I need to compare the ability of two methods to predict an event with a binary response. Each method produces a score, where the higher score indicates 1 and a lower score indicates 0. I am looking to calculate the odds ratio (in univariable and multivariable analysis) to compare these methods. Here is the break down of method data:
Method 1: Probability between 0 and 1.
Method 2: Score between 0 and 12
In univariable analysis, the OR for method 1 will be VERY large, but for method 2 would be quite small. I think that because the two methods have different scales the odds ratios become so vastly different. The unit increase for method one should be 0.1, whereas for method two is 1.
Possible solutions are to binarize both methods, by picking a cutoff, then everything is on the 0 and 1 scale and the OR are comparable, however you loose information when you do this. Also, it can be trickey to pick an objective cutoff.
Are there any suggestions for comparing the odds ratios of continous and discrete variables?