Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 207 / 3 / b / iv

Table of contents
- Solution iv

Solution

The trial uses

N_{1}

observations per arm if it stops at the first analysis and

N_{2}

if it continues. Since

Z_{1} \sim N (δ I_{1}, 1)

,

P_{δ} (continue) = Φ (e_{1} - δ I_{1}) - Φ (f_{1} - δ I_{1}) .

Therefore the expected per-arm sample size is

E_{δ} N = N_{1} + (N_{2} - N_{1}) {Φ (e_{1} - δ I_{1}) - Φ (f_{1} - δ I_{1})} .

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