Devogel N, Auer PL, Manansala R, Wang T. On asymptotic distributions of several test statistics for familial relatedness in linear mixed models.
Stat Med 2023;
42:2962-2981. [PMID:
37345498 DOI:
10.1002/sim.9762]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2021] [Revised: 03/16/2023] [Accepted: 04/26/2023] [Indexed: 06/23/2023]
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.
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