When there are more treated than control, is it possible to do 1-to-1 matching (without replacement)?
It makes sense to do 1-to-1 when there are less treated than control but I am not sure if one can do that if there are more treated. It looks like a good way to introduce bias and doesn't make sense to selectively throw out treated.
I guess full matching is a good possibility when there are less control than treated but what if I want to do 1-to-1 in the same case?
The only way I can think of that may be valid is to randomly sample smaller number of treated than control and do 1-to-1, and do this over many times...