I have data for adherence to medicines which follows a downward linear trend for about 6 months (from 100%) and then plateaus at about 50%. Another way of describing it is by saying that adherence reaches steady state (=50%) at about 6 months after starting a medicine (http://www.ncbi.nlm.nih.gov/pubmed/12132975).
I have been exploring the effect of an intervention on adherence to medicines and have been using a longitudinal study design and a linear model to do this. However, I would like to try fit an exponential decay into the model to see if I can improve the fit. I'm using geeglm in R.
My original model is straightforward
y= Bo + B1(time) +B2(trt group) + B3(post) + B4 (time_post) +b5(posttrt_group) + B6 (time_posttrt_group)
where post= the intervention occurring at a defined point in time (change in intercept) time_post = change in slope after the intervention.
A function that may work to fit the decay is
where A = value at plateau (estimate at 50%) B = difference between plateau value and original intercept value (intercept should typicall be 100% - so B=50%) -k = elimination rate constant t = time
I'm not sure how I would fit this into my model. If anyone has any suggestions for how I could work this out, or could point me to some web-help, that would be really helpful.