Chi-square processes for gene mapping in a population with family structure

Charles-Elie Rabier (), Jean-Marc Azaïs, Jean-Michel Elsen and Céline Delmas
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Charles-Elie Rabier: MIAT, Université de Toulouse, INRA
Jean-Marc Azaïs: Université Paul Sabatier
Jean-Michel Elsen: GenPhyse, Université de Toulouse, INRA
Céline Delmas: MIAT, Université de Toulouse, INRA

Statistical Papers, 2019, vol. 60, issue 1, No 13, 239-271

Abstract: Abstract Detecting a quantitative trait locus, so-called QTL (a gene influencing a quantitative trait which is able to be measured), on a given chromosome is a major problem in Genetics. We study a population structured in families and we assume that the QTL location is the same for all the families. We consider the likelihood ratio test (LRT) process related to the test of the absence of QTL on the interval [0, T] representing a chromosome. We give the asymptotic distribution of the LRT process under the null hypothesis that there is no QTL in any families and under local alternative with a QTL at $$t^{\star }\in [0, T]$$ t ⋆ ∈ [ 0 , T ] in at least one family. We show that the LRT is asymptotically the supremum of the sum of the square of independent interpolated Gaussian processes. The number of processes corresponds to the number of families. We propose several new methods to compute critical values for QTL detection. Since all these methods rely on asymptotic results, the validity of the asymptotic assumption is checked using simulated data. Finally we show how to optimize the QTL detecting process.

Keywords: Chi-square process; Gaussian process; Likelihood ratio test; Mixture models; QTL detection; MCQMC; 62M86; 65C05; 62P10 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s00362-016-0835-y

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