Zeng Ping, Zhao Yang, Li Hongliang, Wang Ting, Chen Feng
Department of Epidemiology and Biostatistics, School of Public Health, Nanjing Medical University, Nanjing, 211166, , Jiangsu, People's Republic of China.
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.
BMC Med Res Methodol. 2015 Apr 22;15:37. doi: 10.1186/s12874-015-0030-1.
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.
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.
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.
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.
在许多医学研究中，似然比检验（LRT）已被广泛应用于在混合效应模型框架内检验随机效应方差分量是否为零；而在广义线性混合模型（GLMM）中，关于基于似然比的方差分量检验的工作做得很少，在GLMM中响应是离散的且对数似然不能精确计算。在GLMM中应用LRT进行方差分量检验之前，需要克服几个困难，包括对数似然的计算、参数估计以及LRT统计量的零分布的推导。
为了克服这些问题，在本文中我们利用惩罚拟似然算法，并基于所得的工作响应和拟似然计算LRT统计量。置换程序用于获得LRT统计量的零分布。我们通过模拟评估基于置换的LRT，并将其与基于得分的方差分量检验以及基于卡方分布混合的检验进行比较。最后，我们将基于置换的LRT应用于病例对照研究中的多位点关联分析，在该研究中可以在逻辑混合效应模型框架下研究该问题。
模拟表明，基于置换的LRT可以有效地控制I型错误率，而得分检验有时略显保守，基于混合的检验不能维持I型错误率。我们的研究还表明，基于置换的LRT比这些现有检验具有更高的检验效能，并且即使随机效应不服从正态分布时仍能保持相当高的检验效能。对GAW17数据的应用也表明，所提出的LRT比得分检验和基于混合的检验有更高的概率识别关联信号。
在本文中，为GLMM中的方差分量开发了基于置换的LRT。该LRT优于现有检验，并且在各种情况下具有相当高的检验效能；此外，它在概念上简单且易于实现。
