A Bayesian joint model of menstrual cycle length and fecundity

Menstrual cycle length (MCL) has been shown to play an important role in couple fecundity, which is the biologic capacity for reproduction irrespective of pregnancy intentions. However, a comprehensive assessment of its role requires a fecundity model that accounts for male and female attributes and the couple's intercourse pattern relative to the ovulation day. To this end, we employ a Bayesian joint model for MCL and pregnancy. MCLs follow a scale multiplied (accelerated) mixture model with Gaussian and Gumbel components; the pregnancy model includes MCL as a covariate and computes the cycle-specific probability of pregnancy in a menstrual cycle conditional on the pattern of intercourse and no previous fertilization. Day-specific fertilization probability is modeled using natural, cubic splines. We analyze data from the Longitudinal Investigation of Fertility and the Environment Study (the LIFE Study), a couple based prospective pregnancy study, and find a statistically significant quadratic relation between fecundity and menstrual cycle length, after adjustment for intercourse pattern and other attributes, including male semen quality, both partner's age, and active smoking status (determined by baseline cotinine level 100ng/mL). We compare results to those produced by a more basic model and show the advantages of a more comprehensive approach.