A composite likelihood approach to predict the sex of the baby

Couples with diseases associated with the sexual chromosomes, as well as families in countries where the desire for a male is extreme, are interested in influencing the sex of the baby. We propose an original composite likelihood approach to analyse the relation between sex of the newborn and timing of the intercourse which leads to conception. Although there exist numerous works on this relation, only few studies have been carried out on independent datasets to validate the existing theories. Since the sex of the newborn is only known in case of conception, the full likelihood of the data is not easily defined without strong assumptions. A composite likelihood is a pseudo likelihood defined as the product of likelihood functions relative to subsets of the data. In particular, we consider two such likelihoods, one modelling the day-specific probabilities of conception and the other modelling the sex of the newborn given a conception has occurred. The methodology is applied to a dataset from a European fecundability study. The results show no significant dependence of the sex of the newborn on the time of intercourse. The method developed may be applied to other situations when data are affected by selective sampling.