Multi-level modelling of conception in artificial insemination by donor.

Data on insemination with donor's sperm have a crossed hierarchical structure due to the coexistence of female factors (ovulatory cycles within pregnancy attempt within women) and male factors (inseminations within donations within donors). A crossed random multi-level logistic model, taking account of this structure, permits an improved estimation of the fixed effects and provides insights into their influence at each level in the hierarchy. We present an efficient algorithm for fitting such models using alternating EM steps. We further discuss the inclusion of compositional covariates to determine what information the quality of a donation conveys regarding the donor basal fecundability and on the specific sperm donation.