Empirical null estimation using zero-inflated discrete mixture distributions and its application to protein domain data

Iris Ivy M. Gauran, Junyong Park*, Johan Lim, Dohwan Park, John Zylstra, Thomas Peterson, Maricel Kann, John L. Spouge

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


In recent mutation studies, analyses based on protein domain positions are gaining popularity over gene-centric approaches since the latter have limitations in considering the functional context that the position of the mutation provides. This presents a large-scale simultaneous inference problem, with hundreds of hypothesis tests to consider at the same time. This article aims to select significant mutation counts while controlling a given level of Type I error via False Discovery Rate (FDR) procedures. One main assumption is that the mutation counts follow a zero-inflated model in order to account for the true zeros in the count model and the excess zeros. The class of models considered is the Zero-inflated Generalized Poisson (ZIGP) distribution. Furthermore, we assumed that there exists a cut-off value such that smaller counts than this value are generated from the null distribution. We present several data-dependent methods to determine the cut-off value. We also consider a two-stage procedure based on screening process so that the number of mutations exceeding a certain value should be considered as significant mutations. Simulated and protein domain data sets are used to illustrate this procedure in estimation of the empirical null using a mixture of discrete distributions. Overall, while maintaining control of the FDR, the proposed two-stage testing procedure has superior empirical power.

Original languageEnglish (US)
Pages (from-to)458-471
Number of pages14
Issue number2
StatePublished - Jun 2018

Bibliographical note

Funding Information:
This research was supported in part by the Intramural Research Program of the NIH, National Library of Medicine.

Publisher Copyright:
© 2017 The Authors. Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society


  • Local false discovery rate
  • Protein domain
  • Zero-in ated generalized poisson

ASJC Scopus subject areas

  • Statistics and Probability
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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