Suppose one has a bunch of drugs $\displaystyle d_1, \dots , d_n $ that have similar effects (e.g. they all treat the flu). But suppose that $\displaystyle d_t $ where $\displaystyle t \in \{1, \dots , n \} $ has the highest response rate. In other words, $\displaystyle d_t $ is chosen to be the drug that combats the flu (even though all the others do as well). Is it the case that $\displaystyle d_t $ will always mask the effects of the rest of the drugs? How does $\displaystyle I/H $ respond in this situation? Note that $\displaystyle I $ is the mutual information and $\displaystyle H $ is the joint entropy. In other words, we are considering

$\displaystyle \frac{I(X,Y)}{H(X,Y)} = \frac{\sum_{x,y} p(x,y) \log \frac{p(x,y)}{p(x)p(y)}}{\sum_{x,y} p(x,y) \log p(x,y)} $