Speaker
Description
Bootstrap calibration grounds on a simple idea: Based on a bootstrap sample, one can compute the bootstrap coverage probability of the desired interval. Then, one can alternate the intervals limits until the bootstrap coverage probability approaches the nominal level, e.g. by alternating the α-level used for interval calculation. Finally, the desired interval is calculated replacing the nominal α-level by its bootstrap-calibrated counterpart.
This idea was already proposed in the 1980ies, and since then, was alternated by several authors in order to yield (simultaneous) confidence, prediction or tolerance intervals. However, a unified framework that enables the calibration of these different intervals is still missing. Closing this gap is the aim of this talk.
The presented algorithm was initially proposed to enable the computation of prediction intervals for different scales and models and is the foundation of the R package predint.
It will be shown, that this approach can be easily generalized to yield (simultaneous) confidence intervals as well as equal-tailed tolerance intervals. The idea behind this approach is the individual calibration of the lower and upper limits of Wald-type intervals adapting the calibrated interval to possible skewness of the underlying distribution, enhance the intervals coverage probability and / or adjust for the multiple testing problem.
Especially, for multiple testing of hypothesis other than differences between parameters, the proposed bootstrap-calibration is extremely promising. The computation of simultaneous confidence intervals for ratios between the means of several treatment groups and a control will be demonstrated based on a clinical multi-arm study regarding the reduction of brain infarct size following mechanical thrombectomy.
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