Efficient allocations in group sequential tests

We derive asymptotically efficient data dependent allocation rules for three group sequential testing procedures: Pocock (1977), O'Brien and Fleming (1979) and Falissard and Lellouch (1992). Sampling costs are defined such that the costs of observing the next group are higher than the cumulative costs of the previous groups. This formulation is used in an attempt to favor procedures that stop early while allocating less patients to the inferior treatment. We use a simulation study to compare the performances of these procedures when the efficient and the "pairwise" allocations are used. An example of applications on data is presented.