If an interim analysis is performed during a trial it is tempting to determine the conditional power to reach a rejection in the trial given the observed results in the interim analysis. Since the true effect size is unknown the conditional power may be calculated by using the effect size, which the study has been powered for in the planning phase or by using an interim estimate of the true size (or a combination of both). In either case the conditional power is a random variable and its density is investigated depending on the analysis time and the true effect size. Under the null hypothesis, in early interim analyses after a small proportion of sample units, the conditional power typically will be close to the overall power when the effect size from the planning stage is used for calculation. In this case the majority of observations must still be made and the small first-stage sample in general will be dominated by the hypothetical second-stage chance based on the wrong parameter value. It is shown that the conditional power in moderately underpowered studies can have a distribution symmetric around 0.5. When using the interim estimate for calculating the conditional power the density in general will be u-shaped. The impact of using conditional power to reassess the sample size using flexible two-stage combination tests is shown for a specific example in terms of overall power and average sample size as compared to the corresponding group sequential design. For small true effect sizes mid-trial sample size recalculation based on an interim estimate may lead to an overly large price to be paid in average sample size in relation to the gain in overall power. Finally, the problem is discussed in terms of estimating the true conditional power.
Copyright 2005 John Wiley & Sons, Ltd.