IDEAS home Printed from https://ideas.repec.org/a/bpj/sagmbi/v13y2014i3p24n2.html
   My bibliography  Save this article

A novel characterization of the generalized family wise error rate using empirical null distributions

Author

Listed:
  • Miecznikowski Jeffrey C.

    (Department of Biostatistics, SUNY University at Buffalo, 433 Kimball Tower, 3435 Main St., Buffalo, NY 14214, USA)

  • Gaile Daniel P.

    (Department of Biostatistics, SUNY University at Buffalo, 706 Kimball Tower, 3435 Main St., Buffalo, NY 14214, USA)

Abstract

We present a novel characterization of the generalized family wise error rate: kFWER. The interpretation allows researchers to view kFWER as a function of the test statistics rather than current methods based on p-values. Using this interpretation we present several theorems and methods (parametric and non-parametric) for estimating kFWER in various data settings. With this version of kFWER, researchers will have an estimate of kFWER in addition to knowing what tests are significant at the estimated kFWER. Additionally, we present methods that use empirical null distributions in place of parametric distributions in standard p-value kFWER controlling schemes. These advancements represent an improvement over common kFWER methods which are based on parametric assumptions and merely report the tests that are significant under a given value for kFWER.

Suggested Citation

  • Miecznikowski Jeffrey C. & Gaile Daniel P., 2014. "A novel characterization of the generalized family wise error rate using empirical null distributions," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(3), pages 1-24, June.
    • Handle: RePEc:bpj:sagmbi:v:13:y:2014:i:3:p:24:n:2
    DOI: 10.1515/sagmb-2013-0032
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/sagmb-2013-0032
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/sagmb-2013-0032?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. Guo Wenge & Romano Joseph, 2007. "A Generalized Sidak-Holm Procedure and Control of Generalized Error Rates under Independence," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 6(1), pages 1-35, January.
    2. Joseph P. Romano & Michael Wolf, 2005. "Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 94-108, March.
    3. L. Finos & A. Farcomeni, 2011. "k-FWER Control without p -value Adjustment, with Application to Detection of Genetic Determinants of Multiple Sclerosis in Italian Twins," Biometrics, The International Biometric Society, vol. 67(1), pages 174-181, March.
    4. Sandrine Dudoit & Mark van der Laan & Katherine Pollard, 2004. "Multiple Testing. Part I. Single-Step Procedures for Control of General Type I Error Rates," U.C. Berkeley Division of Biostatistics Working Paper Series 1137, Berkeley Electronic Press.
    5. Dudoit Sandrine & van der Laan Mark J. & Pollard Katherine S., 2004. "Multiple Testing. Part I. Single-Step Procedures for Control of General Type I Error Rates," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-71, June.
    6. Miecznikowski, Jeffrey C. & Gold, David & Shepherd, Lori & Liu, Song, 2011. "Deriving and comparing the distribution for the number of false positives in single step methods to control k-FWER," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1695-1705, November.
    7. Jin, Jiashun & Cai, T. Tony, 2007. "Estimating the Null and the Proportion of Nonnull Effects in Large-Scale Multiple Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 495-506, June.
    8. Efron, Bradley, 2007. "Correlation and Large-Scale Simultaneous Significance Testing," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 93-103, March.
    Full references (including those not matched with items on IDEAS)

    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. Miecznikowski, Jeffrey C. & Gold, David & Shepherd, Lori & Liu, Song, 2011. "Deriving and comparing the distribution for the number of false positives in single step methods to control k-FWER," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1695-1705, November.
    2. Joseph P. Romano & Michael Wolf, 2008. "Balanced Control of Generalized Error Rates," IEW - Working Papers 379, Institute for Empirical Research in Economics - University of Zurich.
    3. Wen Shi & Xi Chen & Jennifer Shang, 2019. "An Efficient Morris Method-Based Framework for Simulation Factor Screening," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 745-770, October.
    4. Hossain, Ahmed & Beyene, Joseph & Willan, Andrew R. & Hu, Pingzhao, 2009. "A flexible approximate likelihood ratio test for detecting differential expression in microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3685-3695, August.
    5. Christina C. Bartenschlager & Michael Krapp, 2015. "Theorie und Methoden multipler statistischer Vergleiche," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 9(2), pages 107-129, November.
    6. Merrill Birkner & Sandra Sinisi & Mark van der Laan, 2004. "Multiple Testing and Data Adaptive Regression: An Application to HIV-1 Sequence Data," U.C. Berkeley Division of Biostatistics Working Paper Series 1161, Berkeley Electronic Press.
    7. Lim Johan & Kim Jayoun & Kim Sang-cheol & Yu Donghyeon & Kim Kyunga & Kim Byung Soo, 2012. "Detection of Differentially Expressed Gene Sets in a Partially Paired Microarray Data Set," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(3), pages 1-30, February.
    8. Yoshiyuki Ninomiya & Hironori Fujisawa, 2007. "A Conservative Test for Multiple Comparison Based on Highly Correlated Test Statistics," Biometrics, The International Biometric Society, vol. 63(4), pages 1135-1142, December.
    9. Christopher J. Bennett, 2009. "p-Value Adjustments for Asymptotic Control of the Generalized Familywise Error Rate," Vanderbilt University Department of Economics Working Papers 0905, Vanderbilt University Department of Economics.
    10. Wang, Li, 2022. "New testing procedures with k-FWER control for discrete data," Statistics & Probability Letters, Elsevier, vol. 180(C).
    11. 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.
    12. Schumi Jennifer & DiRienzo A. Gregory & DeGruttola Victor, 2008. "Testing for Associations with Missing High-Dimensional Categorical Covariates," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-17, September.
    13. Li Wang, 2019. "Weighted multiple testing procedure for grouped hypotheses with k-FWER control," Computational Statistics, Springer, vol. 34(2), pages 885-909, June.
    14. van der Laan Mark J. & Hubbard Alan E., 2006. "Quantile-Function Based Null Distribution in Resampling Based Multiple Testing," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 5(1), pages 1-30, May.
    15. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Rute M. Caeiro & Pedro C. Vicente, 2020. "Knowledge of vitamin A deficiency and crop adoption: Evidence from a field experiment in Mozambique," Agricultural Economics, International Association of Agricultural Economists, vol. 51(2), pages 175-190, March.
    17. Jessamyn Schaller & Mariana Zerpa, 2019. "Short-Run Effects of Parental Job Loss on Child Health," American Journal of Health Economics, MIT Press, vol. 5(1), pages 8-41, Winter.
    18. Mayya Zhilova, 2015. "Simultaneous likelihood-based bootstrap confidence sets for a large number of models," SFB 649 Discussion Papers SFB649DP2015-031, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    19. Jaschke Philipp & Sulin Sardoschau & Marco Tabellini, 2021. "Scared Straight? Threat and Assimilation of Refugees in Germany," RF Berlin - CReAM Discussion Paper Series 2136, Rockwool Foundation Berlin (RF Berlin) - Centre for Research and Analysis of Migration (CReAM).
    20. Fabian Kosse & Thomas Deckers & Pia Pinger & Hannah Schildberg-Hörisch & Armin Falk, 2020. "The Formation of Prosociality: Causal Evidence on the Role of Social Environment," Journal of Political Economy, University of Chicago Press, vol. 128(2), pages 434-467.

    More about this item

    Statistics

    Access and download statistics

    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:13:y:2014:i:3:p:24:n:2. 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.