Likelihood ratio testing for admixture models with application to genetic linkage analysis

Chong Zhi Di, Kung Yee Liang

Research output: Contribution to journalArticle

Abstract

We consider likelihood ratio tests (LRT) and their modifications for homogeneity in admixture models. The admixture model is a two-component mixture model, where one component is indexed by an unknown parameter while the parameter value for the other component is known. This model is widely used in genetic linkage analysis under heterogeneity in which the kernel distribution is binomial. For such models, it is long recognized that testing for homogeneity is nonstandard, and the LRT statistic does not converge to a conventionalχ 2distribution. In this article, we investigate the asymptotic behavior of the LRT for general admixture models and show that its limiting distribution is equivalent to the supremum of a squared Gaussian process. We also discuss the connection and comparison between LRT and alternative approaches such as modifications of LRT and score tests, including the modified LRT (Fu, Chen, and Kalbfleisch, 2006,Statistica Sinica16, 805-823). The LRT is an omnibus test that is powerful to detect general alternative hypotheses. In contrast, alternative approaches may be slightly more powerful to detect certain type of alternatives, but much less powerful for others. Our results are illustrated by simulation studies and an application to a genetic linkage study of schizophrenia.

Original languageEnglish (US)
Pages (from-to)1249-1259
Number of pages11
JournalBiometrics
Volume67
Issue number4
DOIs
StatePublished - Dec 2011
Externally publishedYes

Fingerprint

Linkage Analysis
Genetic Linkage
Likelihood Ratio
Likelihood Ratio Test
linkage (genetics)
Binomial Distribution
Testing
Schizophrenia
Alternatives
testing
Homogeneity
Modified Likelihood
Model
Omnibus Test
Likelihood Ratio Test Statistic
Score Test
Component Model
Limiting Distribution
Supremum
Mixture Model

Keywords

  • Admixture models
  • Genetic linkage analysis
  • Likelihood ratio test

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability
  • Agricultural and Biological Sciences(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Medicine(all)

Cite this

Likelihood ratio testing for admixture models with application to genetic linkage analysis. / Di, Chong Zhi; Liang, Kung Yee.

In: Biometrics, Vol. 67, No. 4, 12.2011, p. 1249-1259.

Research output: Contribution to journalArticle

Di, Chong Zhi ; Liang, Kung Yee. / Likelihood ratio testing for admixture models with application to genetic linkage analysis. In: Biometrics. 2011 ; Vol. 67, No. 4. pp. 1249-1259.
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