Optimal number of accrual groups and accrual group sizes in longitudinal trials with discrete-time survival endpoints

In longitudinal trials, the number of accrual groups and their sizes should carefully be chosen to ensure a desired power to detect a specified treatment effect. Methods are proposed to obtain a cost-effective combination of the number and size of accrual groups that provides high efficiency at minimal cost. We focus on trials where an event occurs at any point in time, but it is recorded on a discrete scale. The Weibull survival function is considered for modeling the underlying time to event. By using a cost function, it is shown that the ratio of the cost of recruiting and treating subjects to the cost of measuring them and also the survival pattern highly influence the optimal combination of the number and size of accrual groups. A maximin approach is further presented to obtain robust designs with respect to poor specification of these modeling parameters. We also show the application of the proposed optimal design methodology using real examples.