A hierarchical Bayesian approach to modeling embryo implantation following in vitro fertilization

In vitro fertilization and embryo transfer (IVF-ET) is considered a method of last resort for treating infertility. Oocytes taken from a woman are fertilized in vitro, and one or more resulting embryos are transferred into the uterus, with the hope that at least one will implant and result in pregnancy. Successful implantation depends on both embryo viability and uterine receptivity. This has led to the development of the EU model for embryo implantation, wherein uterine receptivity is characterized by a latent binary variable U and embryo viability is characterized by a latent binomial variable E representing the number of viable embryos among those selected for transfer. The observed number of implantations is the product of E and U. Zhou and Weinberg (1998) developed a regression formulation of the EU model in which embryo viabilities are independent within patients. We extend their methodology to a Bayesian hierarchical framework that allows for correlation between the embryo viabilities and gives explicit characterization of patient-level heterogeneity. When some subjects have zero implantations, the likelihood for the hierarchical EU model is relatively flat and therefore using prior information for key parametersis needed. This provides a key motivation for adopting a Bayesian approach. The model is used to assess the effect of hydrosalpinx on embryo implantation in a cohort of 288 women undergoing IVF-ET because of tubal disease. Hydrosalpinx is a build-up of fluid in the Fallopian tubes, which sometimes leaks to the uterus and may reduce the likelihood of implantation. The EU model is well suited to this question because hydrosalpinx is thought to affect implantation by reducing uterine receptivity only. Our analysis indicates substantial subject-level heterogeneity with respect to embryo viability, suggesting the utility of a multi-level model.