False discovery and false nondiscovery rates in single-step multiple testing procedures

By Sanat K. Sarkar. 2006

101 citations recorded by the source corpus.

Results on the false discovery rate (FDR) and the false nondiscovery rate (FNR) are developed for single-step multiple testing procedures. In addition to verifying desirable properties of FDR and FNR as measures of error rates, these results extend previously known results, providing further insights, particularly under dependence, into the notions of FDR and FNR and related measures. First, considering fixed configurations of true and false null hypotheses, inequalities are obtained to explain how an FDR- or FNR-controlling single-step procedure, such as a Bonferroni or Sidak procedure, can potentially be improved. Two families of procedures are then constructed, one that modifies the FDR-controlling and the other that modifies the FNR-controlling Sidak procedure. These are proved to control FDR or FNR under independence less conservatively than the corresponding families that modify the FDR- or FNR-controlling Bonferroni procedure. Results of numerical investigations of the performance of the modified Sidak FDR procedure over its competitors are presented. Second, considering a mixture model where different configurations of true and false null hypotheses are assumed to have certain probabilities, results are also derived that extend some of Storey's work to the dependence case.

Subfields: Hardware and Architecture, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3a00fd37ea0800bddf255722e691af52d41b72de

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Citations in the corpus

A comparison of the Benjamini-Hochberg procedure with some Bayesian rules for multiple testing (2008, methodology): “Lehmann and Romano [17], Sarkar [ 24 ], Storey [31] and references given there) but BH still remains one of the most popular methods of multiple testing.”
Robustness of multiple testing procedures against dependence (2009, background): “…developed optimality theory for multiple testing; Rosenberg, Che and Chen (2006) suggested multiple hypothesis testing methods in a genomic setting; Sarkar (2006) obtained new results on false-discovery rates for single-step, multiple testing procedures; Schmidt and Stadtmüller (2006) and Schmidt…”
To How Many Simultaneous Hypothesis Tests Can Normal, Student's t or Bootstrap Calibration Be Applied? (2006, background): “Examples in the latter setting have been given by Benjamini and Yekutieli (2001), Sarkar (2002, 2006), Dudoit, Shaffer, and Boldrick (2003), Donoho and Jin (2004), Efron (2004), Genovese and Wasserman (2004), Storey, Taylor, and Siegmund (2004), Lehmann and Romano (2005), and Lehmann, Romano, and…”
Large‐scale multiple testing under dependence (2009, methodology): “The effects of correlation on FDR procedures have been discussed by Benjamini and Yekutieli (2001), Finner and Roters (2002), Owen (2005), Sarkar (2006) and Efron (2007), among others.”
On the Benjamini-Hochberg method (2006, background): “Recent parallel developments in this area can be found in [10] and [17].”
The Bayes oracle and asymptotic optimality of multiple testing procedures under sparsity (2010, background): “A prominent area of the application of multiple testing is microarray data analysis, where one wants to simultaneously test expression levels of thousands of genes (e.g. see [15], [14], [35], [18], [25], [26], [27] or [34]).”
On the Simes inequality and its generalization (2008, methodology): “Most importantly, it is closely linked to the inequality establishing the false discovery rate (FDR) control of the Benjamini and Hochberg [1] procedure (Benjamini and Yekutieli [2] and Sarkar [23, 24]), which as a FDR procedure has received the most attention so far in the multiple testing literatu”
On the performance of FDR control: Constraints and a partial solution (2007, unknown): “[1, 2, 5-10, 12, 15-17] and references therein).”
FDR-CONTROLLING STEPWISE PROCEDURES AND THEIR FALSE NEGATIVES RATES (2004, background): “This raises an intersecting question: How does the present unbiasedness property of an FDR-controlling multiple testing procedure relate to the unbiasedness condition of the individual tests? This is discussed in a different communication (Sarkar, 2003).”