An analytic study of the power of popular quantitative-trait-locus mapping methods

Comparison of the power of various statistical methods is an important issue in quantitative-trait-locus mapping analysis. One effective means is to compare the noncentrality parameters of various test statistics. Such comparisons have been conducted in the literature either by using computer simulations or by comparing approximations to the noncentrality parameters. While useful, these approaches are not accurate by nature and could generate erroneous conclusions. For the popular sibpair design, I compare the noncentrality parameters of four popular statistical methods, i.e., a variance components method, a regression-based method, a score statistic and a "robustified" score statistic. Assuming that marker map is fully informative, I show analytically that noncentrality parameters for these methods are in the following order, from the largest to the smallest, the variance components method, the score statistic method, the regression method and the "robustified" score statistic. I also show by using an example that such ordering can fail for family structures other than sibpairs.