Permutation-based variance component test in generalized linear mixed model with application to multilocus genetic association study.

Ping Zeng,Feng Chen,Yang Zhao,Hongliang Li,Ting Wang

doi:10.1186/s12874-015-0030-1

Ping Zeng, Feng Chen + Show 3 more

Open Access

https://doi.org/10.1186/s12874-015-0030-1

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Abstract

BackgroundIn many medical studies the likelihood ratio test (LRT) has been widely applied to examine whether the random effects variance component is zero within the mixed effects models framework; whereas little work about likelihood-ratio based variance component test has been done in the generalized linear mixed models (GLMM), where the response is discrete and the log-likelihood cannot be computed exactly. Before applying the LRT for variance component in GLMM, several difficulties need to be overcome, including the computation of the log-likelihood, the parameter estimation and the derivation of the null distribution for the LRT statistic.MethodsTo overcome these problems, in this paper we make use of the penalized quasi-likelihood algorithm and calculate the LRT statistic based on the resulting working response and the quasi-likelihood. The permutation procedure is used to obtain the null distribution of the LRT statistic. We evaluate the permutation-based LRT via simulations and compare it with the score-based variance component test and the tests based on the mixture of chi-square distributions. Finally we apply the permutation-based LRT to multilocus association analysis in the case–control study, where the problem can be investigated under the framework of logistic mixed effects model.ResultsThe simulations show that the permutation-based LRT can effectively control the type I error rate, while the score test is sometimes slightly conservative and the tests based on mixtures cannot maintain the type I error rate. Our studies also show that the permutation-based LRT has higher power than these existing tests and still maintains a reasonably high power even when the random effects do not follow a normal distribution. The application to GAW17 data also demonstrates that the proposed LRT has a higher probability to identify the association signals than the score test and the tests based on mixtures.ConclusionsIn the present paper the permutation-based LRT was developed for variance component in GLMM. The LRT outperforms existing tests and has a reasonably higher power under various scenarios; additionally, it is conceptually simple and easy to implement.

Highlights

In many medical studies the likelihood ratio test (LRT) has been widely applied to examine whether the random effects variance component is zero within the mixed effects models framework; whereas little work about likelihood-ratio based variance component test has been done in the generalized linear mixed models (GLMM), where the response is discrete and the log-likelihood cannot be computed exactly
The main difficulties of using LRT in GLMM are the computation of the loglikelihood function for the alternative model and the derivation of the null distribution of the likelihood ratio statistic
The simulations show that the score test can control the type I error rate but is sometimes conservative, especially for small sample sizes; the similar result has been observed by Wu, et al [31] and Li, et al [46] under the context of multilocus association studies

Summary

Introduction

In many medical studies the likelihood ratio test (LRT) has been widely applied to examine whether the random effects variance component is zero within the mixed effects models framework; whereas little work about likelihood-ratio based variance component test has been done in the generalized linear mixed models (GLMM), where the response is discrete and the log-likelihood cannot be computed exactly. To test a parametric null model against a nonparametric alternative in the penalized spline regression, Claeskens [7] first constructed a mixed effects model so that the hypothesis testing was reduced to the problem that whether the variance component of random effects was zero, and performed a restricted likelihood ratio lackof-fit test. The variance component test is nonstandard in the sense that under the null the variance component is on the boundary of the parameter space In this situation it is not easy to obtain the null distribution of the likelihood ratio statistic.

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