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

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.

https://doi.org/10.15446/rce.v37n1.44358

A New Method for Detecting Significant p-values with Applications to Genetic Data Una nuevo método para la detección de valores p significativos y su aplicación a datos genéticos JORGE IVÁN VÉLEZ¹, JUAN CARLOS CORREA², MAURICIO ARCOS-BURGOS³

¹The Australian National University, Genomics and Predicitive Medicine Group, Genome Biology Department, John Curtin School of Medical Research, Canberra, ACT, Australia. University of Antioquia, Group of Neurosciences, Medellín, Colombia. National University of Colombia, Research Group in Statistics, Medellín, Colombia. Ph.D Scholar. Email: jorge.velez@anu.edu.au
²National University of Colombia, Research Group in Statistics, Medellín, Colombia. National University of Colombia, Department of Statistics, Medellín, Colombia. Associate professor. Email: jccorrea@unal.edu.co
³The Australian National University, Genomics and Predicitive Medicine Group, Genome Biology Department, John Curtin School of Medical Research, Canberra, ACT, Australia. University of Antioquia, Group of Neurosciences, Medellín, Colombia. Associate professor. Email: mauricio.arcos-burgos@anu.edu.au

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Abstract

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\rightarrow ∞ 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.

Key words: Extreme values theory, p-value, Type I error probability, Multiple testing, Genetic data.

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Resumen

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\rightarrow ∞ 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.

Palabras clave: teoría de valores extremos, valor-p, probabilidad de error tipo I, comparaciones múltiples, datos genéticos.

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[Recibido en noviembre de 2012. Aceptado en enero de 2014]

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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv37n1a05,
    AUTHOR  = {Vélez, Jorge Iván and Correa, Juan Carlos and Arcos-Burgos, Mauricio},
    TITLE   = {{A New Method for Detecting Significant p-values with Applications to Genetic Data}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2014},
    volume  = {37},
    number  = {1},
    pages   = {69-78}
}

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