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Statistics Seminar Series
Wednesday, Sept. 12, 2012, 4:00 PM
Cullimore, Room 611
New Jersey Institute of Technology
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A class of generalized fixed sequence procedures
controlling the FWER under dependence
Zhiying Qiu
Department of Mathematical Sciences, New Jersey Institute of Technology
Abstract
Often, in applications of clinical trials,
the hypotheses to be tested are hierarchically ordered based on their
importance, clinical relevance, or dose concentration, etc, and thus are tested
in a pre-defined sequential order. Although such problem of fixed
sequence multiple testing has received much attention and several popular FWER
controlling procedures such as conventional fixed sequence procedure and
Fallback procedure have been introduced, not much progress has been made yet
advancing its theory and methods.
In this research, we first introduce a class of
generalized fixed sequence procedures whose critical constants are described by
using a function of the numbers of rejections and acceptances, and which allow
each hypothesis to be tested even though some early hypotheses in the sequence
are not rejected. Then, we discuss constructing the least favorable
configuration of these procedures under which the FWER is maximized, and find
out that it is some Dirac-Uniform configuration. Based on such constructed
configuration, we present a necessary and sufficient condition of a given
generalized fixed sequence procedure can strongly control the FWER under
arbitrary dependence. Based on the condition, we develop three specific
generalized fixed sequence procedures controlling the FWER. Through extensive
simulation studies, we illustrate the advantages of these procedures over the
existing FWER controlling procedures in terms of the FWER control and power.
Finally, when the pairwise joint distributions of the
true null p-values are known, we further improve these procedures by
incorporating such pairwise correlation information
while maintaining the control of the FWER.