Likelihood Ratio Testing for Admixture Models with Application to Genetic Linkage Analysis
Article first published online: 8 MAR 2011
© 2011, The International Biometric Society
Volume 67, Issue 4, pages 1249–1259, December 2011
How to Cite
Di, C.-Z. and Liang, K.-Y. (2011), Likelihood Ratio Testing for Admixture Models with Application to Genetic Linkage Analysis. Biometrics, 67: 1249–1259. doi: 10.1111/j.1541-0420.2011.01574.x
- Issue published online: 14 DEC 2011
- Article first published online: 8 MAR 2011
- Received March 2010. Revised December 2010. Accepted December 2010.
- Admixture models;
- Genetic linkage analysis;
- Likelihood ratio test
Summary 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 conventional χ2 distribution. 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 Sinica 16, 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.