This paper illustrates the use of several bootstrap confidence interval methods in a complex yet practical situation. The confidence interval for the difference between two treatments in a simplified sequential paired clinical trial, which is analogous to setting an interval for the drift of a random walk subject to a parabolic stopping boundary, is considered. Three bootstrap methods of construction are applied: the accelerated bias-corrected, the automatic percentile, and the bootstrap-t. The results are compared with a theoretical approximate interval. Difficulties inherent in the use of these bootstrap methods are discussed. The automatic percentile method is shown to be the easiest to apply and to work well.
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