I have two sets of patient-level data for two distinct treatments, unfortunately, the data is only over a 14 week period and I'm hoping to build a predictive model to estimate/simulate what the data may look like at the 6-month mark.
Specifically, I am interested in some simulation that would allow me to estimate the proportion of patients in either treatment arm having a "BVAS score" of 0 or >0 - once I estimate these, comparing the proportions is straightforward.
I've tried a Poisson regression, a zero-inflated Poisson regression, logistic regression, but all seem to hone in on the treatment effect for both too strongly leaving all predicted outcomes to be 0 at the 6-month mark.
An alternative approach I've started to look at is to use a longer-term study and simply sample with replacement patient data at the 6-month mark; however, I cannot do this for one of the treatments as it was not studied in the longitudinal study.
So I have two questions:
1) Is there a way to develop a regression model that draws from some distribution of predicted values based on the coefficients and the corresponding CI so that for 1 patient I can generate multiple estimated outputs? Ideally, some simple R code as an example to this would be helpful. For example, if y = mx + b; instead of always using the same coefficients, altering estimates for m and b based on their CI and underlying distribution (e.g., if I believe them to be normal, Poisson, etc.).
2) If I have only 14-week data for both treatments (as shown below) I would like to have a way that I can leverage the correlation or relationships in either treatment arms variance between the two so that if I were to randomly sample from the longitudinal study mentioned above I could apply some sort of treatment effect estimate to shift the sampling distribution in an effort to model a treatment effect? In short, how can I use the figures below to estimate some sort of treatment effect in the form of a reduced variance or a greater likelihood to have values of 0 or closer to 0?
14-week data of alternative therapy I am trying to model: