= Conditional selection bias after futility continuation
{title2=$E(S\mid X\ge c)-\delta$}
In a two-stage normal trial, conditioning on a first-stage <sample mean> exceeding $c$ raises that mean. With stage standard error $s$, mean parameter $\delta$, and combined mean $S$, the <estimator bias> after continuation is $E(S\mid X\ge c)-\delta=(s/2)\lambda((c-\delta)/s)$, where $\lambda$ is the upper-tail <Inverse Mills ratio>. It is positive and tends to zero as continuation becomes virtually certain.
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