= Solution
Conditioning on continuation selects the upper part of the stage-1 <estimator>'s distribution, since $C=\{\widehat\delta_1\geq f_1/\sqrt{I_1}\}$. Thus $\mathbb E_\delta(\widehat\delta_1\mid C)>\delta$ for every finite threshold. The fresh stage-2 estimate $\widehat\delta_2^*$ is independent of $C$ and remains unbiased for $\delta$. The pooled <estimator> retains a positive weight on the selected stage-1 data, giving
$$
\mathbb E_\delta(\widehat\delta_2\mid C)-\delta
=\frac{n_1}{n_2}\left[\mathbb E_\delta(\widehat\delta_1\mid C)-\delta\right]>0.
$$
\b[Conditional on full enrollment, the ordinary pooled <MLE> overestimates the treatment effect.] This is <conditional selection bias after futility continuation>. Randomization of treatment assignments does not undo selection on the interim outcome.
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