used to secure an overall type 1 error rate $\alpha=0.025$ with a one sided $z$ test. If $Z_1 \le 2.18$, $Z_2$ is also observed, where $$Z_k = \frac{1}{\sqrt{n_{k}}}\sum_{i=n_{(k-1)}+1}^{n_{(k)}} X_{i} = \sqrt{n_{k}} \cdot \bar X_k  \overset{d}{=} N(\theta,1).$$ If there is no possibility of interim stopping, Fisher information from both stages combined is ${\cal{I}}_{(2)}^{fix}=200$. This directly follows from the additivity property of Fisher information for independent data.

\

   $\theta$   Measure   $\widehat\theta_{(1)}$   $\widehat\theta_{(1)}^c$   $\widehat\theta_{(2)}$   $\widehat\theta_{(2)}^c$
  ---------- --------- ------------------------ -------------------------- ------------------------ --------------------------
     0.0       Bias             0.2524                   -0.1865                   -0.0017                    0.0025
     0.0        SD              0.0323                    0.3136                    0.0691                    0.0741
     0.0        MSE             0.0647                    0.1331                    0.0048                    0.0055
     2.18      Bias             0.0796                   -0.1357                   -0.0398                    0.0056
     2.18       SD              0.0599                    0.2972                    0.0584                    0.0852
     2.18       MSE             0.0099                    0.1068                    0.0050                    0.0073

  : \[table1\] Monte-Carlo Simulation study ($100,000$ repetitions) for the two stage Pocock design; $n_1=n_2=100$.

\

\

Figure \[Z\_example\] shows histograms of $\widehat\theta_{(1)}$, $\widehat\theta_{(1)}^c$, $\widehat\theta_{(2)}$, and $\widehat\theta_{(2)}^c$ estimated from $100,000$ Monte-Carlo samples assuming $\theta=2.18$. Table \[table1\] reports Monte-Carlo biases, standard deviations (SD), and mean squared errors (MSE) under $\theta=0$ and under $\theta = 2.18$. In this example, the study is stopped for efficacy at stage 1 if $Z_1>2.18$ and proceeds to stage 2 when $Z_1 \le 2.18$. If the study is stopped at stage 1, the support 