Background
major depression, Alzheimer’s disease, volume loss, depression, Huntington’s Disease
BRAIN ATROPHY, DISEASE, DISEASES
In certain diseases, a person’s condition deteriorates over time. Potential treatments for such a disease might aim to lessen the rate of that deterioration. When conducting a trial of a treatment like this, a common choice of outcome is a continuous variable that can capture any deterioration over time, measured on multiple occasions during follow-up. For example, brain atrophy is used as an outcome for clinical trials measuring deterioration in early-stage manifest Huntington’s Disease [Such a continuous longitudinal trial outcome is often analysed using a mixed-effects model, with a random intercept and slope over time for each participant to allow for the dependence of measurements taken on the same person. The fixed part of the model includes a slope over time in the control group and a slope over time in the treated group, with the treatment effect being the difference between these two slopes. Thus, an effective treatment will slow the mean rate of deterioration in those receiving the trial treatment compared to participants receiving control.A trial sample size can be obtained for a random slopes model by using standard sample-size formulae for mixed-effects models [The random slopes model outlined above assumes that trajectories in both the treatment and control groups are linear over time, and hence that the difference between the means increases linearly over time, but this may not be the case. Imaging and biomarker changes can be markedly non-linear particularly over long periods of time. For example, there was some evidence that the rate of percentage brain volume loss increased as disease severity progressed in 12 patients with Alzheimer’s disease [In addition to trajectories being non-linear, treatment effects are also sometimes found to be non-linear in time. For example, the SmaRT Oncology-2 trial examined an integrated treatment programme for major depression in oncology patients versus usual care. Instead of a steady improvement over the course of the trial, the intervention improved depression scores early in the trial, and this effect was then sustained to the end of follow-up (Fig. The primary aim of this paper is therefore to assess the impact of assuming that outcomes evolve linearly over time when in truth they do not, in terms of specifying the sample size for a future trial from an existing dataset. We use a simulation study and consider scenarios in which the outcome evolves non-linearly over time but the treatment effect on the mean is still proportional to time, and those in which both the trajectory and treatment effect deviate from the assumed linear model.It is possible that investigators might suspect at the design stage that there are non-linear trajectories, but not have sufficient evidence of this in the previously collected dataset. These non-linearities might become more apparent in the trial data. For example, in the AIMS trial [In the next section, we outline the sample-size methodology used. We then go on to describe our simulation study in the "Simulation study" section, including the data generation mechanism and the scenarios considered, and give our results in the "Results" section. We finish by giving a discussion and conclusion of our results.