IDEAS home Printed from https://ideas.repec.org/a/bpj/sagmbi/v8y2009i1n23.html
   My bibliography  Save this article

Weighted Multiple Hypothesis Testing Procedures

Author

Listed:
  • Kang Guolian

    (University of Alabama at Birmingham)

  • Ye Keying

    (University of Texas at San Antonio)

  • Liu Nianjun

    (University of Alabama at Birmingham)

  • Allison David B.

    (University of Alabama at Birmingham)

  • Gao Guimin

    (University of Alabama at Birmingham)

Abstract

Multiple hypothesis testing is commonly used in genome research such as genome-wide studies and gene expression data analysis (Lin, 2005). The widely used Bonferroni procedure controls the family-wise error rate (FWER) for multiple hypothesis testing, but has limited statistical power as the number of hypotheses tested increases. The power of multiple testing procedures can be increased by using weighted p-values (Genovese et al., 2006). The weights for the p-values can be estimated by using certain prior information. Wasserman and Roeder (2006) described a weighted Bonferroni procedure, which incorporates weighted p-values into the Bonferroni procedure, and Rubin et al. (2006) and Wasserman and Roeder (2006) estimated the optimal weights that maximize the power of the weighted Bonferroni procedure under the assumption that the means of the test statistics in the multiple testing are known (these weights are called optimal Bonferroni weights). This weighted Bonferroni procedure controls FWER and can have higher power than the Bonferroni procedure, especially when the optimal Bonferroni weights are used. To further improve the power of the weighted Bonferroni procedure, first we propose a weighted idák procedure that incorporates weighted p-values into the idák procedure, and then we estimate the optimal weights that maximize the average power of the weighted idák procedure under the assumption that the means of the test statistics in the multiple testing are known (these weights are called optimal idák weights). This weighted idák procedure can have higher power than the weighted Bonferroni procedure. Second, we develop a generalized sequential (GS) idák procedure that incorporates weighted p-values into the sequential idák procedure (Scherrer, 1984). This GS idák procedure is an extension of and has higher power than the GS Bonferroni procedure of Holm (1979). Finally, under the assumption that the means of the test statistics in the multiple testing are known, we incorporate the optimal idák weights and the optimal Bonferroni weights into the GS idák procedure and the GS Bonferroni procedure, respectively. Theoretical proof and/or simulation studies show that the GS idák procedure can have higher power than the GS Bonferroni procedure when their corresponding optimal weights are used, and that both of these GS procedures can have much higher power than the weighted idák and the weighted Bonferroni procedures. All proposed procedures control the FWER well and are useful when prior information is available to estimate the weights.

Suggested Citation

  • Kang Guolian & Ye Keying & Liu Nianjun & Allison David B. & Gao Guimin, 2009. "Weighted Multiple Hypothesis Testing Procedures," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-24, April.
    • Handle: RePEc:bpj:sagmbi:v:8:y:2009:i:1:n:23
    DOI: 10.2202/1544-6115.1437
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1544-6115.1437
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.2202/1544-6115.1437?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Shinichi Nakagawa, 2004. "A farewell to Bonferroni: the problems of low statistical power and publication bias," Behavioral Ecology, International Society for Behavioral Ecology, vol. 15(6), pages 1044-1045, November.
    2. Stephen Olejnik & Jianmin Li & Suchada Supattathum & Carl J. Huberty, 1997. "Multiple Testing and Statistical Power With Modified Bonferroni Procedures," Journal of Educational and Behavioral Statistics, , vol. 22(4), pages 389-406, December.
    3. Christopher R. Genovese & Kathryn Roeder & Larry Wasserman, 2006. "False discovery control with p-value weighting," Biometrika, Biometrika Trust, vol. 93(3), pages 509-524, September.
    4. Rubin Daniel & Dudoit Sandrine & van der Laan Mark, 2006. "A Method to Increase the Power of Multiple Testing Procedures Through Sample Splitting," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 5(1), pages 1-20, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Stephen Wai Hang Kwok & Paul Hong Lee & Regina Lai Tong Lee, 2017. "Smart Device Use and Perceived Physical and Psychosocial Outcomes among Hong Kong Adolescents," IJERPH, MDPI, vol. 14(2), pages 1-31, February.
    2. Edsel Peña & Joshua Habiger & Wensong Wu, 2015. "Classes of multiple decision functions strongly controlling FWER and FDR," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 563-595, July.
    3. Yi Nengjun & Xu Shizhong & Lou Xiang-Yang & Mallick Himel, 2014. "Multiple comparisons in genetic association studies: a hierarchical modeling approach," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(1), pages 35-48, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michael A. Langston & Robert S. Levine & Barbara J. Kilbourne & Gary L. Rogers & Anne D. Kershenbaum & Suzanne H. Baktash & Steven S. Coughlin & Arnold M. Saxton & Vincent K. Agboto & Darryl B. Hood &, 2014. "Scalable Combinatorial Tools for Health Disparities Research," IJERPH, MDPI, vol. 11(10), pages 1-25, October.
    2. Nikolaos Ignatiadis & Wolfgang Huber, 2021. "Covariate powered cross‐weighted multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 720-751, September.
    3. Habiger, Joshua D. & Peña, Edsel A., 2014. "Compound p-value statistics for multiple testing procedures," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 153-166.
    4. Gerad A Fox & Allen M Cooper & William K Hayes, 2015. "The Dilemma of Choosing a Reference Character for Measuring Sexual Size Dimorphism, Sexual Body Component Dimorphism, and Character Scaling: Cryptic Dimorphism and Allometry in the Scorpion Hadrurus a," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-23, March.
    5. Tommaso Proietti, 2016. "On the Selection of Common Factors for Macroeconomic Forecasting," Advances in Econometrics, in: Dynamic Factor Models, volume 35, pages 593-628, Emerald Group Publishing Limited.
    6. Fullman, Timothy J. & Bunting, Erin L. & Kiker, Gregory A. & Southworth, Jane, 2017. "Predicting shifts in large herbivore distributions under climate change and management using a spatially-explicit ecosystem model," Ecological Modelling, Elsevier, vol. 352(C), pages 1-18.
    7. Edsel Peña & Joshua Habiger & Wensong Wu, 2015. "Classes of multiple decision functions strongly controlling FWER and FDR," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 563-595, July.
    8. Bunting, Erin L. & Fullman, Timothy & Kiker, Gregory & Southworth, Jane, 2016. "Utilization of the SAVANNA model to analyze future patterns of vegetation cover in Kruger National Park under changing climate," Ecological Modelling, Elsevier, vol. 342(C), pages 147-160.
    9. Nicola-Anne J Rutkowski & Yong Zhi Foo & Therésa M Jones & Kathryn B McNamara, 2023. "Age, but not an immune challenge, triggers terminal investment in the Pacific field cricket, Teleogryllus oceanicus," Behavioral Ecology, International Society for Behavioral Ecology, vol. 34(3), pages 468-479.
    10. Roberto Bonanni & Simona Cafazzo & Arianna Abis & Emanuela Barillari & Paola Valsecchi & Eugenia Natoli, 2017. "Age-graded dominance hierarchies and social tolerance in packs of free-ranging dogs," Behavioral Ecology, International Society for Behavioral Ecology, vol. 28(4), pages 1004-1020.
    11. R. C. Rodríguez-Caro & E. Graciá & S. P. Blomberg & H. Cayuela & M. Grace & C. P. Carmona & H. A. Pérez-Mendoza & A. Giménez & R. Salguero-Gómez, 2023. "Anthropogenic impacts on threatened species erode functional diversity in chelonians and crocodilians," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    12. Jelle J Goeman & Aldo Solari, 2024. "On selection and conditioning in multiple testing and selective inference," Biometrika, Biometrika Trust, vol. 111(2), pages 393-416.
    13. Tilov, Ivan & Weber, Sylvain, 2023. "Heterogeneity in price elasticity of vehicle kilometers traveled: Evidence from micro-level panel data," Energy Economics, Elsevier, vol. 127(PA).
    14. Yankol-Schalck, Meryem, 2022. "The value of cross-data set analysis for automobile insurance fraud detection," Research in International Business and Finance, Elsevier, vol. 63(C).
    15. R. Nicholas Carleton & Tracie O. Afifi & Tamara Taillieu & Sarah Turner & Julia E. Mason & Rosemary Ricciardelli & Donald R. McCreary & Adam D. Vaughan & Gregory S. Anderson & Rachel L. Krakauer & Eli, 2020. "Assessing the Relative Impact of Diverse Stressors among Public Safety Personnel," IJERPH, MDPI, vol. 17(4), pages 1-25, February.
    16. Christopher G. Murphy, 2012. "Simultaneous mate-sampling by female barking treefrogs (Hyla gratiosa)," Behavioral Ecology, International Society for Behavioral Ecology, vol. 23(6), pages 1162-1169.
    17. Andrew Y. Chen & Tom Zimmermann, 2022. "Publication Bias in Asset Pricing Research," Papers 2209.13623, arXiv.org, revised Sep 2023.
    18. Chambers, Ruth M. & Brocato, Jo & Fatemi, Maryam & Rodriguez, Angel Y., 2016. "An innovative child welfare pilot initiative: Results and outcomes," Children and Youth Services Review, Elsevier, vol. 70(C), pages 143-151.
    19. Dana M. Williams & Diogo S.M. Samia & William E. Cooper & Daniel T. Blumstein, 2014. "The flush early and avoid the rush hypothesis holds after accounting for spontaneous behavior," Behavioral Ecology, International Society for Behavioral Ecology, vol. 25(5), pages 1136-1147.
    20. Paul E. Bourdeau, 2013. "Morphological defense influences absolute, not relative, nonconsumptive effects in marine snails," Behavioral Ecology, International Society for Behavioral Ecology, vol. 24(2), pages 505-510.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:sagmbi:v:8:y:2009:i:1:n:23. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.