Bayesian Modeling of Markers of Day-Specific Fertility
Cervical mucus hydration increases during the fertile interval before ovulation. Because sperm can only penetrate mucus having a high water content, cervical secretions provide a reliable marker of the fertile days of the menstrual cycle. This article develops a Bayesian approach for modeling of daily observations of cervical mucus and applies the approach to assess heterogeneity among women and cycles from a given woman with respect to the increase in mucus hydration during the fertile interval. The proposed model relates the mucus observations to an underlying normal mucus hydration score, which varies relative to a peak hydration day. Uncertainty in the timing of the peak is accounted for, and a novel weighted mixture model is used to characterize heterogeneity in distinct features of the underlying mean function. Prior information on the mucus hydration trajectory is incorporated, and a Markov chain Monte Carlo approach is developed. Based on data from a study of daily fecundability, there appears to be substantial heterogeneity among women in detected preovulatory increases in mucus hydration, but only minimal differences among cycles from a given woman.