# Cox survival analysis versus multilevel modeling

I'm debating the wisdom of a couple different approaches.

I am constructing a model that measures whether the amount of a treatment received leads to a person coming back for another treatment or not.

Sample data structure:

Client Treatment dosage Visit # Previous visits A 8 1 0 B 2 1 0 B 6 2 1 C 1 1 0 C 3 2 1 C 2 3 2 C 9 4 3

So, what I want to know is how the dosage contributes/does not contribute to them coming back in the next year. While clients' first visits occurred over a range of dates, I have data on all visits for a consistent time period after their first (two years from date of first visit for everyone).

One way I thought of approaching it was just to include first and second visits (if a second happened), and use a Cox regression to find out the hazard ratio of the event happening in that time period, based on dosage. But since I have data on visits 3, 4, 5, etc., and a change in their dosage in one of those could contribute to whether or not they return later (which could support or undermine the hypothesis), it seems like I'm throwing away a lot of useful data.

Another way of modeling the Cox regression might be to pair observations, even within the clients; i.e., treat client A's first visit and second visit as a pair, then their second visit and third visit as another pair for a new two-year time period, with an added control variable that they are not a new client and have been there before.

FYI, I am not necessarily interested in the survival analysis portion of the Cox model (how long before they're back); just the odds of them coming back in that set time period, with a few other control variables.

My other modeling option was to use a multilevel logistic model, where the client was the grouping level, to try to account for the fact their observations are theoretically correlated, and also use the number of past visits as a control (to see if the dosage is the driver of change, or if there's also a cumulative effect of multiple visits that moderates that).

I would appreciate any thoughts ya'll had.