Mapping quantitative trait loci using both extremely discordant and concordant sib pairs: a unified approach for meta-analysis

Extremely discordant (ED) and concordant (EC) sib pairs are recommended by Risch and Zhang ( 1995, 1996 ) and Zhang and Risch ( 1996 ) for the detection of linkage on the basis of power analysis. They did not, however, include both discordant and concordant sib pairs simultaneously in the test statistic. We construct a new test statistic including both types of sib pairs. The size of the sample needed to identify the sib pairs and parents, who will be genotyped, is reduced substantially by including a hybrid of discordant and concordant sib pairs in the analysis. This mixed design also provides a common parameter that simplifies meta-analysis of sib pair linkage studies.     

Hypothesis testing for quantitative trait locus effects in both location and scale in genetic backcross studies

Testing the existence of a quantitative trait locus (QTL) effect is an important task in QTL mapping studies. Most studies concentrate on the case where the phenotype distributions of different QTL groups follow normal distributions with the same unknown variance. In this paper we make a more general assumption that the phenotype distributions come from a location-scale distribution family. We derive the limiting distribution of the likelihood ratio test (LRT) for the existence of the QTL effect in both location and scale in genetic backcross studies. We further identify an explicit representation for this limiting distribution. As a complement, we study the limiting distribution of the LRT and its explicit representation for the existence of the QTL effect in the location only. The asymptotic properties of the LRTs under a local alternative are also investigated. Simulation studies are used to evaluate the asymptotic results, and a real-data example is included for illustration.