Statistical modelling of data from the embryo transfer process of In-VitroFertilization (IVF) treatments is motivated by the need to perform statisticalinference for potential factors and to develop predictive models for thesetreatments. The biggest issue arising when modelling these treatments is that anumber of embryos are transferred but unless all of the embryos get implantedor fail to implant then it is not possible to identify which of the embryosimplanted. Little work has been done to address this partial observability of theoutcome as it arises in this contextWe adopt an Embryo-Uterus (EU) framework where a patient response hasdistinct uterine and embryo components. This framework is used to constructstatistical models, expand them to allow for clustering effects and develop apackage that will enable the fitting and prediction of these models in STATA.The capabilities of this package are demonstrated in two real datasets, aimed ininvestigating the effect of a new embryo prognostic variable and the effect ofpatient clustering in these treatments.In a simulation study EU models are shown to be capable of identifying apatient covariate either as a predictor of uterine receptivity or embryo viability.However a simulation case study shows that a considerable amount ofinformation about the embryo covariate is lost due to the partial observability ofthe outcome. Further simulation work evaluating the performance of a numberof proposed alternatives to the EU model shows that these alternatives areeither biased or conservative.The partially observed cycles are finally considered as a missing data problemand two novel modelling approaches are developed which are able to handlethe structure of these treatments. These novel models, based on multipleimputation and probability weighting, are compared to the EU model usingsimulation in terms of predictive accuracy and are found to have similarpredictive accuracy to the EU model.