Estimating the proportion of true null hypotheses using the pattern of observed p-values

Tiejun TONG*, Zeny Feng, Julia S. Hilton, Hongyu Zhao

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

7 Citations (Scopus)


Estimating the proportion of true null hypotheses, π0, has attracted much attention in the recent statistical literature. Besides its apparent relevance for a set of specific scientific hypotheses, an accurate estimate of this parameter is key for many multiple testing procedures. Most existing methods for estimating π0 in the literature are motivated from the independence assumption of test statistics, which is often not true in reality. Simulations indicate that most existing estimators in the presence of the dependence among test statistics can be poor, mainly due to the increase of variation in these estimators. In this paper, we propose several data-driven methods for estimating π0 by incorporating the distribution pattern of the observed p-values as a practical approach to address potential dependence among test statistics. Specifically, we use a linear fit to give a data-driven estimate for the proportion of true-null p-values in (λ, 1] over the whole range [0, 1] instead of using the expected proportion at 1-λ. We find that the proposed estimators may substantially decrease the variance of the estimated true null proportion and thus improve the overall performance.

Original languageEnglish
Pages (from-to)1949-1964
Number of pages16
JournalJournal of Applied Statistics
Issue number9
Publication statusPublished - Sept 2013

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • gene expression data
  • multiple testing
  • p-value
  • proportion of true null hypotheses


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