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

Author

Listed:
  • Charles-Elie Rabier

    (MIAT, Université de Toulouse, INRA
    Université Paul Sabatier)

  • Jean-Marc Azaïs

    (Université Paul Sabatier)

  • Jean-Michel Elsen

    (GenPhyse, Université de Toulouse, INRA)

  • Céline Delmas

    (MIAT, Université de Toulouse, INRA)

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.

Suggested Citation

  • Charles-Elie Rabier & Jean-Marc Azaïs & Jean-Michel Elsen & Céline Delmas, 2019. "Chi-square processes for gene mapping in a population with family structure," Statistical Papers, Springer, vol. 60(1), pages 239-271, February.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:1:d:10.1007_s00362-016-0835-y
    DOI: 10.1007/s00362-016-0835-y
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    References listed on IDEAS

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    1. Charles-Elie Rabier & Alan Genz, 2014. "The Supremum of Chi-Square Processes," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 715-729, September.
    2. Charles-Elie Rabier, 2014. "On quantitative trait locus mapping with an interference phenomenon," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 311-329, June.
    3. Vanessa Didelez & Iris Pigeot & Patricia Walter, 2006. "Modifications of the Bonferroni-Holm procedure for a multi-way ANOVA," Statistical Papers, Springer, vol. 47(2), pages 181-209, March.
    4. Chang Myron N & Wu Rongling & Wu Samuel S & Casella George, 2009. "Score Statistics for Mapping Quantitative Trait Loci," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-37, February.
    5. Estrella, Arturo, 2003. "Critical Values And P Values Of Bessel Process Distributions: Computation And Application To Structural Break Tests," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1128-1143, December.
    6. Byoung Jung & Myoungshic Jhun & Seuck Song, 2007. "A new random permutation test in ANOVA models," Statistical Papers, Springer, vol. 48(1), pages 47-62, January.
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