QTL Mapping under Acertainment

The goal of genetic mapping is to locate genes that aect particular traits such as blood pressure, or disease status, either in model organisms or in humans. One important step in gene mapping is the use of statistical methods to identify interesting regions of the genome. Linkage analysis is one way to map trait genes by the analysis of the correlation between trait values and marker genotypes along the genome. In humans, linkage analysis uses pedigree data to detect the cosegregation of the trait and the shared genetic material between relatives. Quantitative trait loci (QTL) are genes that control traits taking on continuous values such as blood pressure and cholesterol level, which may have important implications about the etiology of certain diseases. Although the basic theory associated with linkage methods for QTL mapping presupposes that the pedigrees are randomly sampled, in practice they are often ascertained through one or more family members having particular trait values. In this paper, QTL mapping via ascertained sibships is discussed. Three dierent sampling schemes are compared. We adopt a standard variance component model which models the phenotype Y by variance components arising from the trait genes, polygenic eects, environmental eects, etc (Almsay and Blangero (1998)). A particular parametrization which leads to the orthogonality of the \segregation " parameters and the \linkage " parameters is used (Tang and Siegmund (2001)). This \orthogonality " property allows us to compute score statistics, noncentrality parameter and Fisher information matrices explicitly and also allows us to prove the robustness of the score statistic