Impact of wrongly assuming the treatment effect is proportional to time
Bamia
Having a non-proportional treatment effect does result in incorrectly powered trials, even for a trial that matches the visit schedule of the observational study. Bamia et al. [The incorrect powering is therefore in part due to the wrong target treatment effect being used in the sample size calculation. This leads to over- or under-powered trials, depending on the size of the estimated treatment effect relative to the target treatment effect. When the treatment effect estimated by the random slopes model is close to the target treatment effect, the effect on the power appears to be relatively small. For example, for the intermediate decline trajectory with extra random effect, the empirical power is only a little inflated for a 3-year trial with a non-proportional treatment effect, at 83%. The random slopes model estimates the treatment effect to be -0.055/year, only slightly larger in magnitude than the -0.05/year used in the sample size calculation. In contrast, the mean treatment effect for the random slopes model for the early decline trajectory is -0.080/year, leading to a power of almost 100%. Using an incorrect target treatment effect appears to have a much larger effect on the power than non-linearity of the mean trajectories in this case, although this may not hold more generally for other patterns of non-linearity.