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. 2015 Jul 15;31(14):2303-9.
doi: 10.1093/bioinformatics/btv104. Epub 2015 Mar 2.

Estimating the proportion of true null hypotheses when the statistics are discrete

Isaac Dialsingh  1 , Stefanie R Austin  2 , Naomi S Altman  2
Affiliations

Estimating the proportion of true null hypotheses when the statistics are discrete

Isaac Dialsingh et al. Bioinformatics. .

Abstract

Motivation: In high-dimensional testing problems π0, the proportion of null hypotheses that are true is an important parameter. For discrete test statistics, the P values come from a discrete distribution with finite support and the null distribution may depend on an ancillary statistic such as a table margin that varies among the test statistics. Methods for estimating π0 developed for continuous test statistics, which depend on a uniform or identical null distribution of P values, may not perform well when applied to discrete testing problems.

Results: This article introduces a number of π0 estimators, the regression and 'T' methods that perform well with discrete test statistics and also assesses how well methods developed for or adapted from continuous tests perform with discrete tests. We demonstrate the usefulness of these estimators in the analysis of high-throughput biological RNA-seq and single-nucleotide polymorphism data.

Availability and implementation: implemented in R.

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Figures

Fig. 1.
Fig. 1.
P values from discrete and continuous tests with π0=0.80. a) P-values for continuous tests b) P-values for discrete tests
Fig. 2.
Fig. 2.
P values from real data. (a) Raw P-values from the primate liver RNAseq study with biological replication. (b) Raw P-values from the bovine iron SNP study
Fig. 3.
Fig. 3.
Plots of ϕ^jt versus ϕ0jt for one random sample of RNA-2, m = 10 000, data for two different π0 values. (a) π0 = 0.3. (b) π0 = 0.8
Fig. 4.
Fig. 4.
The 25th percentile of π^0 for different estimators for the RNA-seq simulations. (a) π0 estimates, RNA-1, m = 10 000. (b) π0 estimates, RNA-2, m = 10 000
Fig. 5.
Fig. 5.
The 25th percentile of π^0 for different estimators for the SNP simulations. (a) π0 estimates for SNP study with 50 controls 50 treated, m = 10 000. (b) π0 estimates for SNP study with 80 controls 20 treated, m = 10 000
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