A new approach to multiple testing of grouped hypotheses

Liu, Yan-Ping; Sarkar, Santanu; Zhao, Zhigen

doi:10.1016/j.jspi.2016.07.004

Cited by 25 publications

(36 citation statements)

References 23 publications

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“…The problem of multiple testing with groups and related problems have received substantial attention in the literature (Efron, ; Ferkingstad et al ., ; Cai and Sun, ; Hu et al ., ; Liu et al ., ; Barber and Ramdas, ). It can be shown that, under model (4.2), the oracle statistic (4.1) is reduced to the conditional local false discovery rate CLfdr (Cai and Sun, )

{CLfdr}_{i} = (1 - π_{1}^{k}) f_{10}^{k} (t_{i}) / f_{1}^{k} (t_{i})

for S i = k , k =1,…, K .…”

Section: Extensions and Connections With Existing Workmentioning

confidence: 97%

“…Important recent progress for exploiting the grouping and hierarchical structures among hypotheses under more generic settings has been made in Liu et al . (), wherein an interesting decomposition of the oracle statistic was derived:

T_{OR}^{i} false(t, s false) = 1 - false{1 - P (θ_{2 i} = 0 | t, s) false} false{1 - P (θ_{1 i} = 0 | t, s, θ_{2 i} = 1) false} .

The decomposition explicitly shows how the auxiliary statistic can be used to adjust the Lfdr‐statistic, and provides insights on how the grouping effects S i and individual effects T i interplay in simultaneous testing. The logical correlation (2.2) can be conceptualized as a hierarchical constraint and exploited more efficiently (Sarkar and Zhao, ).…”

Section: Extensions and Connections With Existing Workmentioning

confidence: 99%

See 1 more Smart Citation

Covariate-Assisted Ranking and Screening for Large-Scale Two-Sample Inference

Cai

Sun

Wang

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Two‐sample multiple testing has a wide range of applications. The conventional practice first reduces the original observations to a vector of p‐values and then chooses a cut‐off to adjust for multiplicity. However, this data reduction step could cause significant loss of information and thus lead to suboptimal testing procedures. We introduce a new framework for two‐sample multiple testing by incorporating a carefully constructed auxiliary variable in inference to improve the power. A data‐driven multiple‐testing procedure is developed by employing a covariate‐assisted ranking and screening (CARS) approach that optimally combines the information from both the primary and the auxiliary variables. The proposed CARS procedure is shown to be asymptotically valid and optimal for false discovery rate control. The procedure is implemented in the R package CARS. Numerical results confirm the effectiveness of CARS in false discovery rate control and show that it achieves substantial power gain over existing methods. CARS is also illustrated through an application to the analysis of a satellite imaging data set for supernova detection.

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{CLfdr}_{i} = (1 - π_{1}^{k}) f_{10}^{k} (t_{i}) / f_{1}^{k} (t_{i})

for S i = k , k =1,…, K .…”

Section: Extensions and Connections With Existing Workmentioning

confidence: 97%

T_{OR}^{i} false(t, s false) = 1 - false{1 - P (θ_{2 i} = 0 | t, s) false} false{1 - P (θ_{1 i} = 0 | t, s, θ_{2 i} = 1) false} .

Section: Extensions and Connections With Existing Workmentioning

confidence: 99%

Covariate-Assisted Ranking and Screening for Large-Scale Two-Sample Inference

Cai

Sun

Wang

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…This model will be revisited in later sections. See also Ferkingstad et al (2008), Hu et al (2010) and Liu et al (2016) for related works on multiple testing with groups.…”

Section: Problem Formulationmentioning

confidence: 99%

Weighted False Discovery Rate Control in Large-Scale Multiple Testing

Basu

Cai

Das

et al. 2018

Journal of the American Statistical Association

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The use of weights provides an effective strategy to incorporate prior domain knowledge in large-scale inference. This paper studies weighted multiple testing in a decisiontheoretic framework. We develop oracle and data-driven procedures that aim to maximize the expected number of true positives subject to a constraint on the weighted false discovery rate. The asymptotic validity and optimality of the proposed methods are established. The results demonstrate that incorporating informative domain knowledge enhances the interpretability of results and precision of inference. Simulation studies show that the proposed method controls the error rate at the nominal level, and the gain in power over existing methods is substantial in many settings. An application to a genome-wide association study is discussed.

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“…Liu et al, (), Sarkar and Zhao () proposed a two‐stage procedure where the groups are non‐overlapping. In our approach the groups are generally overlapping and the decisions regarding different hypotheses depend upon each other.…”

Section: A New Bayesian Non‐marginal Multiple Testing Proposalmentioning

confidence: 99%

“…In Web Appendix E.2, we discuss the equivalence of forming groups on the basis of prior correlation and genomic distance between miRNAs and elaborate specifics on group formation. Liu et al (2016), Sarkar and Zhao (2017) proposed a twostage procedure where the groups are non-overlapping. In our approach the groups are generally overlapping and the decisions regarding different hypotheses depend upon each other.…”

Section: New Error Basedmentioning

confidence: 99%

A Novel Bayesian Multiple Testing Approach to Deregulated miRNA Discovery Harnessing Positional Clustering

Chandra

Bhattacharya

2018

Biometrics

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MicroRNAs (miRNAs) are small non-coding RNAs that function as regulators of gene expression. In recent years, there has been a tremendous interest among researchers to investigate the role of miRNAs in normal as well as in disease processes. To investigate the role of miRNAs in oral cancer, we analyse expression levels of miRNAs to identify miRNAs with statistically significant differential expression in cancer tissues. In this article, we propose a novel Bayesian hierarchical model of miRNA expression data. Compelling evidence has demonstrated that the transcription process of miRNAs in the human genome is a latent process instrumental for the observed expression levels. We take into account positional clustering of the miRNAs in the analysis and model the latent transcription phenomenon nonparametrically by an appropriate Gaussian process. For the purpose of testing, we employ a novel Bayesian multiple testing method where we mainly focus on utilizing the dependence structure between the hypotheses for better results, while also ensuring optimality in many respects. Indeed, our non-marginal method yielded results in accordance with the underlying scientific knowledge which are found to be missed by the very popular Benjamini-Hochberg method.

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A new approach to multiple testing of grouped hypotheses

Cited by 25 publications

References 23 publications

Covariate-Assisted Ranking and Screening for Large-Scale Two-Sample Inference

Covariate-Assisted Ranking and Screening for Large-Scale Two-Sample Inference

Weighted False Discovery Rate Control in Large-Scale Multiple Testing

A Novel Bayesian Multiple Testing Approach to Deregulated miRNA Discovery Harnessing Positional Clustering

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