Bayesian selection of predictors of conception probabilities across the menstrual cycle

There is increasing interest in identifying predictors of human fertility, including environmental exposures, behavioural factors, and biomarkers, such as mucus or reproductive hormones. Epidemiological studies typically measure fecundability, the per menstrual cycle probability of conception, using time to pregnancy data. A critical predictor, which is often ignored in the design or analysis, is the timing of non-contracepting intercourse in the menstrual cycle. In order to limit confounding by behavioural differences between exposure groups, it may be preferable to base inferences on day-specific conception probabilities in relation to intercourse timing. This article proposes Bayesian methods for selection of predictors of day-specific conception probabilities. A particular focus is the case in which data on ovulation timing are not available. We focus on the selection of fertile days in the cycle during which conception probabilities are non-negligible and predictors may play a role. Data from recent European and Italian prospective studies of daily fecundability are presented, and the proposed approach is used to estimate cervical mucus effects within a mid-cycle potentially fertile window using data from the Italian study.