Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Published
A New Method for Detecting Significant p-values with Applications to Genetic Data
Un nuevo método para la detección de valores p significativos y su aplicación a datos genéticos
DOI:
https://doi.org/10.15446/rce.v37n1.44358Keywords:
Extreme values theory, p-value, Type I error probability, Multiple testing, Genetic data (en)teoría de valores extremos, valor-p, probabilidad de error tipo I, comparaciones múltiples, datos genéticos (es)
A new method for detecting significant p-values is described in this paper. This method, based on the distribution of the m-th order statistic of a U(0; 1) distribution, is shown to be suitable in applications where m ! 1 independent hypothesis are tested and it is of interest for a fixed type I error probability to determine those being significant while controlling the false positives. Equivalencies and comparisons between our method and others methods based-on p-values are also established, and a graphical representation of the distribution of the test statistic is depicted for different values of m. Finally, our proposal is illustrated with two microarray data sets.
Se describe una nuevo método para la detección de valores p significativos. Este método, basado en el m-ésimo estadístico de orden de la distribución U(0; 1), es adecuado en casos en los que se realizan m ! 1 pruebas de hipótesis independientes y es de interés determinar aquellas que son significativas, controlando los falsos positivos, para una probabilidad de error tipo I predeterminada. Adicionalmente, se realiza una comparación con algunas pruebas clásicas y se grafica la distribución del estadístico de prueba para diferentes valores de m. Finalmente se ilustra el uso de la metodología con dos conjuntos de datos provenientes de estudios con microarreglos.
Downloads
References
Benjamini, Y. & Hochberg, Y. (1995), 'Controlling the false discovery rate: a practical and powerful approach to multiple testing', Journal of the Royal Statistical Society, Series B (Methodological) 57(1), 389-300.
Benjamini, Y. & Yekutieli, D. (2001), 'The control of the false discovery rate in multiple testing under dependency', Annals of Statistics 29(4), 1165 - 1188.
Bonferroni, C. E. (1935), 'Il calcolo delle assicurazioni su gruppi di teste', Studi in Onore del Professore Salvatore Ortu Carboni,, 13-60.
Casella, G. & Berger, R. (2001), Statistical Inference, 2 edn, Duxbury Press, United States of America.
Devroye, L. (1986), Non-Uniform Random Variate Generation, New York: Spring-Verlang.
Gentleman, R., Carey, V., Huber, W. & Hahne, F. (2011), genefilter: Methods for filtering genes from microarray experiments. R package version 1.34.0.
Golub, T., Slonim, D., Tamayo, P., Huard, C., Gaasenbeek, M., Mesirov, J., Coller, H., Loh, M., Downing, J., Caligiuri, M., Bloomfield, C. & Lander, E. (1999), 'Molecular classification of cancer: Class discovery and class prediction by gene expression monitoring', Science 286, 531-537.
Liu, J. Z., Mcrae, A. F., Nyholt, D. R., Medland, S. E., Wray, N. R., Brown, K. M., Hayward, N. K., Montgomery, G. W., Visscher, P. M., Martin, N. G. & Macgregor, S. (2010), 'A versatile gene-based test for genome-wide association studies', The American Journal of Human Genetics 87(1), 139 - 145.
Manolio, T. A. (2010), 'Genomewide association studies and assessment of the risk of disease', New England Journal of Medicine 363(2), 166-176.
Mootha, V. K., Lindgren, C. M., Eriksson, K. F., Subramanian, A., Sihag, S., Lehar, J., Puigserver, P., Carlsson, E., Ridderstráaale, M., Laurila, E., Houstis, N., Daly, M. J., Patterson, N., Mesirov, J. P., Golub, T. R., Tamayo, P., Spiegelman, B., Lander, E. S., Hirschhorn, J. N., Altshuler, D. & Groop, L. C. (2003), 'Pgc-1álpha-responsive genes involved in oxidative phosphorylation are coordinately downregulated in human diabetes', Nature Genetics 34(3), 267-73.
Murdoch, D., Tsai, Y. & Adcock, J. (2008), 'P-values are random variables', The American Statistician 62(3), 242-245.
Nyholt, D. R. (2004), 'A simple correction for multiple testing for single-nucleotide polymorphisms in linkage disequilibrium with each other', The American Journal of Human Genetics 74(4), 765 - 769.
Pollard, K. S., Gilbert, H. N., Ge, Y., Taylor, S. & Dudoit, S. (2011), multtest: Resampling-based multiple hypothesis testing. R package version 2.8.0.
R Core Team, (2013), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. *http://www.R-project.org/
Sackrowitz, H. & Samuel-Cahn, E. (1999), 'P Values as Random Variables-Expected P Values', The American Statistician 53(4), 326-331.
Serfling, R. (1980), Approximation Theorems of Mathematical Statistics, John Wiley & Sons, United States of America.
Shaffer, J. P. (1995), 'Multiple hypothesis testing', Annual Review of Psychology 46, 561-584.
License
Copyright (c) 2014 Revista Colombiana de Estadística
This work is licensed under a Creative Commons Attribution 4.0 International License.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
