Predicting Confidence Interval for the Proportion at the Time of Study Planning in Small Clinical Trials
Confidence intervals are commonly used to assess the precision of parameter estimations. Particularly in small clinical trials, such assessment may be used in place of a power calculation. We discuss `future' confidence interval prediction with binomial outcomes for small clinical trials and sample size calculation, where the term `future' confidence interval emphasizes the confidence interval as a function of a random sample that is not observed at the planning stage of a study. We propose and discuss three probabilistic approaches to future confidence interval prediction when the sample size is small. We demonstrate substantial differences among these approaches in terms of the interval width prediction and sample size calculation. We show that the approach based on the expectation of the boundaries has the most desirable properties and is easy to implement. In this chapter, we primarily discuss prediction of the Clopper-Pearson exact confidence interval, and then extend our discussion to other confidence interval methods. In particular, we discuss the arcsine transformation as a viable alternative to the exact confidence interval.
KeywordsAngular transformation Exact confidence interval Expectation of the confidence interval Likelihood-based approach Small sample Study design
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