Modelling multiple ovulation, fertilization, and embryo loss in human fertility studies

DUNSON, DAVID B.
WEINBERG, CLARICE R.
WILCOX, ALLEN J.

National Institute of Environmental Health Sciences, PO Box 12233, Research Triangle Park, NC 27709, USA. [email protected]

^*To whom correspondence should be addressed.

[Received March 13, 2000; revised June 5, 2000; accepted for publication June 29, 2000]

Biostatistics 2(2):p 131-145, June 2001.

SUMMARY

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.