Surety and Assurance in Estimation
Andrew P. Grieve · 2022
The standard approach to determine sample size is usually based on an assumption that at the end of the study, a hypothesis test will be performed, and this has been the approach in Chapters 2–9. However, in some clinical investigations, it is more appropriate, or desirable, to estimate a treatment effect and its associated confidence interval. In this chapter, we introduce an alternative to power to be used when planning trials for which there is a high probability, which we term surety, that the final confidence interval will be narrower than a pre-defined width. We discuss whether the width of a confidence interval should be the sole determinant of sample size and develop an unconditional approach based on a prior for the variance. Finally, we give a fiducial interpretation to the unconditional approach.