Likelihood ratio test process for quantitative trait locus detection

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 observation is the trait and the composition of the genome at some locations called ‘markers’. 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 some Gaussian process. We give a description of this process as an ‘non-linear interpolated and normalized process’. We propose a simple method to calculate the maximum of the LRT process using only statistics on markers and their ratio. This gives a new method to calculate thresholds for the QTL detection.

[1]  B. Mangin,et al.  Approximate thresholds of interval mapping tests for QTL detection. , 1994, Genetics.

[2]  E. Lander,et al.  Mapping mendelian factors underlying quantitative traits using RFLP linkage maps. , 1989, Genetics.

[3]  E. Gassiat.  Likelihood ratio inequalities with applications to various mixtures , 2002 .

[4]  P. Sen,et al.  On the asymptotic performance of the log likelihood ratio statistic for the mixture model and related results , 1984 .

[5]  J. B. S. Haldane,et al.  The probable errors of calculated linkage values, and the most accurate method of determining gametic from certain zygotic series , 1919, Journal of Genetics.

[6]  Susan McCouch,et al.  RFLP mapping of isozymes, RAPD and QTLs for grain shape, brown planthopper resistance in a doubled haploid rice population , 2004, Molecular Breeding.

[7]  Asymptotic Distribution of the Maximum Likelihood Ratio Test for Gene Detection , 1998 .

[8]  L. L. Cam,et al.  Asymptotic Methods In Statistical Decision Theory , 1986 .

[9]  E. Gassiat,et al.  Asymptotic distribution and local power of the log-likelihood ratio test for mixtures: bounded and unbounded cases , 2006 .

[10]  Rongling Wu,et al.  Score Statistics for Mapping Quantitative Trait Loci , 2009, Statistical applications in genetics and molecular biology.

[11]  Xianggui Qu,et al.  The Statistics of Gene Mapping , 2008, Technometrics.

[12]  Un test asymptotique pour la detection de gènes quantitatifs , 2002 .

[13]  Rongling Wu,et al.  Comprar Statistical Genetics of Quantitative Traits · Linkage, Maps and QTL | Casella, George | 9780387203348 | Springer , 2007 .

[14]  Jean-Marc Azaïs,et al.  The likelihood ratio test for general mixture models with or without structural parameter , 2009 .

[15]  J. Azaïs,et al.  Level Sets and Extrema of Random Processes and Fields , 2009 .

[16]  R. Davies.  Hypothesis testing when a nuisance parameter is present only under the alternative , 1977 .

[17]  B. Mangin,et al.  Comparing power of different methods for QTL detection. , 1995, Biometrics.

[18]  THE LIKELIHOOD RATIO TEST FOR GENERAL MIXTURE MODELS WITH POSSIBLY STRUCTURAL PARAMETER , 2008 .

[19]  Charles-Elie Rabier.  Techniques statistiques pour la détection de gènes à effets quantitatifs , 2010 .

[20]  Michael Harpham.  December , 1855, The Hospital.

[21]  R. Bass,et al.  Review: P. Billingsley, Convergence of probability measures , 1971 .

[22]  R. Wu,et al.  A Statistical Model for Genetic Mapping of Viral Infection by Integrating Epidemiological Behavior , 2009, Statistical applications in genetics and molecular biology.

[23]  A. Genz.  Numerical Computation of Multivariate Normal Probabilities , 1992 .

[24]  D. Siegmund.  Sequential Analysis: Tests and Confidence Intervals , 1985 .

[25]  A. V. D. Vaart,et al.  Asymptotic Statistics: Frontmatter , 1998 .

[26]  E Feingold,et al.  Gaussian models for genetic linkage analysis using complete high-resolution maps of identity by descent. , 1993, American journal of human genetics.