Department of Biostatistics, Epidemiology, and Informatics, The University of Pennsylvania, Philadelphia, Pennsylvania.
Department of Statistical Science, Cornell University, Ithaca, New York.
Biometrics. 2020 Sep;76(3):811-820. doi: 10.1111/biom.13204. Epub 2019 Dec 31.
In biomedical studies, testing for homogeneity between two groups, where one group is modeled by mixture models, is often of great interest. This paper considers the semiparametric exponential family mixture model proposed by Hong et al. (2017) and studies the score test for homogeneity under this model. The score test is nonregular in the sense that nuisance parameters disappear under the null hypothesis. To address this difficulty, we propose a modification of the score test, so that the resulting test enjoys the Wilks phenomenon. In finite samples, we show that with fixed nuisance parameters the score test is locally most powerful. In large samples, we establish the asymptotic power functions under two types of local alternative hypotheses. Our simulation studies illustrate that the proposed score test is powerful and computationally fast. We apply the proposed score test to an UK ovarian cancer DNA methylation data for identification of differentially methylated CpG sites.
在生物医学研究中，检验两组之间的同质性是非常重要的，其中一组由混合模型建模。本文考虑了 Hong 等人（2017）提出的半参数指数族混合模型，并研究了该模型下的同质性得分检验。由于在零假设下，多余参数消失，因此得分检验是非正则的。为了解决这个困难，我们提出了对得分检验的一种修正，使得得到的检验具有 Wilks 现象。在有限样本中，我们表明，对于固定的多余参数，得分检验在局部上是最有效的。在大样本中，我们在两种局部备择假设下建立了渐近功效函数。我们的模拟研究表明，所提出的得分检验是强大和计算快速的。我们将所提出的得分检验应用于英国卵巢癌 DNA 甲基化数据，以识别差异甲基化 CpG 位点。
