A modified Benjamini–Hochberg multiple comparisons procedure for controlling the false discovery rate

When performing simultaneous statistical tests, the Type I error concept most commonly controlled by analysts is the familywise error rate, i.e., the probability of committing at least one Type I error. However, this criterion is unduly stringent for some practical situations and therefore may not be appropriate. An alternative concept of error control was provided by Benjamini and Hochberg (J. Roy. Statist. Soc. B 57 (1995) 289) who advocate control of the expected proportion of falsely rejected hypotheses which they term the false discovery rate or FDR. These authors devised a step-up procedure for controlling the FDR. In this article, when the joint distribution of test statistics is known, continuous, and positive regression dependent on each one from a subset of true null hypotheses, we derive and discuss a modification of their procedure which affords increased power. An example is provided to illustrate our proposed method.

[1]  Charles W. Dunnett,et al.  A Step-Up Multiple Test Procedure , 1992 .

[2]  Morris L. Eaton,et al.  Lectures on topics in probability inequalities , 1988 .

[3]  C. Dunnett.  A Multiple Comparison Procedure for Comparing Several Treatments with a Control , 1955 .

[4]  J. Tukey.  Some thoughts on clinical trials, especially problems of multiplicity. , 1977, Science.

[5]  Seymour M. Kwerel.  Most Stringent Bounds on Aggregated Probabilities of Partially Specified Dependent Probability Systems , 1975 .

[6]  Y. Benjamini,et al.  Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .

[7]  Y. Benjamini,et al.  THE CONTROL OF THE FALSE DISCOVERY RATE IN MULTIPLE TESTING UNDER DEPENDENCY , 2001 .

[8]  R. Elston,et al.  False discoveries in genome scanning , 1997, Genetic epidemiology.

[9]  Calculation of critical values for Dunnett and Tamhane's step-up multiple test procedure , 2000 .

[10]  John W. Tukey,et al.  Controlling Error in Multiple Comparisons, with Examples from State-to-State Differences in Educational Achievement , 1999 .

[11]  Koon Shing Kwong.  An algorithm for construction of multiple hypothesis testing , 2001, Comput. Stat..

[12]  A. Tamhane,et al.  Step-up multiple testing of parameters with unequally correlated estimates. , 1995, Biometrics.

[13]  S. Sarkar,et al.  The Simes Method for Multiple Hypothesis Testing with Positively Dependent Test Statistics , 1997 .

[14]  Y. Benjamini,et al.  On the Adaptive Control of the False Discovery Rate in Multiple Testing With Independent Statistics , 2000 .

[15]  J. Troendle,et al.  Stepwise normal theory multiple test procedures controlling the false discovery rate , 2000 .

[16]  Y. Benjamini,et al.  Resampling-based false discovery rate controlling multiple test procedures for correlated test statistics , 1999 .