Evaluating effects of exposures on embryo viability and uterine receptivity in in vitro fertilization

We consider models for the occurrence of pregnancy following in vitro fertilization. In this clinical protocol, implantation depends on two factors: the receptivity of the uterus and the viability of at least one of the embryos transferred to the uterus. This work is motivated by the need to identify reliable bio-markers for these two factors, in order to enhance the success rate for couples undergoing this procedure. We present a general latent variable structure model for outcomes that take either one of two possible forms: as summed Bernoullis, based on an ultrasound count of gestational sacs, or as aggregated Bernoullis, based only on the outcome of a biochemical pregnancy test. We allow both uterine receptivity and embryo viability to be influenced by covariates. The proposed latent variable structure allows us to utilize the existing statistical packages to maximize an otherwise intractable likelihood function. The method is sufficiently flexible to permit any valid choice of link function. We illustrate by applying the method to a recent study of in vitro fertilization carried out in North Carolina. The number of cells at transfer is evidently a marker for embryo viability.