Optimizing parameters in clinical trials with a randomized start or withdrawal design

Disease-modifying (DM) trials on chronic diseases such as Alzheimer’s disease (AD) require a randomized start or withdrawal design. The analysis and optimization of such trials remain poorly understood, even for the simplest scenario in which only three repeated efficacy assessments are planned for each subject: one at the baseline, one at the end of the trial, and the other at the time when the treatments are switched. Under the assumption that the repeated measures across subjects follow a trivariate distribution whose mean and covariance matrix exist, the DM efficacy hypothesis is formulated by comparing the change of efficacy outcome between treatment arms with and without a treatment switch. Using a minimax criterion, a methodology is developed to optimally determine the sample size allocations to individual treatment arms as well as the optimum time when treatments are switched. The sensitivity of the optimum designs with respect to various model parameters is further assessed. An intersection–union test (IUT) is proposed to test the DM hypothesis, and determine the asymptotic size and the power of the IUT. Finally, the proposed methodology is demonstrated by using reported statistics on the placebo arms from several recently published symptomatic trials on AD to estimate necessary parameters and then deriving the optimum sample sizes and the time of treatment switch for future DM trials on AD.