Hypothesis Tests for Point-Mass Mixture Data with Application to `Omics Data with Many Zero Values

摘要

Data composed of a continuous component plus a point-mass frequently arises in genomicnstudies. The distribution of this type of data is characterized by the proportion of observationsnin the point mass and the distribution of the continuous component. Standard statistical methodsnfocus on one of these effects at a time and can fail to detect differences between experimentalngroups. We propose a novel empirical likelihood ratio test (LRT) statistic for simultaneously test-ning the null hypothesis of no difference in point-mass proportions and no difference in means ofnthe continuous component. This study evaluates the performance of the empirical LRT and threenexisting point-mass mixture statistics: 1) Two-part statistic with a t-test for testing mean differ-nences (Two-part t), 2) Two-part statistic withWilcoxon test for testing mean differences (Two-partnW), and 3) parametric LRT.nOur investigations begin with an analysis of metabolomics data from Arabidopsis thaliana, whichncontains many metabolites with a large proportion of observed concentrations in a point-mass atnzero. All four point-mass mixture statistics identify more significant differences than standardnt-tests and Wilcoxon tests. The empirical LRT appears particularly effective. These findings mo-ntivate a large simulation study that assesses Type I and Type II error of the four test statisticsnwith various choices of null distribution. The parametric LRT is frequently the most powerfulntest, as long as the model assumptions are correct. As is common in ‘omics data, the Arabidop-nsis metabolites have widely varying concentration distributions. A single parametric distributionncannot effectively represent all of these distributions, and individually selecting the optimal para-nmetric distribution to use in the LRT for each metabolite is not practical. The empirical LRT,nwhich does not require parametric assumptions, provides an attractive alternative to parametricnand standard methods.