Response to Letter to the Editor "Comments on 'Novel Non-Linear Models for Clinical Trial Analysis With Longitudinal Data: A Tutorial Using SAS for Both Frequentist and Bayesian Methods'".

In clinical trials with longitudinal continuous data, efficacy inference traditionally focuses on the difference in the mean change from baseline at a single study visit [e.g., mixed models for repeated measures (MMRM)]. Proportional MMRM (pMMRM) reparameterizes this difference as a proportional reduction relative to the placebo mean change. This proportional effect is a nonlinear combination of the means, whereas the difference is a linear combination of the means. It can not only lead to greater power at a single visit by yielding a test statistic lower-bounded by that of the difference but also offers a flexible and intuitive way to combine all or multiple visits for efficacy inference, which can further boost power. It is also asymptotically unbiased. pMMRM with visit-specific proportional effects yields identical parameter estimates to MMRM. When only MMRM outputs are used, the proportional effect calculated by the delta method yields greater power than the difference.