Comparing the Fold Change (Effect size) after a treatment I have been using this site for the past year to get tips on stats but I have run into a problem that I cannot overcome. It isn't too complicated, but I am not sure how to determine significance or if my ideas are correct. Hopefully some of you can help out a bit. Thanks ahead of time.
I have a situation where I have two strains of mice. In one strain of mouse, they have a high incidence of a disease while another has a lower incidence of the same disease. The disease is binary, either they have it or they do not.
If I treat a population of either mouse strain with Drug A, they both get a reduction in the incidence of the disease. The high incidence mouse strain has the disease incidence drop from 30% -> 15%. The low incidence mouse strain sees a drop from 10% -> 1% after treatment.
From this experiment, if I looked the absolute drop in the incidence it would appear that the drug is more effective in the high incidence group that has a decrease of 15%, compared to 9% in the other. However, (to me) it is clear that the drug is far more effective in the low incidence mouse strain because the fold change is a 10-fold reduction, while the high incidence mice only have a 2-fold reduction.
Hopefully the scenario made sense... My question is:
If I want to determine if the fold reduction in the lower incidence mice is significantly greater that in the high incidence, what kind of statistical test should I do?
I am thinking that I should log(2) transform the incidences and then test the effect of treatment with a linear model or ANOVA. I am not sure if this is kosher, especially with my binary response variable and no replicates (impossible to do replicates due to large number of mice ~3000).
Any of your suggestions/answers would be great and highly appreciated. 
 A: This type of situation with binary outcomes is usually handled by logistic regression, which in your case would use the disease/no-disease states of the 3000 mice to estimate the log of the odds of having disease as a function of predictor variables. Here, you would include the mouse strain and the drug treatment as predictor variables; also, since you are interested in whether the drug is more "effective" in one mouse strain, you would include an interaction term between strain and drug. A significant interaction term would support the hypothesis that drug responses, in terms of influence on log-odds of having disease, differ between mouse strains. The results expressed in terms of log-odds can be translated back to probability scales and thus to fold differences in incidence of disease if you wish.
That said, I suggest that you think some more about your definition of "more effective"; I'll translate from mice to people to put this into a public health perspective. Say that there were 1000 people in a high-incidence group and 1000 in a low-incidence group. Say that the drug costs \$1 per dose, and you only had \$1000 dollars to spend. 
Which group should you spend the money on? You would prevent disease in 150 people by giving it to the high-incidence group, but only in 90 people if you give it to the low-incidence group. From this cost-benefit perspective, the drug is more effective if used on the high-incidence group, even if the fold-change in incidence is greater in the low-incidence group.
