Many clinical studies have more than one objective, either formally or informally, but this is not usually taken into account in the determination of the sample size. We investigated the overall power of a study, that is, the probability that all the objectives will be met.
We calculated the overall power in the case that the study has two primary outcome variables and in the case that one outcome variable is evaluated on two subsets, in particular, the Per Protocol group and the Intention to Treat group.
A power of 80% for each of the two end points leads to poor power for the end points combined. However, a power of 90% preserves better the overall power. The power of the Per Protocol analysis can be higher or lower than the power of the Intention to Treat analysis.
Power should be calculated for all end points combined, and it should be at least 90% for each primary end point. If the sample size for the intention-to-treat analysis is determined by adding a percentage of "nonevaluable subjects" to the sample size required for the per protocol analysis, then this may lead to an underpowered study.