| Title: | On asymptotic distributions of several test statistics for familial relatedness in linear mixed models |
| Journal: | Statistics in Medicine |
| Published: | 9 May 2023 |
| Pubmed: | https://pubmed.ncbi.nlm.nih.gov/37345498/ |
| DOI: | https://doi.org/10.1002/sim.9762 |
Publication 7841
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Abstract
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.4 Authors
- Nicholas Devogel
- Paul L. Auer
- Regina Manansala
- Tao Wang
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