On the choice of times for data analysis in group sequential clinical trials

Planned interim analysis of randomized clinical trials has been implemented for over a decade. While the initial proposal advocated analyzing after equal numbers of patients were evaluated, a later modification by Lan and DeMets (1983, Biometrika 70, 659-663) allowed for more flexible boundaries. Rather than fixing the times of analysis at equal numbers of patients, they fixed the rate at which overall alpha was used up according to a use function alpha * (t) on t in with alpha * (0) = 0 and alpha * (1) = alpha. Here we consider how flexible Lan and DeMets' procedure is. We show that the choice of alpha * (t) for a particular trial affects the permissible analysis times if other desirable properties of the sequence of nominal significance levels are to hold. To overcome the difficulties posed by patterns of late analysis, piecewise linear convex use functions are proposed.