Models for assisted conception data with embryo-specific covariates.

Assisted conception routinely involves multiple embryo implantation within each recipient mother, with the outcome of interest being the number and multiplicity of live births. Here we consider the situation in which covariate information, potentially predictive of outcome, is available at the embryo level for each individual implanted embryo. This presents two challenges: firstly the outcome is measured at a higher, recipient, level than the covariates of interest; and secondly it is generally not known which of the implanted embryos developed to give a successful pregnancy. In practice such data have usually been analysed by aggregation of the embryo-level covariates to the recipient-level. Here we consider and compare two alternative approaches which respect the structure of the data alongside the aggregated approach. The first is a deterministic model with separate embryo and recipient success probabilities, each determined by a set of covariates, as first proposed by Spiers and extended by Zhou and Weinberg. The second is based on a multilevel model with the correlations between embryos in the same recipient modelled by a recipient level random effect. These models are compared using two real data sets, and the model properties further explored in a simulation study.