their cumulative versions $\mathbf{Z}=\left(Z_{(1)},\ldots,Z_{(K)}\right)$, holds without sequential adaptations. The use of an early stopping criterion, however, eliminates the possibility of some realizations of $\mathbf{Z}$. On its true *adaptation-rule driven support*, the distribution of $\mathbf{Z}$ differs from normal. Thus, unadapted distributional assumptions should be considered together with the planned adaptation scheme to identify the adaptation-rule driven support of $\mathbf{Z}$ and its distribution on this adapted support.

Many indications that joint normality does not hold after interim adaptations have been reported. @Demets1994 pointed out that the distribution of $Z_{(k)}$ is not normal and should be estimated recursively. @jennison1999 plotted the density of a normal test statistic in GSD settings, where discontinuity points clearly showed non-normality. @Li2002 found the joint density of stage 1 and stage 2 standardized test statistics not to be bivariate normal. Local asymptotic non-normality was established following sample size recalculations (SSRs) that depend on an interim observed treatment effect \[@Tarima2019\]; and a GSD with a single interim analysis can be viewed as a special case of an SSR. Maximum likelihood estimators (MLEs) converging to random mixtures of normal variables have been found in other adaptive designs \[@Ivanova2000, @Ivanova2001, @May2010, @Lane2012\].

In studying estimation, several authors have investigated the effect 