Generalized fiducial methods for testing the homogeneity of a three-sample problem with a mixture structure

Recently, the likelihood ratio (LR) test was proposed to test the homogeneity of a three-sample model with a mixture structure. Because of the presence of the mixture structure, the null limiting distribution of the LR test has a complicated supremum form, which leads to challenges in determining p-values. In addition, the LR test cannot control type-I errors well under small to moderate sample size. In this paper, we propose seven generalized fiducial methods to test the homogeneity of the three-sample model. Via simulation studies, we find that our methods perform significantly better than the LR test method in controlling the type-I errors under small to moderate sample size, while they have comparable powers in most cases. A halibut data example is used to illustrate the proposed methods.

Two-sample test for correlated data under outcome-dependent sampling with an application to self-reported weight loss data

Standard methods for two-sample tests such as the t-test and Wilcoxon rank sum test may lead to incorrect type I errors when applied to longitudinal or clustered data. Recent alternatives of two-sample tests for clustered data often require certain assumptions on the correlation structure and/or noninformative cluster size. In this paper, based on a novel pseudolikelihood for correlated data, we propose a score test without knowledge of the correlation structure or assuming data missingness at random. The proposed score test can capture differences in the mean and variance between two groups simultaneously. We use projection theory to derive the limiting distribution of the test statistic, in which the covariance matrix can be empirically estimated. We conduct simulation studies to evaluate the proposed test and compare it with existing methods. To illustrate the usefulness proposed test, we use it to compare self-reported weight loss data in a friends' referral group, with the data from the Internet self-joining group.

PLMET: A Novel Pseudolikelihood-Based EM Test for Homogeneity in Generalilzed Exponential Tilt Mixture Models

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 non-differentially 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 non-identifiability 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 data set to identify differentially methylated sites between ovarian cancer subjects and normal subjects.

Case-Control Genome-wide Joint Association Study Using Semiparametric Empirical Model and Approximate Bayes Factor

We propose a semiparametric approach for the analysis of case-control genome-wide association study. Parametric components are used to model both the conditional distribution of the case status given the covariates and the distribution of genotype counts, whereas the distribution of the covariates are modeled nonparametrically. This yields a direct and joint modeling of the case status, covariates and genotype counts, and gives better understanding of the disease mechanism and results in more reliable conclusions. Side information, such as the disease prevalence, can be conveniently incorporated into the model by empirical likelihood approach and leads to more efficient estimates and powerful test in the detection of disease-associated SNPs. Profiling is used to eliminate a nuisance nonparametric component, and the resulting profile empirical likelihood estimates are shown to be consistent and asymptotically normal. For the hypothesis test on disease association, we apply the approximate Bayes factor (ABF) which is computationally simple and most desirable in genome-wide association studies where hundreds of thousands to a million genetic markers are tested. We treat the approximate Bayes factor as a hybrid Bayes factor which replaces the full data by the maximum likelihood estimates of the parameters of interest in the full model and derive it under a general setting. The deviation from Hardy-Weinberg Equilibrium (HWE) is also taken into account and the ABF for HWE using cases is shown to provide evidence of association between a disease and a genetic marker. Simulation studies and an application are further provided to illustrate the utility of the proposed methodology.