Member are being enrolled in a program every month. The goal of the program to reduce health-care costs. Some members have been in the program for 9 months and some have been for less than a month. To evaluate the program I am building a matched cohort using propensity score matching. My question is how do I find the matched comparison group? Should I match also match on the time they enrolled? Or should I ignore the time and simply adjust the members by the length of time they have been in the program. For example, say the treated member, X, who has been in the program for 9 months is matched to cohort member Y. So simply compare the 9-month cost of X with 9-month cost of Y. Is propensity score the right way to do it or are there other statistical methods that is better suited to this situation?
If you want to to measure the effectiveness of the program in reducing healthcare costs, you will need to have a control group of people who are not enrolled in the program. This is because there may be some unmeasured qualities that make you samples 'self-select' themselves and enrol into the program. In your case, people who enrol into this program have an intention to reduce their healthcare costs so they may try to do so even if they do not enrol. Therefore, your findings that the health care costs of your members decrease over time may not come from the program.
Propensity Score Matching (PSM) can be used to control for self-selection bias. It does so by matching the members (the treated group) with non-members (the controlled group) who have the same qualities (RHS variables in your probit regression). However, you will need to have a control group of non-members. Without them, you cannot make any inference about the program's effectiveness.