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We investigate the conditional power under the framework of linear regression models so that it can be applied to most actual clinical trials in which multiple treatment effects and covariate effects are included. It is well known that the standard power of a regular test for a treatment contrast depends on unknown parameters only through the contrast itself. However it is not true in general for conditional power. Conditions for this to happen are established here and some instances are illustrated. We also show that similar arguments can be made about the sufficient statistics for the conditional power.
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