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A Generalized Sidak-Holm Procedure and Control of Generalized Error Rates under Independence

  • Wenge Guo and Joseph Romano
Published/Copyright: January 25, 2007
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Statistical Applications in Genetics and Molecular Biology
From the journal Statistical Applications in Genetics and Molecular Biology Volume 6 Issue 1

For testing multiple null hypotheses, the classical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of even one false rejection. In many applications, one might be willing to tolerate more than one false rejection provided the number of such cases is controlled, thereby increasing the ability of the procedure to detect false null hypotheses. This suggests replacing control of the FWER by controlling the probability of k or more false rejections, which is called the k-FWER. In Hommel and Hoffmann (1987) and Lehmann and Romano (2005a), single step and stepdown procedures are derived that control the k-FWER, without making any assumptions concerning the dependence structure of the p-values of the individual tests. However, if the p-values are mutually independent, one can improve the procedures. In fact, Sarkar (2005) provided such an improvement. However, we show other improvements are possible which appear to be generally much better, and are sometimes unimprovable. When k=1, the procedure reduces to the classical method of Sidak, and the stepdown procedure is unimprovable and strictly dominates that of Sarkar. Under a monotonicity condition, an unimprovable procedure is obtained. In the case k=2, the monotonicity condition is satisfied, and the condition can be checked numerically in general. We then develop a stepdown method that controls the false discovery proportion. Except for the case of k-FWER control with k=1, the gains are surprisingly dramatic, and theoretical and numerical evidence is given.

Keywords: false discovery proportion; generalized familywise error rate; multiple testing; p-value; Sidak procedure; stepdown procedure
Published Online: 2007-1-25

©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston

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https://doi.org/10.2202/1544-6115.1247
Keywords for this article
false discovery proportion; generalized familywise error rate; multiple testing; p-value; Sidak procedure; stepdown procedure

Articles in the same Issue

  1. Article
  2. Accounting for Dependence in Similarity Data from DNA Fingerprinting
  3. Normalization of Dye Bias in Microarray Data Using the Mixture of Splines Model
  4. A Generalized Sidak-Holm Procedure and Control of Generalized Error Rates under Independence
  5. Using Duplicate Genotyped Data in Genetic Analyses: Testing Association and Estimating Error Rates
  6. Likelihood-Based Inference for Multi-Color Optical Mapping
  7. Sparse Logistic Regression with Lp Penalty for Biomarker Identification
  8. Super Learning: An Application to the Prediction of HIV-1 Drug Resistance
  9. Supervised Detection of Conserved Motifs in DNA Sequences with Cosmo
  10. Accurate Ranking of Differentially Expressed Genes by a Distribution-Free Shrinkage Approach
  11. Statistical Inference for Quantitative Polymerase Chain Reaction Using a Hidden Markov Model: A Bayesian Approach
  12. A Bayesian Model of AFLP Marker Evolution and Phylogenetic Inference
  13. Sequential Quantitative Trait Locus Mapping in Experimental Crosses
  14. Case-Control Inference of Interaction between Genetic and Nongenetic Risk Factors under Assumptions on Their Distribution
  15. Inference on the Limiting False Discovery Rate and the P-value Threshold Parameter Assuming Weak Dependence between Gene Expression Levels within Subject
  16. Reconstructing Gene Regulatory Networks with Bayesian Networks by Combining Expression Data with Multiple Sources of Prior Knowledge
  17. Cox Survival Analysis of Microarray Gene Expression Data Using Correlation Principal Component Regression
  18. A Method for Meta-Analysis of Case-Control Genetic Association Studies Using Logistic Regression
  19. Approximating the Variance of the Conditional Probability of the State of a Hidden Markov Model
  20. Using Linear Mixed Models for Normalization of cDNA Microarrays
  21. Experimental Design for Two-Color Microarrays Applied in a Pre-Existing Split-Plot Experiment
  22. The Cyclohedron Test for Finding Periodic Genes in Time Course Expression Studies
  23. H-Tuple Approach to Evaluate Statistical Significance of Biological Sequence Comparison with Gaps
  24. Multiple Testing Issues in Discriminating Compound-Related Peaks and Chromatograms from High Frequency Noise, Spikes and Solvent-Based Noise in LC - MS Data Sets
  25. A Bayesian Approach to Estimation and Testing in Time-course Microarray Experiments
  26. Super Learner
  27. Testing for Trends in Dose-Response Microarray Experiments: A Comparison of Several Testing Procedures, Multiplicity and Resampling-Based Inference
  28. On the Operational Characteristics of the Benjamini and Hochberg False Discovery Rate Procedure
  29. A Comparison of Methods to Control Type I Errors in Microarray Studies
  30. Selection of Biologically Relevant Genes with a Wrapper Stochastic Algorithm
  31. T-BAPS: A Bayesian Statistical Tool for Comparison of Microbial Communities Using Terminal-restriction Fragment Length Polymorphism (T-RFLP) Data
  32. Population Structure and Covariate Analysis Based on Pairwise Microsatellite Allele Matching Frequencies
  33. Estimating the Arm-Wise False Discovery Rate in Array Comparative Genomic Hybridization Experiments
  34. An Expectation Maximization Approach to Estimate Malaria Haplotype Frequencies in Multiply Infected Children
  35. Estimation of Expression Levels in Spotted Microarrays with Saturated Pixels
  36. Improving Divergence Time Estimation in Phylogenetics: More Taxa vs. Longer Sequences
  37. Fully Bayesian Mixture Model for Differential Gene Expression: Simulations and Model Checks
  38. Multiple Testing for SNP-SNP Interactions
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