content_image/319111.jpg content_image/319112.jpg content_image/319113.jpg content_image/319114.jpg content_image/319115.jpg content_image/319116.jpg
rate to α for this design using the following sum of integrals 

<img src='content_image/319111.jpg'>

Additionally, suppose that we wish to power this trial to reject a particular null hypothesis, without loss of generality H$_{01}$ , at some clinically relevant difference τ$_{1}$ = δ . The type-II error rate β for H$_{11}$ is then given by 

<img src='content_image/319112.jpg'>

Moreover, denoting by N and O the total number of patients and observations required by the trial respectively, we can compute the expected sample size, E ( N | τ ), or expected number of observations, E ( O | τ ), for any τ , according to 

<img src='content_image/319113.jpg'>

<img src='content_image/319114.jpg'>

Here, N( ω , ψ ) and O( ω , ψ ) are functions that give the number of patients and observations respectively, required by a trial that progresses according to ( ω , ψ ). Specifically 

where I { ω$_{d}$ ≥ l } = 1 if ω$_{d}$ ≥ l , and is 0 otherwise. 

## 3. EXAMPLE: TOMADO 

<img src='content_image/319115.jpg'>

<img src='content_image/319116.jpg'>

As an example of how to design a group sequential crossover trial with strong control of the familywise error rate, we will make use of the TOMADO crossover randomized controlled trial (Quinnell et al., 2014). This open-label trial compared three experimental treatments to a single control for the treatment 

