I want to design an RCT (randomised controlled trial) with interim analysis using the O’Brien Fleming interim stoppage criteria to control the Type I error.
I wan to have 3 interim analysis and then the final one then at each analysis I need to have to following p-values to reject $H_0$:
- 0.00005
- 0.0039
- 0.0184
- 0.0412
I know these works fine if I use the Wald or Z-statistic $$ Z = \frac{ \delta_j }{ \text{se}(\delta) } = \frac{\hat{p}_2 - \hat{p}_1}{ \sqrt{ \frac{\hat{p}_1\hat{q}_1}{n_1} + \frac{\hat{p}_2\hat{q}_2}{n_2} } } $$
Bu I want to adjust for some covariates and use logistic regression and test if the $\beta$ coefficient of the group variable (no treatment/treatment) is significant.
To test the significance of the $\beta_1$ I will use the Wald ref.
Can I still use the group sequential boundaries for the interim analysis when I use logistic regression to assess the difference between the groups?
If do can someone give me a reference or an explanation of why? If not what else can I do?
This paper states that "the sequential test statistics need to have the independent increments covariance structure in order to control Type I error " and uses an information criteria to control the Type I error ($\alpha$). But I would rather use the O'Brian Flemming boundaries if possible.
