Statistical inference for saved time based on disease progression curves in Alzheimer's disease research

Saved time is an easy interpretation metric that provides information to patients on how long a new treatment can delay the disease progression in time as compared to the placebo. The frequently used projection approach for saved time estimation utilizes limited information from the available data. To address that limitation, the area above the disease progression curve was proposed to estimate saved time by using more information from data. However, it is a challenge to derive the closed-form statistical inference (e.g., confidence interval of saved time) as area above the curve is quadratic relative to visit time and saved time based on the curves is nonlinearly related to the area above the curve. In this article, we derived the closed-form variance of saved time based on the area above curve approach by using Taylor expansion. We then compared the performance of the closed-form method and the existing simulation-based method to construct the confidence interval for saved time based on the area above curve approach with regard to coverage probability and interval width under various scenarios. The simulation results indicate that the proposed closed-form method has similar performance as compared to the existing method, while the closed-form method can be computationally easy in practice without additional simulations in the existing method. Data from the completed phase 2 donanemab trial were used to illustrate the application of the proposed method.