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An advanced intercross line (AIL) is an easier and more cost-effective approach compared to recombinant inbred lines for fine mapping of quantitative trait loci (QTL) identified by F2 designs. In an AIL, a complex binary trait can be mapped through analysis of either continuously distributed proxy traits for the liability of the binary trait or the liability itself, the latter presenting the greater statistical challenge. In another work, we successfully applied both approaches in an AIL to fine map previously identified QTL underlying anatomical parameters of the cardiac inter-atrial septum including patent foramen ovale. Here, we describe the statistical methods that we used to analyse complex binary traits in our AIL design. This is achieved using a likelihood-based method, with the expectation-maximisation algorithm allowing use of standard logistic regression methods for model fitting. [ABSTRACT FROM AUTHOR]