Detecting two-locus gene-gene effects using monotonisation of the penetrance matrix

As more genetic loci are genotyped simultaneously and as the interest in effects of combinations of loci increases, the need for more powerful analysis methods is increased. In the present paper we present a method aimed at increasing the power of likelihood ratio tests for case-control studies investigating possible two-locus effects. The method is based on the notion that the expected effect pattern of one locus, as well as the expected pattern of a penetrance matrix representing the effect of two loci, is a monotone one. By using an algorithm for making the estimated penetrance matrix monotone, the alternative hypothesis is restricted to monotone penetrance matrices only. The evaluation of the likelihood ratio tests for several underlying monotone models shows that the power is substantially increased by using a monotone alternative as compared to when an unrestricted alternative is used.