  Group sequential design (GSD) is widely used in clinical trials in which
correlated tests of multiple hypotheses are used. Multiple primary objectives
resulting in tests with known correlations include evaluating 1) multiple
experimental treatment arms, 2) multiple populations, 3) the combination of
multiple arms and multiple populations, or 4) any asymptotically multivariate
normal tests. In this paper, we focus on the first 3 of these and extend the
framework of the weighted parametric multiple test procedure from fixed designs
with a single analysis per objective to a GSD setting where different
objectives may be assessed at the same or different times, each in a group
sequential fashion. Pragmatic methods for design and analysis of weighted
parametric group sequential design(WPGSD) under closed testing procedures are
proposed to maintain the strong control of familywise Type I error rate (FWER)
when correlations between tests are incorporated. This results in the ability
to relax testing bounds compared to designs not fully adjusting for known
correlations, increasing power or allowing decreased sample size. We illustrate
the proposed methods using clinical trial examples and conduct a simulation
study to evaluate the operating characteristics.
