An Improved Hommel-Hochberg Hybrid Procedure

• Activity Number: 661
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Jiangtao Gou*+ and Dror Rom and Ajit C. Tamhane and Dong Xi
• Companies: Northwestern University and Prosoft Software, Inc. and Northwestern University and Northwestern University
• Keywords: Multiple comparisons ; Hochberg procedure ; Hommel procedure ; Familywise error rate

Abstract

Let p1,p2,.,pn be independent p-values associated with null hypotheses H1,H2,.,Hn, and let p(1),p(2),.,p(n) be the ordered p-values with H(1),H(2),.,H(n) the corresponding null hypotheses. We want to test H1,H2,.,Hn at the familywise error rate (FWER) level a. Hochberg's (1988) procedure uses a simple step-up algorithm which tests the hypotheses beginning with H(n) and stops and rejects all remaining hypotheses in the sequence if at step i, p(n-i+1) < a/i. Hommel's (1988) procedure is more powerful than Hochberg's but uses a more complicated algorithm: if at step i, p(n-j+1) < (i-j+1)a/i for at least one j = 1,.,i then it rejects all hypotheses with pj < a/(i-1). We propose a procedure that combines the simple step-up algorithm of Hochberg with Hommel's rejection rule: if at step i, p(n-i+1) < ci*a and then reject all hypotheses with pj < a/i. We show that this procedure controls the FWER if ci = (i+1)a/2i; more exact values can be numerically computed of which these values are limits. Power comparisons are made via simulation with competing procedures including that of Rom (1990).