for $\bar X_1$ starts at $2.18\sqrt{100}=0.218 $ and stretches to $+\infty$. If the study continues through stage 2, support for $\bar X_1$ ranges from $-\infty$ to $0.218$. However, it is still possible to obtain a conditional MLE outside the range of support, that is, above or below $0.218$ at stage 1. Figure \[likelihood\] shows that conditional likelihoods do not allow accurate estimation of $\theta$ when observed $Z_1$ is close to the critical value for deciding to stop, and the conditional MLEs start diverging to $\pm \infty$.

In GSDs, the “information fraction” is used to justify times or sample sizes of interim analyses. In two-stage designs, the information fraction is often estimated as ${\cal{I}}_{(1)}^{fix}/{\cal{I}}_{(2)}^{fix}$, which in the Pocock example is equal to $1/2$ since ${\cal{I}}_{(1)}^{fix}=100$ and ${\cal{I}}_{(2)}^{fix} = 200$. This information fraction argument silently assumes that study stops at a pre-determined sample size. In Figure \[FisherInf\], ${\cal{I}}_{(1)}^{fix}$ and ${\cal{I}}_{(2)}^{fix}$ are plotted as a function of $\theta$ with dotted horizontal lines. Figure \[FisherInf\] also graphs information in conditional and unconditional likelihoods.

New Group Sequential Designs Relying on Mixture Distributions {#mixtureD}
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Even though the normality does not hold when there is a possibility of early stopping, the critical values for controlling type 