content_image/318422.jpg content_image/318423.jpg content_image/318424.jpg content_image/318425.jpg content_image/318427.jpg content_image/318426.jpg content_image/318428.jpg
as follows 

<img src='content_image/318422.jpg'>

<img src='content_image/318423.jpg'>

<img src='content_image/318424.jpg'>

<img src='content_image/318425.jpg'>

<img src='content_image/318427.jpg'>

<img src='content_image/318426.jpg'>

As a final step we must compute the sum across sequences, i.e. over the index i . We can see instantly that we have confirmed the elements proposed to be 0 in ∑ | S$_{r}$ | i =1 n X T $_{s$_{ri}$}$Σ − 1 r X$_{s}$$_{ri}$ / | S$_{r}$ | are indeed so, and we therefore need only concentrate on the non-zero terms suggested; A , B , C and E . 

However, other than Π T $_{jr}$Σ − 1 r T$_{ks}$$_{ri}$ , all the elements above have been identified as independent of sequence s$_{ri}$ . Therefore computing the sum over the s$_{ri}$ ∈ S$_{r}$ can be done easily, and gives the forms proposed for A , B and C in the statement of the Lemma immediately, on multiplying through by n/ | S$_{r}$ | . But, by our imposed constraint that sequences be balanced for period we can also sum over the Π T $_{jr}$Σ − 1 r T$_{ks}$$_{ri}$ 

<img src='content_image/318428.jpg'>

since exactly | S$_{r}$ | /r patients receive each treatment at each time period. This confirms the form proposed for E , and the proof is complete. 

Theorem 4.3. (Theorem 2.1 from Section 2) Let β = ( µ$_{0}$, π$_{2}$, . . . , π$_{D}$, τ$_{1}$, . . . , τ$_{D}$$_{−}$$_{1}$ ) $^{T}$. Consider an analysis to be performed after some number of stages l . Then 

