Most of my reference on matching has been Rosenbaum's book "Observational Studies". From what I understand, the usual process of matching involves administering a treatment that is represented by a binary value of either 0 or 1, depending on whether the patient got the treatment or not. In the case that I am looking at, the treatment is represented as a continuous value with no particular meaning given to "0" treatment, making it difficult/non-applicable to assign a control.
In my hypothesis there is a linear relationship between the amount of treatment and the outcome and I want to test for that. During these tests I need to apply all the corrections for overt biases included in the Matching procedure. What is the best method for testing for a linear relationship?
What I have been doing, perhaps naively, is sampling at 2 different levels of treatment, $x_1$ and $x_2$, and with their mean outcomes, $u_1$ and $u_2$, I've been estimating the relationship as the line given by the two-point equation passing through $(x_1, u_1)$ and $(x_2, u_2)$. This turns out to be too inaccurate. Would it be better for me to sample at several levels of treatment $x_1, x_2, x_3, \dots,x_n$ and do a linear regression on that data or is there another standard way of doing it?