Likelihood Ratio Test Process for Quantitative Trait Loci Detection

• Activity Number: 133
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: ENAR
• Author(s): Charles-Elie Rabier*+ and Jean-Marc Azaïs and Céline Delmas
• Companies: University of Wisconsin and Université Paul Sabatier and Station d'Amélioration Génétique des Animaux
• Keywords: QTL Detection ; Likelihood Ratio Test ; Mixture models ; Chi Square Process ; Gaussian process ; Interval Mapping

Abstract

We address the problem of detecting Quantitative Trait Loci, so-called QTLs (genes influencing a quantitative trait which is able to be measured) on a given chromosome (modelized by a segment [0,T]). Lander and Botstein (1989) proposed the "Interval Mapping" : with the help of genetic markers, we scan the chromosome, performing a Likelihood Ratio Test (LRT) of the absence of a QTL at every location on [0,T]. So, it leads to a LRT process. In presence of several QTLs, Jansen (1993) and Zeng (1994) proposed the ``Composite Interval Mapping" (CIM), which consists in combining Interval Mapping on two flanking markers and multiple regression analysis on other markers. This way, the QTLs effects of the QTLs located outside the interval tested, are removed due to multiple regression analysis. In our work, we give the asymptotic distribution of the LRT process under the general alternative that there exist m QTL on [0,T]. It allows us to propose to estimate the number of QTLs and their positions using the LASSO. Our method does not require the choice of cofactors which is the main drawback of CIM. Using simulated data, we show that our method gives better performances than CIM.