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Double truncation method for controlling local false discovery rate in case of spiky null

Author

Listed:
  • Shinjune Kim

    (Inha University Hospital)

  • Youngjae Oh

    (Korea National Statistics Office)

  • Johan Lim

    (Seoul National University)

  • DoHwan Park

    (University of Maryland)

  • Erin M. Green

    (University of Maryland)

  • Mark L. Ramos

    (National Institute of Health)

  • Jaesik Jeong

    (Chonnam National University
    Chonnam National University)

Abstract

Many multiple test procedures, which control the false discovery rate, have been developed to identify some cases (e.g. genes) showing statistically significant difference between two different groups. However, a common issue encountered in some practical data sets is the presence of highly spiky null distributions. Existing methods struggle to control type I error in such cases due to the “inflated false positives," but this problem has not been addressed in previous literature. Our team recently encountered this issue while analyzing SET4 gene deletion data and proposed modeling the null distribution using a scale mixture normal distribution. However, the use of this approach is limited due to strong assumptions on the spiky peak. In this paper, we present a novel multiple test procedure that can be applied to any type of spiky peak data, including situations with no spiky peak or with one or two spiky peaks. Our approach involves truncating the central statistics around 0, which primarily contribute to the null spike, as well as the two tails that may be contaminated by alternative distributions. We refer to this method as the “double truncation method." After applying double truncation, we estimate the null density using the doubly truncated maximum likelihood estimator. We demonstrate numerically that our proposed method effectively controls the false discovery rate at the desired level using simulated data. Furthermore, we apply our method to two real data sets, namely the SET protein data and peony data.

Suggested Citation

  • Shinjune Kim & Youngjae Oh & Johan Lim & DoHwan Park & Erin M. Green & Mark L. Ramos & Jaesik Jeong, 2025. "Double truncation method for controlling local false discovery rate in case of spiky null," Computational Statistics, Springer, vol. 40(2), pages 745-766, February.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:2:d:10.1007_s00180-024-01510-4
    DOI: 10.1007/s00180-024-01510-4
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    References listed on IDEAS

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    1. Iris Ivy M. Gauran & Junyong Park & Johan Lim & DoHwan Park & John Zylstra & Thomas Peterson & Maricel Kann & John L. Spouge, 2018. "Empirical null estimation using zero†inflated discrete mixture distributions and its application to protein domain data," Biometrics, The International Biometric Society, vol. 74(2), pages 458-471, June.
    2. Liang, Kun & Nettleton, Dan, 2010. "A Hidden Markov Model Approach to Testing Multiple Hypotheses on a Tree-Transformed Gene Ontology Graph," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1444-1454.
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    5. Efron, Bradley, 2004. "Large-Scale Simultaneous Hypothesis Testing: The Choice of a Null Hypothesis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 96-104, January.
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