Bayesian Inferences on Predictors of Day-Specific Conception Probabilities

For couples attempting pregnancy, it is important to identify 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. Due to this aggregated Bernoulli data structure and to dependency among the multiple cycles from a woman, implementing analyses has proven challenging, particularly when predictors are day-specific. This article proposes a Bayesian approach for addressing this problem, 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 underlying variables formulation which facilitates efficient posterior computation. A conjugate variable selection prior is proposed, which allows one-sided hypothesis testing, and the methods are applied to simulated and real data examples.