Efficient estimation of the number of false positives in high-throughput screening

Abstract

This paper develops new methods to handle false positives in High-Throughput Screening experiments. The setting is very highly multiple testing problems where testing is done at extreme significance levels and with low degrees of freedom, and where the true null distribution may differ from the theoretical one. We answer the question 'How many of the positive test results are false?' by showing that the conditional distribution of the number of false positives, given that there is in all r positives, approximately has a binomial distribution, and find efficient estimators for its success probability parameter. Furthermore we provide efficient methods for estimation of the true null distribution resulting from a preprocessing method, and techniques to compare it with the theoretical null distribution. Analysis is based on a simple polynomial model for the tail of the distribution of p-values. We provide asymptotics which motivate this model, exhibit properties of estimators of the parameters of the model, and point to model checking tools. The methods are tried out on two large genomic studies and on an fMRI brain scan experiment.

Supplementary materials

Main file contains introduction to the SmartTail software; proofs of Theorems 1, 2, and 3 in the paper; derivation of equation (10); additional results and discussion for dependent p-values; sandwich estimators for dependent p-values; additional plots for the yeast genome and salt stress screening data; and two additional examples: association mapping in Arabidopsis Thaliana and a fMRI brain scan experiment; MATLAB scripts to simulate from the tail mixture model, and to compute the maximum likelihood estimates of the parameters of the mixture model (8) for the cases (i)-(iii) described in the paper.

SmartTail - software for the analysis of false discovery rates in high-throughput-screening experiments.

Reference

Rootzén, H. and Zholud, D. (2015). Efficient estimation of the number of false positives in high-throughput screening, Biometrika, Vol. 102, No. 3, pp. 695-704.

BiBTeX

@article{RootzenZholud2015,
  Author = {Rootz\`{e}n, H. and Zholud, D.},
  Year = {2015},
  Title = {Efficient estimation of the number of false positives in high-throughput screening},
  Journal = {Biometrika},
  Volume = {102},
  Number = {3},
  Pages = {695--704}
}

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Update 2018