Affiliations: [a] Food and Drug Administration, Silver Spring, MD, USA | [b] SAS Institute Inc., NC, USA
Correspondence:
[*]
Corresponding author: Boris G. Zaslavsky, Food and Drug Administration, 10903 New Hampshire Avenue Building #71 Room 1248, Silver Spring, MD 20993-0002, USA. Tel.: +1 240 402 8842; Fax: +1 301 595 1240; E-mail:[email protected]
Abstract: Statistical analyses of commonly occurring clinical trials that have
correlated primary endpoints are often complex because multiple comparison
adjustments are necessary. In practice, most statisticians resort to
numerical simulation, even though such approaches can be computationally
demanding and are often restricted to specific scenarios. The paper provides
an analytical approach to one-sided multiple comparisons adjustment for mean
values of multivariate normal data that have known positive definite
covariance matrices. We use the maximum of test statistics to control the
familywise error rate (FWER). This approach is equivalent to adjusting the
minimum p-value but is simple to use and enables analytical evaluation. We
derive a formula for the cumulative probability functions (CDFs) of the
maximal test statistics when the correlations are known to be sufficiently
small. When the correlations are considered to be more pronounced, we
provide majorizing inequalities for the CDFs of the maximal test statistics.
In addition, we address calculation of power and testing of conditional
hypotheses for correlated primary endpoints. Theoretical results are
illustrated by examples and are supported by extensive numerical studies.
Keywords: Significance level, multivariate normal distribution, maximal statistics, multiple testing, conditional distribution
