I'm trying to get the "productivity" of treatments like sending an email, calling or sending an SMS and their combinations in the paying debtor's probability.
I couldn't find one model that satisfies the most basic hypothesis I need to fulfill. For example, I can't use a simple decision tree, with, for example, quantity of SMS as a variable, because more SMS means that during the period we have that client, we sent him, let's suppose 3 SMS, but because he didn't pay (if he would had paid during the first days he wouldn't have received any SMS). In a logistic regression I would have the same issue.
So I thought that the time should be important in this type of analysis. Let's say someone with the same 'survival' time getting more SMS has (I think) more chances to pay (die in the model).
So I was thinking that we should stratified clients regarding their survival time. But I was wondering how can I add this to those models or if there is a more suitable model to do this. I read about stratified Cox Models, but I wasn't sure if it was going to be able to capture this.
My question is, what model would you recommend to do this and how would you insert the fact that if we have more time since the client was loaded in the system, the treatments (which are supposed to have a positive impact) will increase but because is more difficult that this client pays.
Maybe some model where the class is is someone heal or not depending on how much medicine you gave him...So, you will have both effects, more medicine more chances to heal, but more medicine is related to more time with no healing. Really don't know.