Skip to main content

Multiple Hypothesis Testing: A Methodological Overview

  • Protocol
  • First Online:
Statistical Methods for Microarray Data Analysis

Part of the book series: Methods in Molecular Biology ((MIMB,volume 972))

Abstract

The process of screening for differentially expressed genes using microarray samples can usually be reduced to a large set of statistical hypothesis tests. In this situation, statistical issues arise which are not encountered in a single hypothesis test, related to the need to identify the specific hypotheses to be rejected, and to report an associated error. As in any complex testing problem, it is rarely the case that a single method is always to be preferred, leaving the analysts with the problem of selecting the most appropriate method for the particular task at hand. In this chapter, an introduction to current multiple testing methodology was presented, with the objective of clarifying the methodological issues involved, and hopefully providing the reader with some basis with which to compare and select methods.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Protocol
USD 49.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Scherzer CR, Eklund AC, Morse LJ, Liao Z, Locascio JJ, Fefer D, Schwarzschild MA, Schlossmacher MG, Hauser MA, Vance JM, Sudarsky LR, Standaert DG, Growdon JH, Jensen RV, Gullans SR (2007) Molecular markers of early Parkinson’s disease based on gene expression in blood. PNAS 104:955–960

    Article  PubMed  CAS  Google Scholar 

  2. Benjamini Y, Braun H (2002) John W. Tukey’s contributions to multiple comparisons. Ann Stat 30:1576–1594

    Article  Google Scholar 

  3. Yang YH, Speed T (2003) Statistical analysis of gene expression microarray data. In: Speed T (ed) Design and analysis of comparitive microarray experiments. Chapman and Hall, Boca Raton, FL, pp 35–92

    Google Scholar 

  4. Dudoit S, Shaffer JP, Boldrick JC (2003) Multiple hypothesis testing in microarray experiments. Stat Sci 18:71–103

    Article  Google Scholar 

  5. Dudoit S, van der Laan MJ (2008) Multiple testing procedures with applications to genomics. Springer, New York, NY

    Book  Google Scholar 

  6. Chu T, Glymour C, Scheines R, Spirtes P (2003) A statistical problem for inference to regulatory structure from associations of gene expression measurementswith microarrays. Bioinformatics 19:1147–1152

    Google Scholar 

  7. Holm S (1979) A simple sequentially rejective multiple test procedure. Scand J Stat 6:65–70

    Google Scholar 

  8. Shaffer JP (1986) Modified sequentially rejective test procedures. JASA 81:826–830

    Article  Google Scholar 

  9. Šidák Z (1967) Rectangular confidence regions for the means of multivariate normal distribution. JASA 62:626–633

    Google Scholar 

  10. Šidák Z (1971) On probabilities of rectangles in multivariate Student distributions: their dependence on correlations. Ann Math Stat 42:169–175

    Article  Google Scholar 

  11. Jogdeo K (1977) Association and probability inequalities. Ann Stat 5:495–504

    Article  Google Scholar 

  12. Holland BS, Copenhaver MD (1987) An improved sequentially rejective rejective Bonferroni test procedure. Biometrics 43:417–423

    Article  Google Scholar 

  13. Dykstra RL, Hewett JE, Thompson WA (1973) Events which are almost independent. Ann Stat 1:674–681

    Article  Google Scholar 

  14. Simes RJ (1986) An improved Bonferroni procedure for multiple tests of significance. Biometrika 73:751–754

    Article  Google Scholar 

  15. Hommel G (1988) A stagewise rejective multiple test procedure based on a modified Bonferroni test. Biometrika 75:383–386

    Article  Google Scholar 

  16. Hochberg Y (1988) A sharper Bonferroni procedure for multiple tests of significance. Biometrika 75:800–802

    Article  Google Scholar 

  17. Sarkar SK (1998) Some probability inequalities for ordered MTP2 random variable: a proof of the Simes conjecture. Ann Stat 26:494–504

    Article  Google Scholar 

  18. Sarkar SK, Chang C-K (1997) The Simes method for multiple hypothesis testing with positively dependent test statistics. JASA 92:1601–1608

    Article  Google Scholar 

  19. Rom DR (1990) A sequentially rejective test procedure based on a modified Bonferroni inequality. Biometrika 77:663–665

    Article  Google Scholar 

  20. Huang Y, Hsu JC (2007) Hochberg’s step-up method: cutting corners off Holm’s step-down methods. Biometrika 94:965–975

    Article  Google Scholar 

  21. Westfall PH, Young S (1993) Resampling-based multiple testing. Wiley, New York, NY

    Google Scholar 

  22. Pollard KS, Dudoit S, van der Laan MJ (2005) Bioinformatics and Compu-tational Biology Solutions Using R and Bioconductor. In: Gentleman R, Huber W, Carey VJ, Irizarry RA, Dudoit S (eds) chapter Multiple testing­procedures: the multest package and applications to genomics (pp 249–271). Springer, New York, NY,

    Google Scholar 

  23. Benjamini Y, Hochberg D (1995) Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Stat Soc Ser B 57:289–300

    Google Scholar 

  24. Benjamini Y, Yekutieli D (2001) The control of the false discovery rate in multiple testing under dependency. Ann Stat 29:1165–1188

    Article  Google Scholar 

  25. Storey JD (2003) The positive false discovery rate: a Bayesian interpretation and the q-value. Ann Stat 31:2013–2035

    Article  Google Scholar 

  26. Storey JD (2002) A direct approach to false discovery rates. JSS-B 64:479–498

    Article  Google Scholar 

  27. Efron B (2003) Robbins, empirical Bayes and microarrays. Ann Stat 31:366–378

    Article  Google Scholar 

  28. Efron B (2004) Large-scale simultaneous hypothesis testing: the choice of a null hypothesis. JASA 99:96–104

    Article  Google Scholar 

  29. Kall L, Storey JD, MacCross MJ, Noble WS (2008) Posterior error probabilities and false discovery rates: two sides of the same coin. J Proteome Res 7:40–44

    Article  PubMed  Google Scholar 

  30. Efron B, Tibshirani R, Storey JD, Tusher V (2001) Empirical Bayes analysis of a microarray experiment. JASA 96:1151–1160

    Article  Google Scholar 

  31. Allison DB, Gadbury GL, Moonseong H, Fernandez JR, Cheol-Koo L, Prolla TA, Weindruch R (2002) A mixture model approach for the analysis of microarray gene expression data. Comput Stat Data Anal 39:1–20

    Article  Google Scholar 

  32. Newton MA, Wang P, Kendziorski C (2006) Hierarchical mixture models for expression profiles. In: Do K, Muller P, Vannucci M (eds) Bayesian inference for gene expression and proteomics. Cambridge University Press, New York, NY, pp 40–52

    Google Scholar 

  33. Newton MA, Kendziorski CM, Richmond CS, Blattner FR, Tsui KW (2001) On differential variability of expression ratios: improving statistical inference about gene expression changes from microarray data. J Comput Biol 8:37–52

    Article  PubMed  CAS  Google Scholar 

  34. Newton MA, Noueiry A, Sarkar D, Ahlquist P (2004) Detecting differential gene expression with a semiparametric hierarchical mixture method. Biostatistics 5:155–176

    Article  PubMed  Google Scholar 

  35. Lewin A, Richardson S, Marshall C, Glazier A, Aitman T (2006) Bayesian modeling of differntial gene expression. Biometrics 62:1–9

    Article  PubMed  Google Scholar 

  36. Gottardo R, Raftery AE, Yeung KY, Bumgarner RE (2006) Bayesian robust inference for differential gene expression in microarrays with multiple samples. Biometrics 62:10–18

    Article  PubMed  Google Scholar 

  37. Do K, Muller P, Vannucci M (2006) Bayesian inference for gene expression and proteomics. Cambridge University Press, New York, NY

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Anthony Almudevar .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this protocol

Cite this protocol

Almudevar, A. (2013). Multiple Hypothesis Testing: A Methodological Overview. In: Yakovlev, A., Klebanov, L., Gaile, D. (eds) Statistical Methods for Microarray Data Analysis. Methods in Molecular Biology, vol 972. Humana Press, New York, NY. https://doi.org/10.1007/978-1-60327-337-4_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-60327-337-4_3

  • Published:

  • Publisher Name: Humana Press, New York, NY

  • Print ISBN: 978-1-60327-336-7

  • Online ISBN: 978-1-60327-337-4

  • eBook Packages: Springer Protocols

Publish with us

Policies and ethics