PLEMT: A Novel Pseudolikelihood-Based EM Test for Homogeneity in Generalized Exponential Tilt Mixture Models

• Published in: Journal of the American Statistical Association Vol. 112; no. 520; pp. 1393 - 1404
• Main Authors: Hong, Chuan, Ning, Yang, Wang, Shuang, Wu, Hao, Carroll, Raymond J., Chen, Yong
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 02.10.2017; Taylor & Francis Group,LLC; Taylor & Francis Ltd
• Subjects: Applications and Case Studies; Asymptotics; Between-subjects design; Cancer; Chi-square test; Computer simulation; Conditional likelihood; data collection; Deoxyribonucleic acid; DNA; DNA methylation; Epigenetics; Nonregular problem; Ovarian cancer; ovarian neoplasms; Penalized likelihood; Penalty function; Permutations; Power; Regression analysis; Semiparametric mixture model; Simulation; Statistical methods; statistical models; Statistical tests; Statistics; variance
• ISSN: 0162-1459; 1537-274X; 1537-274X
• DOI: 10.1080/01621459.2017.1280405

Motivated by analyses of DNA methylation data, we propose a semiparametric mixture model, namely, the generalized exponential tilt mixture model, to account for heterogeneity between differentially methylated and nondifferentially methylated subjects in the cancer group, and capture the differences in higher order moments (e.g., mean and variance) between subjects in cancer and normal groups. A pairwise pseudolikelihood is constructed to eliminate the unknown nuisance function. To circumvent boundary and nonidentifiability problems as in parametric mixture models, we modify the pseudolikelihood by adding a penalty function. In addition, the test with simple asymptotic distribution has computational advantages compared with permutation-based test for high-dimensional genetic or epigenetic data. We propose a pseudolikelihood-based expectation-maximization test, and show the proposed test follows a simple chi-squared limiting distribution. Simulation studies show that the proposed test controls Type I errors well and has better power compared to several current tests. In particular, the proposed test outperforms the commonly used tests under all simulation settings considered, especially when there are variance differences between two groups. The proposed test is applied to a real dataset to identify differentially methylated sites between ovarian cancer subjects and normal subjects. Supplementary materials for this article are available online.