Size, power and false discovery rates

By Bradley Efron. 2007

441 citations recorded by the source corpus.

Modem scientific technology has provided a new class of large-scale simultaneous inference problems, with thousands of hypothesis tests to consider at the same time. Microarrays epitomize this type of technology, but similar situations arise in proteomics, spectroscopy, imaging, and social science surveys. This paper uses false discovery rate methods to carry out both size and power calculations on large-scale problems. A simple empirical Bayes approach allows the false discovery rate (fdr) analysis to proceed with a minimum of frequentist or Bayesian modeling assumptions. Closed-form accuracy formulas are derived for estimated false discovery rates, and used to compare different methodologies: local or tail-area fdr's, theoretical, permutation, or empirical null hypothesis estimates. Two microarray data sets as well as simulations are used to evaluate the methodology, the power diagnostics showing why nonnull cases might easily fail to appear on a list of "significant" discoveries.

Subfields: Biophysics, Molecular Biology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0cc325ee022c258b30da3247a60828f7adf4d14c

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Citations in the corpus

Why We (Usually) Don't Have to Worry About Multiple Comparisons (2009, background): “Classical Type 1 and Type 2 errors and false discovery rates are based on the idea that the true eﬀect could really be zero (see Johnstone and Silverman, 2004, and Efron, 2006, for connections between these ideas and hierarchical Bayes methods).”
Large-scale inference (2010, methodology): “Most of this chapter’s material comes from Efron (2009a), where tests for column-wise independence are investigated more thoroughly, and Efron (2007a).”
DNA regions bound at low occupancy by transcription factors do not drive patterned reporter gene expression in Drosophila (2012, positive): “From the local FDR, only one of the 104 KR-bound TTRs is expected to be falsely discovered (Dataset S2), almost certainly one of the lowest-ranked members of the bottom cohort.”
Estimation of a two‐component mixture model with applications to multiple testing (2012, methodology): “We also compare our results with α̂0 , the estimator that was proposed in Efron (2007) using the central matching method, computed using the locfdr function in the R library locfdr. Jin (2008) and Cai and Jin (2010) proposed estimators when the model is a mixture of Gaussian distributions; we denote”
Correlation and Large-Scale Simultaneous Significance Testing (2007, methodology): “This is the idea behind the empirical null (Efron 2004, 2006), whose most important job is predicting the conditional expectation of the tail null counts.”
RNA Sequencing Data: Hitchhiker's Guide to Expression Analysis (2018, background): “A study has suggested that co-regulation of genes induces intergene correlations, which can alter the null distribution of the statistical test [163]; local FDR approaches were introduced that empirically estimate the null distribution [164].”
Significance Analysis of Spectral Count Data in Label-free Shotgun Proteomics*S (2008, methodology): “The rate of false positives in the selection of differentially expressed proteins based on Bayes factors can be estimated using a mixture model-based method of local FDR control (33, 34).”
Covariate‐assisted ranking and screening for large‐scale two‐sample inference (2019, background): “, 2005), the average power (Efron, 2007) and false non-discovery or false negative rate (Genovese and Wasserman, 2002; Sarkar, 2002).”