# A weighted FDR procedure under discrete and heterogeneous null distributions

@article{Chen2020AWF, title={A weighted FDR procedure under discrete and heterogeneous null distributions}, author={Xiongzhi Chen and Rebecca W. Doerge and Sanat K. Sarkar}, journal={Biometrical Journal}, year={2020}, volume={62}, pages={1544 - 1563} }

Multiple testing (MT) with false discovery rate (FDR) control has been widely conducted in the “discrete paradigm” where p‐values have discrete and heterogeneous null distributions. However, in this scenario existing FDR procedures often lose some power and may yield unreliable inference, and for this scenario there does not seem to be an FDR procedure that partitions hypotheses into groups, employs data‐adaptive weights and is nonasymptotically conservative. We propose a weighted p‐value‐based…

## 14 Citations

### New FDR bounds for discrete and heterogeneous tests

- Computer Science
- 2018

New FDR bounds are provided that make it possible to construct BH-type procedures that incorporate the discrete and heterogeneous structure of the data and provably control the FDR for any number of null hypotheses (under independence).

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This manuscript presents my contributions in three areas of multiple testing where data heterogeneity can be exploited to better detect false null hypotheses or improve signal detection while…

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This article proposes a novel multiple testing procedure for better FDR control on heterogeneous discrete tests and proves that the set of detections made by the method contains every detection made by a naive application of the widely-used q-value method.

### A grouped, selectively weighted false discovery rate procedure.

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- 2019

A grouped, selectively weighted FDR procedure, which is referred to as "sGBH", which identifies groups of hypotheses of interest, weights p- values in each such group only, and tests only the selected hypotheses using the weighted p-values.

### On Benjamini–Hochberg procedure applied to mid p-values

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### Controlling the false discovery exceedance for heterogeneous tests

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Several classical methods exist for controlling the false discovery exceedance (FDX) for large scale multiple testing problems, among them the Lehmann-Romano procedure ([LR] below) and the Guo-Romano…

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The paper reviews the statistical methods in a non-technical way, provides a detailed description of the implementation in DiscreteFDR and presents some sample code and analyses.

### Uniformly consistently estimating the proportion of false null hypotheses via Lebesgue-Stieltjes integral equations

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### An extended SGoF multiple testing method for discrete data

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The Sequential Goodness-of-Fit (SGoF) multiple testing method has recently been proposed as an alternative to the FWERand the FDR-controlling procedures in highdimensional problems. For discrete data…

### Online multiple testing with super-uniformity reward

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The method of super-uniformity reward (SURE) is introduced, which yields several new “rewarded” procedures that theoretically control online error criteria based either on the family-wise error rate (FWER) or the marginal false discovery rate (mFDR).

## References

SHOWING 1-10 OF 68 REFERENCES

### Multiple testing with discrete data: Proportion of true null hypotheses and two adaptive FDR procedures

- MathematicsBiometrical journal. Biometrische Zeitschrift
- 2018

A new estimator of the proportion of true null hypotheses is proposed and demonstrated that it is less upwardly biased than Storey's estimator and two other estimators, and it is proved that the adaptive BH (aBH) procedure is conservative nonasymptotically.

### False discovery rate control for multiple testing based on discrete p‐values

- MathematicsBiometrical journal. Biometrische Zeitschrift
- 2020

An adaptive version of the BH+ procedure is proposed, its conservativeness under certain conditions is proved, and evidence on its excellent performance via simulation studies is provided.

### New FDR bounds for discrete and heterogeneous tests

- Computer Science
- 2018

New FDR bounds are provided that make it possible to construct BH-type procedures that incorporate the discrete and heterogeneous structure of the data and provably control the FDR for any number of null hypotheses (under independence).

### Adaptive False Discovery Rate Control under Independence and Dependence

- MathematicsJ. Mach. Learn. Res.
- 2009

This paper focuses on the issue of false discovery rate (FDR) control and presents new adaptive multiple testing procedures with control of the FDR and proposes adaptive versions of step-up procedures that have provably controlled FDR under positive dependence and unspecified dependence of the p-values.

### A direct approach to false discovery rates

- Business
- 2002

The calculation of the q‐value is discussed, the pFDR analogue of the p‐value, which eliminates the need to set the error rate beforehand as is traditionally done, and can yield an increase of over eight times in power compared with the Benjamini–Hochberg FDR method.

### Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unified approach

- Mathematics
- 2004

Summary. The false discovery rate (FDR) is a multiple hypothesis testing quantity that describes the expected proportion of false positive results among all rejected null hypotheses. Benjamini and…

### Multiple testing with the structure‐adaptive Benjamini–Hochberg algorithm

- Computer ScienceJournal of the Royal Statistical Society: Series B (Statistical Methodology)
- 2018

The main theoretical result proves that the SABHA method controls the FDR at a level that is at most slightly higher than the target FDR level, as long as the adaptive weights are constrained sufficiently so as not to overfit too much to the data.

### A direct approach to false discovery rates by decoy permutations

- Computer Science
- 2018

The target-decoy procedure simply builds on the ordering of hypotheses by some statistic, and directly estimates the false target discoveries using the competing decoy hypotheses constructed by permutation, and it is proved that this approach can control the FDR.

### False discovery rate estimation for large‐scale homogeneous discrete p‐values

- MathematicsBiometrics
- 2016

It is shown that a broad class of FDR estimators is simultaneously conservative over all support points under some weak dependence condition in the asymptotic setting and a novel class of conservative FDR estimator is proposed in the finite sample setting.

### Large‐scale multiple testing under dependence

- Mathematics
- 2009

Summary. The paper considers the problem of multiple testing under dependence in a compound decision theoretic framework. The observed data are assumed to be generated from an underlying two‐state…