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

Author

Listed:
  • Taylor Sandra

    (University of California, Davis)

  • Pollard Katherine

    (University of California, San Francisco)

Abstract

Data composed of a continuous component plus a point-mass frequently arises in genomic studies. The distribution of this type of data is characterized by the proportion of observations in the point mass and the distribution of the continuous component. Standard statistical methods focus on one of these effects at a time and can fail to detect differences between experimental groups. We propose a novel empirical likelihood ratio test (LRT) statistic for simultaneously testing the null hypothesis of no difference in point-mass proportions and no difference in means of the continuous component. This study evaluates the performance of the empirical LRT and three existing point-mass mixture statistics: 1) Two-part statistic with a t-test for testing mean differences (Two-part t), 2) Two-part statistic with Wilcoxon test for testing mean differences (Two-part W), and 3) parametric LRT.Our investigations begin with an analysis of metabolomics data from Arabidopsis thaliana, which contains many metabolites with a large proportion of observed concentrations in a point-mass at zero. All four point-mass mixture statistics identify more significant differences than standard t-tests and Wilcoxon tests. The empirical LRT appears particularly effective. These findings motivate a large simulation study that assesses Type I and Type II error of the four test statistics with various choices of null distribution. The parametric LRT is frequently the most powerful test, as long as the model assumptions are correct. As is common in `omics data, the Arabidopsis metabolites have widely varying concentration distributions. A single parametric distribution cannot effectively represent all of these distributions, and individually selecting the optimal parametric distribution to use in the LRT for each metabolite is not practical. The empirical LRT, which does not require parametric assumptions, provides an attractive alternative to parametric and standard methods.

Suggested Citation

  • Taylor Sandra & Pollard Katherine, 2009. "Hypothesis Tests for Point-Mass Mixture Data with Application to `Omics Data with Many Zero Values," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-43, February.
    • Handle: RePEc:bpj:sagmbi:v:8:y:2009:i:1:n:8
    DOI: 10.2202/1544-6115.1425
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    References listed on IDEAS

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    1. Jing, Bing-Yi, 1995. "Two-sample empirical likelihood method," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 315-319, September.
    2. Chen, Song Xi & Qin, Jing, 2003. "Empirical likelihood-based confidence intervals for data with possible zero observations," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 29-37, October.
    3. Zhou Xiao-Hua & Wanzhu Tu, 1999. "Comparison of Several Independent Population Means When Their Samples Contain Log-Normal and Possibly Zero Observations," Biometrics, The International Biometric Society, vol. 55(2), pages 645-651, June.
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    Cited by:

    1. Taylor Sandra L. & Kim Kyoungmi & Leiserowitz Gary S., 2013. "Accounting for undetected compounds in statistical analyses of mass spectrometry ‘omic studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(6), pages 703-722, December.
    2. Wang, Chunlin & Marriott, Paul & Li, Pengfei, 2018. "Semiparametric inference on the means of multiple nonnegative distributions with excess zero observations," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 182-197.
    3. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2014. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 89-121.
    4. Wang, Chunlin & Marriott, Paul & Li, Pengfei, 2017. "Testing homogeneity for multiple nonnegative distributions with excess zero observations," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 146-157.

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