  This manuscript investigates unconditional and conditional-on-stopping
maximum likelihood estimators (MLEs), information measures and information loss
associated with conditioning in group sequential designs (GSDs). The
possibility of early stopping brings truncation to the distributional form of
MLEs; sequentially, GSD decisions eliminate some events from the sample space.
Multiple testing induces mixtures on the adapted sample space. Distributions of
MLEs are mixtures of truncated distributions. Test statistics that are
asymptotically normal without GSD, have asymptotic distributions, under GSD,
that are non-normal mixtures of truncated normal distributions under local
alternatives; under fixed alternatives, asymptotic distributions of test
statistics are degenerate. Estimation of various statistical quantities such as
information, information fractions, and confidence intervals should account for
the effect of planned adaptations. Calculation of adapted information fractions
requires substantial computational effort. Therefore, a new GSD is proposed in
which stage-specific sample sizes are fully determined by desired operational
characteristics, and calculation of information fractions is not needed.
