IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0206902.html
   My bibliography  Save this article

Estimating the local false discovery rate via a bootstrap solution to the reference class problem

Author

Listed:
  • Farnoosh Abbas-Aghababazadeh
  • Mayer Alvo
  • David R Bickel

Abstract

Methods of estimating the local false discovery rate (LFDR) have been applied to different types of datasets such as high-throughput biological data, diffusion tensor imaging (DTI), and genome-wide association (GWA) studies. We present a model for LFDR estimation that incorporates a covariate into each test. Incorporating the covariates may improve the performance of testing procedures, because it contains additional information based on the biological context of the corresponding test. This method provides different estimates depending on a tuning parameter. We estimate the optimal value of that parameter by choosing the one that minimizes the estimated LFDR resulting from the bias and variance in a bootstrap approach. This estimation method is called an adaptive reference class (ARC) method. In this study, we consider the performance of ARC method under certain assumptions on the prior probability of each hypothesis test as a function of the covariate. We prove that, under these assumptions, the ARC method has a mean squared error asymptotically no greater than that of the other method where the entire set of hypotheses is used and assuming a large covariate effect. In addition, we conduct a simulation study to evaluate the performance of estimator associated with the ARC method for a finite number of hypotheses. Here, we apply the proposed method to coronary artery disease (CAD) data taken from a GWA study and diffusion tensor imaging (DTI) data.

Suggested Citation

  • Farnoosh Abbas-Aghababazadeh & Mayer Alvo & David R Bickel, 2018. "Estimating the local false discovery rate via a bootstrap solution to the reference class problem," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-15, November.
    • Handle: RePEc:plo:pone00:0206902
    DOI: 10.1371/journal.pone.0206902
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0206902
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0206902&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0206902?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
    ---><---

    References listed on IDEAS

    as
    1. Efron B. & Tibshirani R. & Storey J.D. & Tusher V., 2001. "Empirical Bayes Analysis of a Microarray Experiment," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1151-1160, December.
    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. Pounds Stanley B. & Gao Cuilan L. & Zhang Hui, 2012. "Empirical Bayesian Selection of Hypothesis Testing Procedures for Analysis of Sequence Count Expression Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(5), pages 1-32, October.
    2. 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.
    3. 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.
    4. Daniel Yekutieli, 2015. "Bayesian tests for composite alternative hypotheses in cross-tabulated data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 287-301, June.
    5. Ghosh Debashis, 2012. "Incorporating the Empirical Null Hypothesis into the Benjamini-Hochberg Procedure," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-21, July.
    6. Yu Lianbo & Gulati Parul & Fernandez Soledad & Pennell Michael & Kirschner Lawrence & Jarjoura David, 2011. "Fully Moderated T-statistic for Small Sample Size Gene Expression Arrays," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-22, September.
    7. Werft, W. & Benner, A. & Kopp-Schneider, A., 2012. "On the identification of predictive biomarkers: Detecting treatment-by-gene interaction in high-dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1275-1286.
    8. HyungJun Cho & Jaewoo Kang & Jae Lee, 2009. "Empirical Bayes analysis of unreplicated microarray data," Computational Statistics, Springer, vol. 24(3), pages 393-408, August.
    9. He, Yi & Pan, Wei & Lin, Jizhen, 2006. "Cluster analysis using multivariate normal mixture models to detect differential gene expression with microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 641-658, November.
    10. Hossain Ahmed & Beyene Joseph, 2013. "Estimation of weighted log partial area under the ROC curve and its application to MicroRNA expression data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(6), pages 743-755, December.
    11. Kafadar, Karen & Phang, Tzulip, 2003. "Transformations, background estimation, and process effects in the statistical analysis of microarrays," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 313-338, October.
    12. Gordon, Alexander & Chen, Linlin & Glazko, Galina & Yakovlev, Andrei, 2009. "Balancing type one and two errors in multiple testing for differential expression of genes," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1622-1629, March.
    13. Cipolli III, William & Hanson, Timothy & McLain, Alexander C., 2016. "Bayesian nonparametric multiple testing," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 64-79.
    14. Volodymyr Melnykov & Xuwen Zhu, 2019. "An extension of the K-means algorithm to clustering skewed data," Computational Statistics, Springer, vol. 34(1), pages 373-394, March.
    15. Guo Wenge & Peddada Shyamal, 2008. "Adaptive Choice of the Number of Bootstrap Samples in Large Scale Multiple Testing," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-21, March.
    16. Dazard, Jean-Eudes & Sunil Rao, J., 2012. "Joint adaptive mean–variance regularization and variance stabilization of high dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2317-2333.
    17. Alessio Farcomeni, 2006. "More Powerful Control of the False Discovery Rate Under Dependence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(1), pages 43-73, May.
    18. Bickel David R., 2012. "Empirical Bayes Interval Estimates that are Conditionally Equal to Unadjusted Confidence Intervals or to Default Prior Credibility Intervals," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(3), pages 1-34, February.
    19. Nik Tuzov & Frederi Viens, 2011. "Mutual fund performance: false discoveries, bias, and power," Annals of Finance, Springer, vol. 7(2), pages 137-169, May.
    20. Leek Jeffrey T & Storey John D., 2011. "The Joint Null Criterion for Multiple Hypothesis Tests," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-22, June.

    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:plo:pone00:0206902. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.