Assessing accuracy in linkage analysis by means of confidence regions

When statistical linkage to a certain chromosomal region has been found, it is of interest to develop methods quantifying the accuracy with which the disease locus can be mapped. In this paper, we investigate the performance of three different types of confidence regions, with asymptotically correct coverage probability as the number of pedigrees grows. Our setup is that of a saturated map of marker data. We allow for arbitrary combinations of pedigree structures, and treat various kinds of genetic models (e.g. binary and quantitative phenotypes) in a unified way. The linkage scores are weighted sums of the individual family scores, with NPL and lod scores as special cases. We show that the expected length of the confidence region is inversely proportional to the slope-to-noise ratio, or equivalently, inversely proportional to the product of the square of the noncentrality parameter and a certain normalized slope-to-noise ratio. Our investigations reveal that maximal expected linkage scores can be quite different from estimation-based performance criteria based on expected length of confidence regions. The main reason is that there is no simple relationship between peak height and peak slope of the mean linkage score. One application of our results is planning of linkage studies: given a certain genetic model, we can approximate the number of pedigrees needed to obtain a confidence region with given coverage probability and expected length.