Impact of using other analysis models
As expected, using a less restrictive model to analyse the trial having powered for a random slopes model results in some loss of power when trajectories are truly linear. This is also often the case for the non-linear trajectories. For example, the free trajectories, free covariance model has powers of 70–75% for the scenarios with a smaller residual error variance, and the power loss is greater when the residual error variance is increased relative to the size of the between-person variance.Analysts writing a statistical analysis plan for a future trial may be unsure whether any treatment effect will have a shape that is compatible with the random slopes model. In such a case, one option would be to use the random slopes model as a first-line approach, but to specify that the free trajectories, free covariance model will be used as a sensitivity analysis. The potential power loss induced by switching to a less constrained analysis model should be considered, perhaps by powering to a higher level with the random slopes model if that is possible.If there is strong reason to suspect a non-linear treatment effect in the proposed trial, then the difference in slopes between the groups is not an appropriate estimand. Instead, interest may lie in the difference in means between the two groups at the end of follow-up, and a free trajectories, free covariance model could be used at both the sample size calculation and analysis stage. Alternatively, if a specific polynomial form for the treatment effect is suspected, then the trial could be planned on that basis [We also considered the linear trajectories, free covariance model. This model gives the same treatment effect as the free control-group trajectory, free covariance model. An analyst might therefore consider its use when there are non-linear trajectories, but the treatment effect is still expected to be linear or close to linear. However, we found that such a model does not gain much in terms of performance compared to the random slopes model.Fitting a random slopes model can result in boundary problems, with an estimated correlation between random slopes and intercepts of + 1 or -1. The rate of convergence to a boundary was greater for mean trajectories with large amounts of non-linearity, and for scenarios with a larger residual error variance. Using a model with an unstructured covariance model avoids this particular convergence issue.