Hochberg Step-Up Multiple Test Procedure Under Negative Dependence

• Activity Number: 599
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Jiangtao Gou*+ and Ajit C Tamhane
• Companies: Northwestern University and Northwestern University
• Keywords: Hochberg Test ; Negative Dependence ; Familywise Error Rate ; Step-up Procedure

Abstract

Hochberg's (1988) step-up multiple test procedure is a conservative shortcut to Hommel's (1988) procedure which is an exact closed procedure based on Simes' (1986) identity and hence controls the familywise error rate (FWER). Simes identity was originally proven for independent test statistics. Sarkar and Chang (1997) and Sarkar (1998) later showed that it is a conservative inequality if the test statistics have certain positively dependent distributions. So Hommel's (1988) procedure and hence Hochberg's procedure are conservative under positive dependence. On the other hand, Block et al (2008) showed that Simes' identity is an anti-conservative inequality for a class of negatively dependent distributions. So it is generally assumed that both Hommel's and Hochberg's procedures are anti-conservative under negative dependence. By representing the Hochberg procedure as an exact closed procedure based on a conservative version of Simes' identity, we show that it controls FWER for some negatively dependent cases. Simulations show that Hochberg's procedure controls FWER if the test statistics follow negatively equicorrelated multivariate normal distribution for four or more hypotheses.