On asymptotic distributions of several test statistics for familial relatedness in linear mixed models. Stat Med 2023 Jul 30;42(17):2962-2981
Date
06/22/2023Pubmed ID
37345498DOI
10.1002/sim.9762Scopus ID
2-s2.0-85158096218 (requires institutional sign-in at Scopus site) 1 CitationAbstract
In this study, the asymptotic distributions of the likelihood ratio test (LRT), the restricted likelihood ratio test (RLRT), the F and the sequence kernel association test (SKAT) statistics for testing an additive effect of the expected familial relatedness (FR) in a linear mixed model are examined based on an eigenvalue approach. First, the covariance structure for modeling the FR effect in a LMM is presented. Then, the multiplicity of eigenvalues for the log-likelihood and restricted log-likelihood is established under a replicate family setting and extended to a more general replicate family setting (GRFS) as well. After that, the asymptotic null distributions of LRT, RLRT, F and SKAT statistics under GRFS are derived. The asymptotic null distribution of SKAT for testing genetic rare variants is also constructed. In addition, a simple formula for sample size calculation is provided based on the restricted maximum likelihood estimate of the effect size for the expected FR. Finally, a power comparison of these test statistics on hypothesis test of the expected FR effect is made via simulation. The four test statistics are also applied to a data set from the UK Biobank.
Author List
Devogel N, Auer PL, Manansala R, Wang TAuthors
Paul L. Auer PhD Professor in the Data Science Institute department at Medical College of WisconsinTao Wang PhD Associate Professor in the Data Science Institute department at Medical College of Wisconsin
MESH terms used to index this publication - Major topics in bold
Computer SimulationHumans
Likelihood Functions
Linear Models
Models, Genetic
