title: Modelling multiple ovulation, fertilization, and embryo loss in human fertility studies.
abstract: Models of human fertility that incorporate information on timing of intercourse have assumed that a single ovum is released each menstrual cycle. These models are misspecified if two or more viable ova are sometimes released in a single cycle, which is known to occur in dizygotic twin pregnancies. In this paper, we propose a model for multiple ovulation in humans. We assume that the unobservable number of viable ova in each cycle follows a multinomial distribution. Successful fertilization of each ovum depends on the ability of the cycle to support a pregnancy and on the aggregate of a set of unobservable Bernoulli trials representing the fertilizing effects of intercourse on various days. Our model accommodates general covariate effects, allows for heterogeneity among couples, and accounts for a sterile subpopulation of couples. Information on early detection of pregnancy can be incorporated to estimate the probability of embryo loss. We outline a Markov chain Monte Carlo algorithm for estimation of the posterior distributions of the parameters. The methods are applied to data from a North Carolina pregnancy study, and applications to studies of assisted reproduction are described.
authors.affiliation: National Institute of Environmental Health Sciences, PO Box 12233, Research Triangle Park, NC 27709, USA. dunson1@niehs.nih.gov
authors.forename: D B
authors.initials: DB
authors.lastname: Dunson
authors.forename: C R
authors.initials: CR
authors.lastname: Weinberg
authors.forename: A J
authors.initials: AJ
authors.lastname: Wilcox