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Cited by 225Statistical Methods in Clinical TrialsGene expression and cancer classificationStatistical Methods and Inference

The DOI matches its Crossref record; 34 of the 35 references it cites were found in a registry or an index, and 1 are not checked yet.

Effects of dependence in high-dimensional multiple testing problems

Open access
Kim, Kyung In, van de Wiel, Mark A·2008·BMC Bioinformatics
DOI 10.1186/1471-2105-9-114PMC PMC2375137
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Abstract

BACKGROUND: We consider effects of dependence among variables of high-dimensional data in multiple hypothesis testing problems, in particular the False Discovery Rate (FDR) control procedures. Recent simulation studies consider only simple correlation structures among variables, which is hardly inspired by real data features. Our aim is to systematically study effects of several network features like sparsity and correlation strength by imposing dependence structures among variables using random correlation matrices. RESULTS: We study the robustness against dependence of several FDR procedures that are popular in microarray studies, such as Benjamin-Hochberg FDR, Storey's q-value, SAM and resampling based FDR procedures. False Non-discovery Rates and estimates of the number of null hypotheses are computed from those methods and compared. Our simulation study shows that methods such as SAM and the q-value do not adequately control the FDR to the level claimed under dependence conditions. On the other hand, the adaptive Benjamini-Hochberg procedure seems to be most robust while remaining conservative. Finally, the estimates of the number of true null hypotheses under various dependence conditions are variable. CONCLUSION: We discuss a new method for efficient guided simulation of dependent data, which satisfy imposed network constraints as conditional independence structures. Our simulation set-up allows for a structural study of the effect of dependencies on multiple testing criterions and is useful for testing a potentially new method on pi0 or FDR estimation in a dependency context.

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Figure 1 Average FDR results under dependence when π0 = 0.8. The x-axis corresponds to the proportion of edges in the network and the y-axis corresponds to FDR estimates for various procedures. Testing cut-off c is tuned such that true FDR is 0.1 under independence. FDR(c) (solid black) represents true FDR values in terms of (5) using the fixed c. The FDR procedures and corresponding lines in this figure are the following ones: BH (dashed red), BY (dotted green), SAM (dot-dashed blue), Qvalue (dashed cyan), ABH (purple), the upper limit RBH (dashed black), the point RBH (dotted red).
Figure 1 Average FDR results under dependence when π0 = 0.8. The x-axis corresponds to the proportion of edges in the network and the y-axis corresponds to FDR estimates for various procedures. Testing cut-off c is tuned such that true FDR is 0.1 under independence. FDR(c) (solid black) represents true FDR values in terms of (5) using the fixed c. The FDR procedures and corresponding lines in this figure are the following ones: BH (dashed red), BY (dotted green), SAM (dot-dashed blue), Qvalue (dashed cyan), ABH (purple), the upper limit RBH (dashed black), the point RBH (dotted red).CC BY · PubMed Central
Figure 2 Average FDR results under dependence when π0 = 0.95. See Figure 1 for explanation.
Figure 2 Average FDR results under dependence when π0 = 0.95. See Figure 1 for explanation.CC BY · PubMed Central
Figure 3 Average FNR results under dependence when π0 = 0.8. The y-axis corresponds to FNR estimates for various procedures. For the other explanation, see Figure 1.
Figure 3 Average FNR results under dependence when π0 = 0.8. The y-axis corresponds to FNR estimates for various procedures. For the other explanation, see Figure 1.CC BY · PubMed Central
Figure 4 Average π0 estimates under dependence when π0 = 0.8. The x-axis corresponds to the proportion of edges in the network and the y-axis corresponds to π0 estimates for various procedures. The π0 estimators and corresponding lines are SAM (solid black), Qvalue (dashed red), ABH (dotted green) and the convex estimator of Langaas et al [10] (dot-dashed).
Figure 4 Average π0 estimates under dependence when π0 = 0.8. The x-axis corresponds to the proportion of edges in the network and the y-axis corresponds to π0 estimates for various procedures. The π0 estimators and corresponding lines are SAM (solid black), Qvalue (dashed red), ABH (dotted green) and the convex estimator of Langaas et al [10] (dot-dashed).CC BY · PubMed Central
Figure 5 Variances of correlations and FDR(c) when π0 = 0.8. The solid line represents variance of correlations and the dashed line represents FDR(c). For comparison, we transform var(ρij) to var(ρij)/10 + 0.1 so that two quantities have same scale.
Figure 5 Variances of correlations and FDR(c) when π0 = 0.8. The solid line represents variance of correlations and the dashed line represents FDR(c). For comparison, we transform var(ρij) to var(ρij)/10 + 0.1 so that two quantities have same scale.CC BY · PubMed Central
Figure 6 FDR(c) with different M values. For various M - m values, FDR(c) is computed. The M - m values and corresponding lines are 1001 (solid black), 1010 (dashed red), 1025 (dotted green), 1046 (dot-dashed blue) and 1073 (dashed cyan).
Figure 6 FDR(c) with different M values. For various M - m values, FDR(c) is computed. The M - m values and corresponding lines are 1001 (solid black), 1010 (dashed red), 1025 (dotted green), 1046 (dot-dashed blue) and 1073 (dashed cyan).CC BY · PubMed Central
Figure 7 Graphical representation of conditional independence structures when m = 4. A sequence of possible nested structure is depicted when the number of nodes is 4. The left most graph represents complete independence between variables and the right most graph represents complete dependence between variables. The dependence structure of every left graph is contained to the structure of the graph right to it.
Figure 7 Graphical representation of conditional independence structures when m = 4. A sequence of possible nested structure is depicted when the number of nodes is 4. The left most graph represents complete independence between variables and the right most graph represents complete dependence between variables. The dependence structure of every left graph is contained to the structure of the graph right to it.CC BY · PubMed Central

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Metadata

Authors
Kim, K. I., & van de Wiel, M. A.
Affiliations
Eindhoven University of Technology (NL)
Corresponding author
Kim, Kyung In
Venue
BMC Bioinformatics
Publisher
Springer Science and Business Media LLC
Published
2008-02-25
Volume
9
Issue
1
Pages
114-114
ISSN
1471-2105 (ISSN-L)
DOI
10.1186/1471-2105-9-114
PMC
PMC2375137
OpenAlex
W2116319049
Cited by
220
References
34
Citations by year
2026: 3 · 2025: 5 · 2024: 6 · 2023: 15 · 2022: 11 · 2021: 13 · 2020: 29 · 2019: 33 · 2018: 15 · 2017: 19 · 2016: 14 · 2015: 10 · 2014: 14 · 2013: 5 · 2012: 5
FWCI
7.24
Type
journal article
Language
en
Open access
Licence
Locations
  • BMC Bioinformatics (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • Amsterdam UMC (VU Amsterdam) - Institutional Repository (publishedVersion, other-oa)
  • TU/e Research Portal (publishedVersion, other-oa)
  • Pure Amsterdam UMC (submittedVersion, other-oa)
  • TU/e Research Portal (submittedVersion, other-oa)
  • TU/e Research Portal (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • VU Research Portal (submittedVersion, other-oa)
  • Data Archiving and Networked Services (DANS) (submittedVersion, other-oa)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene expression and cancer classification
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
Keywords
multiple comparisons, false discovery rate, high-dimensional data, microarray data, conditional independence structure, sparsity
MeSH terms
Algorithms, Sensitivity and Specificity, Statistics as Topic, Reproducibility of Results, Artifacts, Oligonucleotide Array Sequence Analysis, Gene Expression Profiling

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