I'm sorry to have gotten into such a long discussion about this, because it's not really important. The important thing is that 50% of patients who fail Crizotinib had brain metastases and that 113 appears to be effective in brain metastases.
However, I still have a problem even with your simple explanation. If you had 1000 patients with NSCLC, I agree you would expect 50 to have the ALK translocation. However, I disagree that the paper you pointed to suggests that 26 would have ALK+ brain metastases.
From the paper, 2.6% of patients with brain mets, not total NSCLC patients, were ALK+. You are using their number for all the patients with NSCLC (not just those with brain mets) to ask what % have ALK+ brain mets.
The best way to explain would probably be in your example, say in patients who have NSCLC 50% have brain mets at any given time. Then:
1000 patients total - 50 with ALK+ primary tumors.
500 patients with brain mets total.
2.6% of the 500 brain mets are ALK+ = 13 patients with ALK+ brain mets.
In this case, 13/50 ALK patients would have brain mets = 26%
The number Ariad gives of 50% of Criz progressors having brain mets seems high, but I think that is due to the fact that they are so advanced that they have much higher rates of metastasis.
