/RCT2_HW3

Part I. K-stage design

i) What is the goal for Simon’s two-stage design? (10%)

  • minimize the number of patients exposed to a possibly ineffective therapy.

  • minimize the sample size under the constraint imposed by the operating characteristics of the design

ii) What is the null and alternative hypothesis for Simon’s two-stage design? (10%)

H0: the true response rate is less than or equal to some pre-specified value

Hα: the true response rate is greater than some pre-specified value

iii) How do you determine the sample size for Simon’s two-stage design? (10%)

Two strategy:

  • optimal design

  • minimax design

iv) What is the difference between minmax and optimal design for Simon’s two-stage procedure? (10%)

Optimal design aim to minimize the expected number of patients treated under H0, while minimax design aim to minimize the total number of patients enrolled in the study.

v) What are the drawbacks for Simon’s two-stage design? (10%)

May not allow early termination even if there is a long run of failures for p0 = 0.10 and above

vi) How can you overcome the drawbacks? (10%)

Using k-stage designs.

Part II. Write the statistical section of a protocol for a non-superiority trial comparing a testing drug to an placebo control using a continuous outcome.

We set the hypothesis as H0: pT − pC ≥ Δ, H1: pT − pC < Δ. And choose type I error 0.2 and type II error 0.05, and choose superior threshold Δ = 0.1, where we got all them from corresponding superiority trial.

And we will be using one-sided t test, where $t_{0} = \frac{\hat{p}_{T} - \hat{p}_{C} - \Delta_{0}}{\sigma\sqrt{1/n_{T} + 1/n_{C}}}$. And $\Delta_{0} = (Z_{\alpha} + Z_{\beta})\sigma\sqrt{\frac{1}{n_{T}} - \frac{1}{n_{C}}}$.

Given that we could calculate the sample size as N = (Zα + Zβ)2 × [pT(1 − pT)+pC(1 − pC)]/Δ2. Therefore the necessary number of patients would be 2N.

  • If we reject H0, we could state that there is sufficient evidence to support that treatment is not much better than placebo, so we should stop trial.

  • If we fail to reject H0, we cannot rule out that treatment is much better than placebo, so we can move forward to next stage.