The Will Rodgers effect
My last post on ALL (Acute Lymphoblastic Leukemia) reminded me of an interesting statistical phenomenon referred to as the Will Rodgers effect: if you have divided a sample into two groups, one at higher probability of succesful outcome, changing the criteria in order to make more individuals members of the low success group will improve the outcomes of both groups. Obviously you could extend this to more than 2 groups.
As an example in leukemia, some patients are characterized as "high-risk" based on characteristics that make them less likely to be cured by standard therapy (age, T cell, high initial white blood cell count, etc). Changing the criteria so that more patients are characterized as high risk will improve survival in both groups, even as overall survival stays constant.