A random-effects model for cycle viability in fertility studies

The authors describe a random-effects fertility model based upon the assumption that the menstrual cycle viability probability varies from couple to couple according to a beta distribution. An EM algorithm is used to fit the model. The proposed estimating procedure is fully expandable to allow covariate effects on the beta variate. The method can be applied generally whenever dependency among Bernoulli trials is induced by a susceptibility state and the outcomes can be observed only in the aggregate. Based upon data from a cohort of 221 couples with no known fertility problems who were attempting pregnancy, cycle viability was found to be heterogeneous among couples. Stratification on the presence or absence of prenatal exposure of the woman to her mother's cigarette smoking revealed a statistically significant difference in the two-cycle viability distributions. Differences are discussed in the interpretation of the beta model compared to the marginal approach based upon generalized estimating equations.