So lets say that there are several different treatments for being underweight. One way to deal with this is to make repeated measurements of each patient's weight across time. So I can fit a model to the panel data, regressing weight on treatment as an indicator variable, and then plot the different fitted mean trajectories along with their point wise confidence bands. Basically a plot of response vs time for all groups but accounting for the uncertainty of the paths as well. Also, say that scatterplot of suggests that curves might not linear so I have to do some sort of polynomial interpolation on the right hand side of the equation. Moreover, say that I notice that some of the bands are convex for some treatment groups and some are not for others. Can I interpret this as some of the treatments have accelerating returns and some have diminishing returns? I'm thinking that even if a confidence band for a particular trajectory is convex, I can imagine the true path being concave as a possible path within the band if the bands are particularly wide. Even if a convex shaped band were not wide, the true path may be concave for short intervals of time.