Often time, in clinical studies, the clinical, regulatory and commercial decisions might be made on more than one single primary endpoint, in which case multiple primary endpoints are used to capture a more complete characterization of treatment effect. The interim analysis is widely used in clinical studies. The interim decisions including the sample size re-estimation are often based on the conditional power (CP) which is applicable only for a single endpoint in the current paradigm based on data collected before the interim analysis.
In this paper, I will expand the concept of conditional power to the case with multiple co-primary endpoints, which can be called as the generalized conditional power (GCP). GCP takes consideration of correlation of co-primary endpoints. It may be used as the basis of interim decision rules for correlated co-primary endpoints. This paper will focus on the two co-primary normal distributed endpoints, which can be extended to more general cases. The relationship between the generalized conditional power (GCP) and regular conditional power (CP) will be discussed. The method for adjusting the sample size based on the generalized conditional power will also be proposed. An example will be provided to describe this method.
