Statistical testing of genetic linkage under heterogeneity

Recent advances in human genetics have led to a renewed interest in statistical methods for the detection of linkage from family data--for example, between marker loci and disease traits. Statistical analysis of linkage between two loci is carried out almost exclusively by means of the lod (log-odds) score test, equivalent to a likelihood ratio test. The current practice is to declare genetic linkage between loci when the maximum lod score exceeds 3. As will be discussed here, the lod-score approach is not appropriate for the detection of linkage from heterogeneous data, e.g., when families consist of a mixture of linked and unlinked types. Heterogeneity may arise, for example, when rare mutations at different genetic loci are responsible for the same disease trait. As an alternative approach to account for possible heterogeneity in the detection of linkage, we propose the application of large-sample test statistics that are members of Neyman's class of C(alpha), or partial score tests. The convergence of the proposed test statistics to their asymptotic distributions is investigated via Monte Carlo simulation for typical study designs applicable in human genetics.