The Baumgartner-Wei?-Schindler test for the detection of differentially expressed genes in replicated microarray experiments

MOTIVATION An important application of microarray experiments is to identify differentially expressed genes. Because microarray data are often not distributed according to a normal distribution nonparametric methods were suggested for their statistical analysis. Here, the Baumgartner-Weiss-Schindler test, a novel and powerful test based on ranks, is investigated and compared with the parametric t-test as well as with two other nonparametric tests (Wilcoxon rank sum test, Fisher-Pitman permutation test) recently recommended for the analysis of gene expression data. RESULTS Simulation studies show that an exact permutation test based on the Baumgartner-Weiss-Schindler statistic B is preferable to the other three tests. It is less conservative than the Wilcoxon test and more powerful, in particular in case of asymmetric or heavily tailed distributions. When the underlying distribution is symmetric the differences in power between the tests are relatively small. Thus, the Baumgartner-Weiss-Schindler is recommended for the usual situation that the underlying distribution is a priori unknown. AVAILABILITY SAS code available on request from the authors.

[1]  Peter E. Kennedy.  Randomization Tests in Econometrics , 1995 .

[2]  Russ B. Altman,et al.  Nonparametric methods for identifying differentially expressed genes in microarray data , 2002, Bioinform..

[3]  Terence P. Speed,et al.  A benchmark for Affymetrix GeneChip expression measures , 2004, Bioinform..

[4]  E. Dougherty,et al.  Gene-expression profiles in hereditary breast cancer. , 2001, The New England journal of medicine.

[5]  J. L. Rasmussen,et al.  An evaluation of parametric and non‐parametric tests on modified and non‐modified data , 1986 .

[6]  J. Thomas,et al.  An efficient and robust statistical modeling approach to discover differentially expressed genes using genomic expression profiles. , 2001, Genome research.

[7]  Markus Neuhäuser,et al.  An exact two-sample test based on the baumgartner-weiss-schindler statistic and a modification of lepage's test , 2000 .

[8]  Markus Neuhäuser.  A note on the exact test based on the Baumgartner-Weiß-Schindler statistic in the presence of ties , 2003, Comput. Stat. Data Anal..

[9]  J. J. Higgins,et al.  A Comparison of the Power of Wilcoxon's Rank-Sum Statistic to that of Student'st Statistic Under Various Nonnormal Distributions , 1980 .

[10]  Xiaochun Li,et al.  A Comparison of Parametric Versus Permutation Methods with Applications to General and Temporal Microarray Gene Expression Data , 2003, Bioinform..

[11]  Li Liu,et al.  Robust singular value decomposition analysis of microarray data , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[12]  J. J. Higgins,et al.  Effect of tail weight and outliers on power and type-i error of robust permutation tests for location , 1987 .

[13]  T. Speed,et al.  Summaries of Affymetrix GeneChip probe level data. , 2003, Nucleic acids research.

[14]  G. Gibson.  Microarrays in ecology and evolution: a preview , 2002, Molecular ecology.

[15]  Rebecca W. Doerge,et al.  Gene expression data: The technology and statistical analysis , 2003 .

[16]  Bruno D. Zumbo,et al.  The relative power of parametric and nonparametric statistical methods. , 1993 .

[17]  Gideon Keren,et al.  A Handbook for data analysis in the behavioral sciences : methodological issues , 1993 .

[18]  Michael A. Hunter,et al.  Some myths concerning parametric and nonparametric tests. , 1993 .

[19]  Ingrid Lönnstedt.  Replicated microarray data , 2001 .

[20]  John D. Storey,et al.  Statistical significance for genomewide studies , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Lawrence Hunter,et al.  GEST: a gene expression search tool based on a novel Bayesian similarity metric , 2001, ISMB.

[22]  Thomas D. Wu,et al.  Analysing gene expression data from DNA microarrays to identify candidate genes , 2001, The Journal of pathology.

[23]  Wulfert P. van den Brink,et al.  A comparison of the power of the t test, Wilcoxon's test, and the approximate permutation test for the two‐sample location problem , 1989 .

[24]  Hisashi Tanizaki,et al.  Power comparison of non-parametric tests: Small-sample properties from Monte Carlo experiments , 1997 .

[25]  C Eng,et al.  Gene expression in papillary thyroid carcinoma reveals highly consistent profiles , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Andreas Magusin.  Complementary techniques of clustering and composite pattern analysis to Saccharomyces cerevisiae gene expression. , 2003, Applied bioinformatics.

[27]  David Kipling,et al.  Normality of oligonucleotide microarray data and implications for parametric statistical analyses , 2003, Bioinform..

[28]  William Stafford Noble,et al.  The effect of replication on gene expression microarray experiments , 2003, Bioinform..

[29]  Wei Pan,et al.  Modified Nonparametric Approaches to Detecting Differentially Expressed Genes in Replicated Microarray Experiments , 2003, Bioinform..

[30]  B S Weir,et al.  Truncated product method for combining P‐values , 2002, Genetic epidemiology.

[31]  Rafael A Irizarry,et al.  Exploration, normalization, and summaries of high density oligonucleotide array probe level data. , 2003, Biostatistics.

[32]  Werner Baumgartner,et al.  A Nonparametric Test for the General Two-Sample Problem , 1998 .

[33]  Markus Neuhäuser.  One-Sided two-sample and trend tests based on a modified baumgartner-weiss-schindler statistic , 2001 .

[34]  E. Pitman.  Significance Tests Which May be Applied to Samples from Any Populations , 1937 .

[35]  Frank Dudbridge,et al.  Rank truncated product of P‐values, with application to genomewide association scans , 2003, Genetic epidemiology.

[36]  A. I.,et al.  Neural Field Continuum Limits and the Structure–Function Partitioning of Cognitive–Emotional Brain Networks , 2023, Biology.

[37]  J. J. Higgins,et al.  On the relative power of the U and t tests , 1980 .

[38]  B. Manly.  Randomization, Bootstrap and Monte Carlo Methods in Biology , 2018 .

[39]  K. Jöckel,et al.  Tumor classification based on gene expression profiling shows that uveal melanomas with and without monosomy 3 represent two distinct entities. , 2003, Cancer research.

[40]  Markus Neuhäuser,et al.  The Baumgartner-Weiss-Schindler test in the presence of ties. , 2002, Biometrics.

[41]  David B. Allison,et al.  Randomization tests for small samples: an application for genetic expression data , 2003 .

[42]  Wei Pan,et al.  A comparative review of statistical methods for discovering differentially expressed genes in replicated microarray experiments , 2002, Bioinform..