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.