Testing disease progression under the proportional reduction in decline in Alzheimer's disease studies

To assess the treatment-placebo difference in Alzheimer's disease (AD) trials, saved time measure provides an easy interpretation of the treatment effect in months as an alternative measure to the treatment-placebo difference at the pre-specified visit that is often estimated from the fitted model. The current method to estimate saved time utilizes the disease progression curve of the placebo group, and this method is primarily descriptive. To fill the gap of the statistical inference for saved time, we propose to develop the likelihood ratio test and the score test under the proportional reduction in decline model. One AD trial data set was utilized to compare the proposed tests and the existing Wald-type test with regard to type I error rate and statistical power. We found that the likelihood ratio test and the score test have similar statistical power, but the score test has better control with regard to type I error rate. The two new tests are more powerful than the Wald test when a new treatment has proportional reduction in decline or constant delay, while the Wald test can have a higher statistical power when a constant treatment effect is expected from a new treatment.