On the Operational Characteristics of the Benjamini and Hochberg False Discovery Rate Procedure

2007 ◽  
Vol 6 (1) ◽  
Author(s):  
Gerwyn H Green ◽  
Peter J. Diggle
Keyword(s):  
False Discovery Rate ◽  
Multiple Testing ◽  
False Positives ◽  
Experimental Conditions ◽  
Single Experiment ◽  
Testing Procedures ◽  
False Discovery ◽  
Expression Studies ◽  
Operational Characteristics ◽  
Gene Expression Studies

Multiple testing procedures are commonly used in gene expression studies for the detection of differential expression, where typically thousands of genes are measured over at least two experimental conditions. Given the need for powerful testing procedures, and the attendant danger of false positives in multiple testing, the False Discovery Rate (FDR) controlling procedure of Benjamini and Hochberg (1995) has become a popular tool. When simultaneously testing hypotheses, suppose that R rejections are made, of which Fp are false positives. The Benjamini and Hochberg procedure ensures that the expectation of Fp/R is bounded above by some pre-specified proportion. In practice, the procedure is applied to a single experiment. In this paper we investigate the across-experiment variability of the proportion Fp/R as a function of three experimental parameters. The operational characteristics of the procedure when applied to dependent hypotheses are also considered.

SOME COMMENTS ON INSTABILITY OF FALSE DISCOVERY RATE ESTIMATION

2006 ◽  
Vol 04 (05) ◽  
pp. 1057-1068 ◽  
Author(s):  
XING QIU ◽  
ANDREI YAKOVLEV
Keyword(s):  
False Discovery Rate ◽  
Microarray Data ◽  
Multiple Testing ◽  
Microarray Data Analysis ◽  
Expression Data ◽  
Testing Procedures ◽  
Empirical Estimates ◽  
False Discovery ◽  
Multiple Testing Procedures ◽  
False Discovery Rate Estimation

Some extended false discovery rate (FDR) controlling multiple testing procedures rely heavily on empirical estimates of the FDR constructed from gene expression data. Such estimates are also used as performance indicators when comparing different methods for microarray data analysis. The present communication shows that the variance of the proposed estimators may be intolerably high, the correlation structure of microarray data being the main cause of their instability.

scholarly journals Differentially private false discovery rate control

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Cynthia Dwork ◽  
Weijie Su ◽  
Li Zhang
Keyword(s):  
False Discovery Rate ◽  
Multiple Testing ◽  
Differential Privacy ◽  
Broad Class ◽  
Multiple Hypothesis Testing ◽  
P Value ◽  
P Values ◽  
Testing Procedures ◽  
False Discovery ◽  
Rigorous Framework

Differential privacy provides a rigorous framework for privacy-preserving data analysis. This paper proposes the first differentially private procedure for controlling the false discovery rate (FDR) in multiple hypothesis testing. Inspired by the Benjamini-Hochberg procedure (BHq), our approach is to first repeatedly add noise to the logarithms of the p-values to ensure differential privacy and to select an approximately smallest p-value serving as a promising candidate at each iteration; the selected p-values are further supplied to the BHq and our private procedure releases only the rejected ones. Moreover, we develop a new technique that is based on a backward submartingale for proving FDR control of a broad class of multiple testing procedures, including our private procedure, and both the BHq step- up and step-down procedures. As a novel aspect, the proof works for arbitrary dependence between the true null and false null test statistics, while FDR control is maintained up to a small multiplicative factor.

scholarly journals Assessment of common housekeeping genes as reference for gene expression studies using RT-qPCR in mouse choroid plexus

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Kim Hoa Ho ◽  
Annarita Patrizi
Keyword(s):  
Gene Expression ◽  
Choroid Plexus ◽  
Sensory Deprivation ◽  
Housekeeping Genes ◽  
Housekeeping Gene ◽  
Experimental Conditions ◽  
Brain Repair ◽  
Expression Studies ◽  
Testing Algorithms ◽  
Gene Expression Studies

AbstractChoroid plexus (ChP), a vascularized secretory epithelium located in all brain ventricles, plays critical roles in development, homeostasis and brain repair. Reverse transcription quantitative real-time PCR (RT-qPCR) is a popular and useful technique for measuring gene expression changes and also widely used in ChP studies. However, the reliability of RT-qPCR data is strongly dependent on the choice of reference genes, which are supposed to be stable across all samples. In this study, we validated the expression of 12 well established housekeeping genes in ChP in 2 independent experimental paradigms by using popular stability testing algorithms: BestKeeper, DeltaCq, geNorm and NormFinder. Rer1 and Rpl13a were identified as the most stable genes throughout mouse ChP development, while Hprt1 and Rpl27 were the most stable genes across conditions in a mouse sensory deprivation experiment. In addition, Rpl13a, Rpl27 and Tbp were mutually among the top five most stable genes in both experiments. Normalisation of Ttr and Otx2 expression levels using different housekeeping gene combinations demonstrated the profound effect of reference gene choice on target gene expression. Our study emphasized the importance of validating and selecting stable housekeeping genes under specific experimental conditions.

scholarly journals Validation of Reference Genes for Studying Different Abiotic Stresses in oat (Avena sativa L.) by RT-qPCR

Plants ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 1272
Author(s):  
Judit Tajti ◽  
Magda Pál ◽  
Tibor Janda
Keyword(s):  
Gene Expression ◽  
Avena Sativa ◽  
Abiotic Stresses ◽  
Reference Genes ◽  
Nutritional Value ◽  
Tissue Type ◽  
Future Research ◽  
Experimental Conditions ◽  
Expression Studies ◽  
Gene Expression Studies

Oat (Avena sativa L.) is a widely cultivated cereal with high nutritional value and it is grown mainly in temperate regions. The number of studies dealing with gene expression changes in oat continues to increase, and to obtain reliable RT-qPCR results it is essential to establish and use reference genes with the least possible influence caused by experimental conditions. However, no detailed study has been conducted on reference genes in different tissues of oat under diverse abiotic stress conditions. In our work, nine candidate reference genes (ACT, TUB, CYP, GAPD, UBC, EF1, TBP, ADPR, PGD) were chosen and analysed by four statistical methods (GeNorm, Normfinder, BestKeeper, RefFinder). Samples were taken from two tissues (leaves and roots) of 13-day-old oat plants exposed to five abiotic stresses (drought, salt, heavy metal, low and high temperatures). ADPR was the top-rated reference gene for all samples, while different genes proved to be the most stable depending on tissue type and treatment combinations. TUB and EF1 were most affected by the treatments in general. Validation of reference genes was carried out by PAL expression analysis, which further confirmed their reliability. These results can contribute to reliable gene expression studies for future research in cultivated oat.

On the Adaptive Control of the False Discovery Rate in Multiple Testing With Independent Statistics

2000 ◽  
Vol 25 (1) ◽  
pp. 60-83 ◽  
Author(s):  
Yoav Benjamini ◽  
Yosef Hochberg
Keyword(s):  
False Discovery Rate ◽  
Multiple Testing ◽  
Meta Analysis ◽  
Test Statistics ◽  
Adaptive Procedure ◽  
New Approach ◽  
False Discovery ◽  
Behavioral Studies ◽  
Simultaneous Testing ◽  
Independent Test

A new approach to problems of multiple significance testing was presented in Benjamini and Hochberg (1995), which calls for controlling the expected ratio of the number of erroneous rejections to the number of rejections–the False Discovery Rate (FDR). The procedure given there was shown to control the FDR for independent test statistics. When some of the hypotheses are in fact false, that procedure is too conservative. We present here an adaptive procedure, where the number of true null hypotheses is estimated first as in Hochberg and Benjamini (1990), and this estimate is used in the procedure of Benjamini and Hochberg (1995). The result is still a simple stepwise procedure, to which we also give a graphical companion. The new procedure is used in several examples drawn from educational and behavioral studies, addressing problems in multi-center studies, subset analysis and meta-analysis. The examples vary in the number of hypotheses tested, and the implication of the new procedure on the conclusions. In a large simulation study of independent test statistics the adaptive procedure is shown to control the FDR and have substantially better power than the previously suggested FDR controlling method, which by itself is more powerful than the traditional family wise error-rate controlling methods. In cases where most of the tested hypotheses are far from being true there is hardly any penalty due to the simultaneous testing of many hypotheses.

scholarly journals Selecting and validating reference genes for quantitative real-time PCR in Plutella xylostella (L.)

Genome ◽  
2018 ◽  
Vol 61 (5) ◽  
pp. 349-358 ◽  
Author(s):  
Yanchun You ◽  
Miao Xie ◽  
Liette Vasseur ◽  
Minsheng You
Keyword(s):  
Gene Expression ◽  
Real Time ◽  
Plutella Xylostella ◽  
Real Time Pcr ◽  
Reference Genes ◽  
Developmental Stages ◽  
Quantitative Real Time Pcr ◽  
Experimental Conditions ◽  
Expression Studies ◽  
Gene Expression Studies

Gene expression analysis provides important clues regarding gene functions, and quantitative real-time PCR (qRT-PCR) is a widely used method in gene expression studies. Reference genes are essential for normalizing and accurately assessing gene expression. In the present study, 16 candidate reference genes (ACTB, CyPA, EF1-α, GAPDH, HSP90, NDPk, RPL13a, RPL18, RPL19, RPL32, RPL4, RPL8, RPS13, RPS4, α-TUB, and β-TUB) from Plutella xylostella were selected to evaluate gene expression stability across different experimental conditions using five statistical algorithms (geNorm, NormFinder, Delta Ct, BestKeeper, and RefFinder). The results suggest that different reference genes or combinations of reference genes are suitable for normalization in gene expression studies of P. xylostella according to the different developmental stages, strains, tissues, and insecticide treatments. Based on the given experimental sets, the most stable reference genes were RPS4 across different developmental stages, RPL8 across different strains and tissues, and EF1-α across different insecticide treatments. A comprehensive and systematic assessment of potential reference genes for gene expression normalization is essential for post-genomic functional research in P. xylostella, a notorious pest with worldwide distribution and a high capacity to adapt and develop resistance to insecticides.

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