Gómez Villegas, Miguel A. and Ausin, A.C and Gonzalez-Perez, B. and Rodríguez-Bernal, María Teresa and Salazar, I. and Sanz San Miguel, Luis
(2011)
*Bayesian Analysis of Multiple Hypothesis Testing with Applications to Microarray Experiments.*
Communications in statistics. Theory and methods, 40
(13).
pp. 2276-2291.
ISSN 0361-0926

PDF
Restringido a Repository staff only hasta 2020. 504kB |

Official URL: http://www.tandfonline.com/loi/lsta20

## Abstract

Recently, the field of multiple hypothesis testing has experienced a great expansion, basically because of the new methods developed in the field of genomics.

These new methods allow scientists to simultaneously process thousands of hypothesis tests.

The frequentist approach to this problem is made by using different testing error measures that allow to control the Type I error rate at a certain desired level. Alternatively, in this article, a Bayesian hierarchical model based on mixture distributions and an empirical Bayes approach are proposed in order to produce a list of rejected hypotheses that will be declared significant and interesting for a more detailed posterior analysis.

In particular, we develop a straightforward implementation of a Gibbs sampling scheme where all the conditional posterior distributions are explicit.

The results are compared with the frequentist False Discovery Rate (FDR) methodology. Simulation examples show that our model improves the FDR procedure in the sense that it diminishes the percentage of false negatives keeping an acceptable percentage of false positives.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Empirical Bayes methods; False discovery rate; Gibbs sampler; Mixture models; Multiple hypothesis testing;False Discovery Rate; Gene-Expression; Empirical Bayes; Model;Statistics & Probability |

Subjects: | Sciences > Mathematics > Mathematical statistics |

ID Code: | 15635 |

References: | Alon, U., Barkai, N., Notterman, D. A., Gish, K., Ybarra, S., Mack, D., Levine, A. J. (1999).Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proc. Natn. Acad. Sci. USA 96:6745–6750. Bansal, N. K. (2007). Decision theoretic Bayesian hypothesis testing with the selection goal. Statist. Dec. 25:19–39. Barbieri, M., Berger, J. (2004). Optimal predictive model selection. Ann. Statist. 32:870–897. Benjamini, Y., Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. Roy. Statist. Soc. Ser. B 57:289–300. Casella, G. (2001). Empirical Bayes Gibbs sampling. Biostatistics 2(4):485–500. Datta, S., Datta, S. (2005). Empirical Bayes screening of many p-values with applications to microarray studies. Bioinformatics 21(9):1987–1944. Do, K.-A., Müller, P., Tang, F. (2005).A nonparametric Bayesian mixture model for gene expression. J. Roy. Statist. Soc. C 54(3):627–644. Dudoit, S., Shaffer, J. P., Boldrick, J. C. (2003). Multiple hypothesis testing in microarray experiments. Statist. Sci. 18(1):71–103.Efron, B. (2003). Robbins, empirical Bayes and microarrays. Ann. Statist. 31:366–378. Efron, B., Tibshirani, R. (2007). On testing the significance of sets of genes. Ann. Appl. Statist. 1(1):107–129. Efron, B., Tibshirani, R., Storey, J. D., Tusher, V. (2001). Empirical Bayes analysis of a microarray experiment. J. Amer. Statist. Assoc. 96:1151–1160. Gordon, A., Glazko, G., Qiu, X., Ykovlev, A. (2007). Control of the mean number of false discoveries, Bonferroni and stability of multiple testing. Ann. Appl. Statist. 1(1):179–190. Kendziorski, C. M., Newton, M. A., Lan, H., Gould, M. N. (2003). On parametric empirical Bayes methods for comparing multiple groups using replicated gene expression profiles. Statist. Med. 22:3899–3914. Lönnstedt, I., Britton, T. (2005). Hierarchical Bayes models for cDNA microarray gene expression. Biostatistics 6:279–291. Newton, M. A., Kendziorski, C. M., Richmond, C. S., Blatter, F. R., Tsui, K. W. (2001). On differential variability of expression ratios: improving statistical inference about gene expression changes from microarray data. J. Comp. Biol. 8:37–52. Robert, C. P., Casella, G. (2004). Monte Carlo Statistical Methods. 2nd ed. New York: Springer. Robbins, H. (1956). An empirical Bayes approach to statistics. Proc. Third Berkeley Symp. Math. Statist. Probab. Vol. 1. Berkeley: University California Press, pp. 157–163. Robbins, H. (1964). The empirical Bayes approach to statistical decision problems. Ann. Math. Statist. 35:1–20. Scott, J. G., Berger, J. O. (2006). An exploration of aspects of Bayesian multiple testing. J. Statist. Plan. Infer. 136:2144–2162. Shaffer, J. P. (1995). Multiple hypothesis testing: a review. Ann. Rev. Psychol. 46:561–584. Storey, J. D. (2003). The positive false discovery rate: a Bayesian interpretation and the q-value. Ann. Statist. 31(6):2013–2035. Sun, W., Cai, T. (2007). Oracle and adaptive compound decision rules for false discovery rate control. J. Amer. Statist. Assoc. 102(479):901–912. Waller, R. A., Duncan, D. B. (1969). A Bayes rule for the symmetric multiple comparison problem. J. Amer. Statist. Assoc. 64:1484–1503. |

Deposited On: | 14 Jun 2012 10:37 |

Last Modified: | 04 Mar 2016 16:15 |

Repository Staff Only: item control page