Sample size determination for a study with variable follow-up time

For a study to detect the outcome change at the follow-up visit from baseline, the pre-test and post-test design is commonly used to assess the treatment-control difference. Several existing methods were developed for sample size calculation including the subtraction method, analysis of covariance (ANCOVA), and linear mixed model. The first two methods can be used when the follow-up time is the same as scheduled. Although the linear mixed model can analyze the repeated measures by including the actual visit time to account for the variability of the follow-up time, it often assumes a constant treatment-control difference at any follow-up time which may not be correct in practice. We propose to develop a new statistical model to compare the treatment-control difference at the planned follow-up time while controlling for the follow-up time variation. The spline functions are used to estimate the trajectories of the treatment arm and the control arm. We compared the performance of these methods with regards to type I error rate, statistical power, and sample size under various conditions. These four methods all control for the type I error rate. The new method and the ANCOVA method are often more powerful than the other two methods, and they have similar statistical power when a linear disease progression is satisfied. For a study with non-linear disease progression, the new method can be more powerful than the ANCOVA method. We used data from a completed Alzheimer's disease trial to illustrate the application of the proposed method.