Likelihood Ratio Test for Multi-Sample Mixture Model and Its Application to Genetic Imprinting

Abstract

Genomic imprinting is a known aspect of the etiology of many diseases. The imprinting phenomenon depicts differential expression levels of the allele depending on its parental origin. When the parental origin is unknown, the expression level has a finite normal mixture distribution. In such applications, a random sample of expression levels consists of three subsamples according to the number of minor alleles an individual possesses, of which one is the mixture and the other two are homogeneous. This understanding leads to a likelihood ratio test (LRT) for the presence of imprinting. Because of the nonregularity of the finite mixture model, the classical asymptotic conclusions on likelihood-based inference are not applicable. We show that the maximum likelihood estimator of the mixing distribution remains consistent. More interestingly, thanks to the homogeneous subsamples, the LRT statistic has an elegant and rather distinct 0.5χ²₁ + 0.5χ²₂ null limiting distribution. Simulation studies confirm that the limiting distribution provides precise approximations of the finite sample distributions under various parameter settings. The LRT is applied to expression data. Our analyses provide evidence for imprinting for a number of isoform expressions.

• EM-algorithm
• EM-test
• Imprinting
• Likelihood ratio test
• Normal mixture model
• Quantitative trait
• SNP

Additional information

Notes on contributors

Shaoting Li

Shaoting Li, Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024 China (E-mail: [email protected]).

Jiahua Chen

Jiahua Chen, Department of Statistics, University of British Columbia, Vancouver, V6T 1Z2 Canada (E-mail: [email protected]).

Jianhua Guo

Jianhua Guo, Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China (E-mail: [email protected]).

Bing-Yi Jing

Bing-Yi Jing, Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China (E-mail: [email protected]).

Shui-Ying Tsang

Shui-Ying Tsang (E-mail: [email protected])

Hong Xue

Hong Xue (E-mail: [email protected]), Division of Life Science, Applied Genomics Center and Center for Statistical Science, Hong Kong University of Science and Technology, Hong Kong, China.