A Note on the Asymptotic Null Distribution of Likelihood-Ratio Tests for Multivariate Genetic Linkage in Variance Components Models

• Activity Number: 513
• Type: Contributed
• Date/Time: Thursday, August 7, 2008 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Summer S. Han*+ and Joseph T. Chang
• Companies: Yale University and Yale University
• Keywords: Likelihood-ratio test ; boundary condition ; mixing probability ; asymptotic null distribution ; multivariate genetic linkage

Abstract

This study concerns the asymptotic null distribution of likelihood ratio tests for detecting genetic linkage in multivariate variance component models. In a number of previous papers, the asymptotic null distribution has been stated to be a mixture of several chi-squared distributions, with binomial mixing probabilities. We performed simulations for null distributions of k-trait likelihood ratio tests (k=2, 3, 4, 5) and found that the distribution is not actually a mixture of chi-square distributions and the mixing proportions are not binomial, giving the highest probability to the case where all variance parameters are estimated nonzero. Correcting the null distribution gives more conservative critical values than previously stated, yielding P values up to 10 times larger. Geometric arguments are given to explain the results.