A RANDOM-EFFECTS MODEL FOR CYCLE VIABILITY IN FERTILITY STUDIES

Models for fertility that take into account the timing of intercourse relative to ovulation are needed to estimate the influence of both end ogenous and exogenous factors on human fertility. The classical model assumes that some menstrual cycles are ''viable'' and some are not, wh ere ''viability'' is determined by whether hormonal, uterine, and game te-related factors are favorable to gestation. Within each viable cycl e, the various days with intercourse are assumed to act independently; within each nonviable cycle, the days with intercourse can have no ef fect. Cycle viability for individual cycles is latent in that it is no t ascertainable when conception does not occur. The classical model ne glects the statistical dependency of outcomes among menstrual cycles w ithin individual couples. Current marginal approaches cannot determine the degree to which heterogeneity in fecundability is biologically ba sed versus the degree to which it is secondary to variation in interco urse behavior from couple to couple. We describe a random-effects mode l based on assuming that the cycle viability probability varies from c ouple to couple according to a beta distribution, and we use an EM alg orithm to fit the model. The proposed estimating procedure is fully ex pandable to allow covariate effects on the beta variate. Our method ca n be applied more generally whenever dependency among Bernoulli trials is induced by a susceptibility state and the outcomes can be observed only in the aggregate. Based on data from a cohort of couples with no known fertility problems who were attempting pregnancy, cycle viabili ty is found to be heterogeneous among couples. Stratification on the p resence or absence of prenatal exposure of the woman to her mother's c igarette smoking revealed a statistically significant difference in th e two cycle viability distributions. We discuss differences in the int erpretation of the beta model compared to the marginal approach based on generalized estimating equations.