Likelihood ratio test for the disease progression model to measure saved time in Alzheimer's disease

Saved time provides an intuitive interpretation comparing a new treatment to the placebo in a randomized trial with repeated measures. The projection approach is frequently used to estimate saved time by using the placebo group disease progression curve and the last visit data from the treatment group. Disease modifying therapies for Alzheimer's disease (AD) are expected to slow disease progression. For that reason, several disease progression models were developed to assess the effectiveness of the new treatment. These models require patient level data which are often challenging to obtain. Therefore, we propose to develop a likelihood ratio (LR) test to assess whether a new treatment can delay disease progression in time (e.g. proportional time delayed over the course of a trial) as compared to the placebo, by using the summary statistics from the published results instead of patient level data. We compare the performance of the LR test and the existing tests with regard to type I error rate and statistical power. The proposed LR test is often more powerful than the existing Wald type test when the placebo group has slower disease progression rates in later visits. We then use the summary statistics from the recent donanemab phase 3 trial to illustrate the application of the proposed LR test.