On stochastic processes for Quantitative Trait Locus mapping under selective genotyping

Charles-Elie Rabier (1, 2, 3)

1 University of Wisconsin-Madison
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 SAGA - Station d'Amélioration Génétique des Animaux

We consider the likelihood ratio test (LRT) process related to the test of the absence of QTL (a QTL denotes a quantitative trait locus, i.e. a gene with quantitative effect on a trait) on the interval [0,T] representing a chromosome. The originality is in the fact that we are under selective genotyping : only the individuals with extreme phenotypes are genotyped. We give the asymptotic distribution of this LRT process under the null hypothesis that there is no QTL on [0,T] and under local alternatives with a QTL at t* on [0,T]. We show that the LRT is asymptotically the square of a '' non-linear interpolated and normalized Gaussian process ''. We have an easy formula in order to compute the supremum of the square of this interpolated process. We prove that we have to genotype symetrically and that the threshold is exactly the same as in the situation where all the individuals are genotyped.

Mots clés: Gaussian process; Likelihood Ratio Test; Mixture models; Nuisance parameters present only under the alternative; QTL detection; selective genotyping

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Charles-Elie Rabier. On stochastic processes for Quantitative Trait Locus mapping under selective genotyping. Statistics, 2013, 49 (1), pp.19-34. ⟨10.1080/02331888.2013.858720⟩. ⟨hal-00675414v4⟩