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Increasing the sample size at interim for a two-sample experiment without Type I error inflation



For the case of a one-sample experiment with known variance σ2=1, it has been shown that at interim analysis the sample size (SS) may be increased by any arbitrary amount provided: (1) The conditional power (CP) at interim is ⩾50% and (2) there can be no decision to decrease the SS (stop the trial early). In this paper we verify this result for the case of a two-sample experiment with proportional SS in the treatment groups and an arbitrary common variance. Numerous authors have presented the formula for the CP at interim for a two-sample test with equal SS in the treatment groups and an arbitrary common variance, for both the one- and two-sided hypothesis tests. In this paper we derive the corresponding formula for the case of unequal, but proportional SS in the treatment groups for both one-sided superiority and two-sided hypothesis tests. Finally, we present an SAS macro for doing this calculation and provide a worked out hypothetical example. In discussion we note that this type of trial design trades the ability to stop early (for lack of efficacy) for the elimination of the Type I error penalty. The loss of early stopping requires that such a design employs a data monitoring committee, blinding of the sponsor to the interim calculations, and pre-planning of how much and under what conditions to increase the SS and that this all be formally written into an interim analysis plan before the start of the study. Copyright © 2009 John Wiley & Sons, Ltd.