title: Permutation-based variance component test in generalized linear mixed model with application to multilocus genetic association study.
abstract: BACKGROUND
  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. 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.
  
  
  METHODS
  To 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.
  
  
  RESULTS
  The 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.
  
  
  CONCLUSIONS
  In 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.
authors.affiliation: Department of Epidemiology and Biostatistics, School of Public Health, Nanjing Medical University, Nanjing, 211166, , Jiangsu, People's Republic of China. zpstat@xzmc.edu.cn.|Department of Epidemiology and Biostatistics, Center of Medical Statistics and Data Analysis, School of Public Health, Xuzhou Medical College, Xuzhou, 221004, Jiangsu, People's Republic of China. zpstat@xzmc.edu.cn.
authors.forename: Ping
authors.initials: P
authors.lastname: Zeng
authors.affiliation: Department of Epidemiology and Biostatistics, School of Public Health, Nanjing Medical University, Nanjing, 211166, , Jiangsu, People's Republic of China. zhaoyang@njmu.edu.cn.
authors.forename: Yang
authors.initials: Y
authors.lastname: Zhao
authors.affiliation: Center for Disease Control and Prevention of Pudong New Area, Pudong New Area, Shanghai, 200136, People's Republic of China. lhl_001@126.com.
authors.forename: Hongliang
authors.initials: H
authors.lastname: Li
authors.affiliation: Department of Epidemiology and Biostatistics, Center of Medical Statistics and Data Analysis, School of Public Health, Xuzhou Medical College, Xuzhou, 221004, Jiangsu, People's Republic of China. wangtgw@163.com.
authors.forename: Ting
authors.initials: T
authors.lastname: Wang
authors.affiliation: Department of Epidemiology and Biostatistics, School of Public Health, Nanjing Medical University, Nanjing, 211166, , Jiangsu, People's Republic of China. fengchen@njmu.edu.cn.
authors.forename: Feng
authors.initials: F
authors.lastname: Chen
mesh_terms: D000465:Algorithms; D001699:Biometry / Q000379:methods; D016009:Chi-Square Distribution; D003198:Computer Simulation; D056726:Genetic Association Studies / Q000379:methods*; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D015203:Reproducibility of Results