Affected relative pairs and simultaneous search for two-locus linkage in the presence of epistasis

It is commonly believed that multiple interacting genes increase the susceptibility of genetically complex diseases, yet few linkage analyses of human diseases scan for more than one locus at a time. To overcome some of the statistical and computational limitations of a simultaneous search for two disease susceptibility loci in the presence of epistasis, we developed new score statistics to simultaneously scan for two disease susceptibility loci in pedigree data. These model-free score statistics are based on developments for model-free maximum lod scores, which in turn are based on variance components for indicators of disease status. To overcome reduced power caused by many parameters in the general two-locus model, we impose constraints on ratios of variance components, much like those used for robust single-locus linkage statistics (e.g., minimax constraints). The resulting three-degree of freedom score statistic, constrained as a one-sided multivariate test, can be computed rapidly, making simultaneous search feasible for human genetic linkage studies. Furthermore, using recent developments to rapidly compute simulation P-values for score statistics, it is feasible to empirically evaluate the statistical significance of the proposed score statistics. Application of these methods to two large studies of the genetic linkage of prostate cancer illuminates their strengths and limitations. The results provide weak suggestions for linkage of several pairs of chromosomal regions (chromosome pairs 1-21, 3-13, 5-9, and 14-19), all of which showed stronger linkage signals when the score statistics accounted for epistasis. These novel score statistics should prove useful for linkage studies of other complex human diseases.