our results show that this micro-technique for freezing testicular tissue is effective not only for obstructive azoospermia, but also for non-obstructive azoospermia when only very few spermatozoa can be extracted from the testis.