Estimand of interest
If trajectories are truly linear, then the estimand of interest is the difference in slopes between the treatment groups. However, if trajectories are non-linear, then various alternative differences between treatment groups could be chosen as the estimand of interest. We could choose the difference in a linear contrast of the mean levels at the various follow-up times, or a difference in mean levels at a particular point in time. We think that a comparison of means at the end of follow-up is likely to have most appeal for researchers. We therefore consider the final time-point treatment effect to be an additional estimand of interest, i.e. the difference between the mean levels in the treated and untreated groups at 5 years for a 5-year trial and 3 years for a 3-year trial. In order to compare estimated treatment effects from the different models, when summarising our results, we convert all differences in slopes to the corresponding difference in mean levels at the end of follow-up. For the random slopes model with means at baseline in the two treatment groups constrained to be the same, we can switch from a difference in slopes to a difference in final levels by multiplying by the follow-up time.