I am working on a project where I am using observational data from patients and trying to find a causal relationship on how Treatment dose affects Patient recovery. Since the data is observational, I am using Propensity Score Matching to match Control Subjects to the Treated subjects, to make the experiment as close to a Randomized experiment as possible.
I have 120 Treated subjects and 175 Control subjects. To my understanding, if I am picking the best match for each Treated subject, I should have 120 subjects in the matched Control pool.
When using the "Match" function from the "Matching" package in R, one of the parameters I have to specify is whether the estimand is calculated using ATT or ATE. From what I understand, ATE (Average Treatment Effect) and ATT(Average Treatment effect on the Treated) are parameters not used for finding matches, but for estimating the causal effect after matching.
When I use "ATT", I find that my Treatment group and matched Control group have 120 subjects each, as expected. But when I use "ATE", when I investigate the result of my matching model, I notice that both my Treated and Control groups have 295 subjects each, with 120 unique values (of all treated subjects) in the treated group, and 175 unique values (of all control subjects) in the control group. I am not entirely sure what is happening here, and I was expecting to see 120 values in the Treated and the matched Control (similar to what I get when using ATE). Could someone please explain what is happening?