Strategies for conditional two-locus nonparametric linkage analysis

In this article we deal with two-locus nonparametric linkage (NPL) analysis, mainly in the context of conditional analysis. This means that one incorporates single-locus analysis information through conditioning when performing a two-locus analysis. Here we describe different strategies for using this approach. Cox et al. [Nat Genet 1999;21:213-215] implemented this as follows: (i) Calculate the one-locus NPL process over the included genome region(s). (ii) Weight the individual pedigree NPL scores using a weighting function depending on the NPL scores for the corresponding pedigrees at speci fi c conditioning loci. We generalize this by conditioning with respect to the inheritance vector rather than the NPL score and by separating between the case of known (prede fi ned) and unknown (estimated) conditioning loci. In the latter case we choose conditioning locus, or loci, according to prede fi ned criteria. The most general approach results in a random number of selected loci, depending on the results from the previous one-locus analysis. Major topics in this article include discussions on optimal score functions with respect to the noncentrality parameter (NCP), and how to calculate adequate p values and perform power calculations. We also discuss issues related to multiple tests which arise from the two-step procedure with several conditioning loci as well as from the genome-wide tests.