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Exact confidence limits after a group sequential single arm binary trial
Author(s) -
Lloyd Chris J.
Publication year - 2021
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.8909
Subject(s) - inference , realization (probability) , binary number , computer science , confidence interval , exact test , test statistic , statistic , algorithm , construct (python library) , exact statistics , multiple comparisons problem , sample size determination , statistical hypothesis testing , mathematics , statistics , artificial intelligence , arithmetic , programming language
Group sequential single arm designs are common in phase II trials as well as attribute testing and acceptance sampling. After the trial is completed, especially if the recommendation is to proceed to further testing, there is interest in full inference on treatment efficacy. For a binary response, there is the potential to construct exact upper and lower confidence limits, the first published method for which is Jennison and Turnbull (1983). We place their method within the modern theory of exact confidence limits and provide a new general result that ensures that the exact limits are consistent with the test result, an issue that has been largely ignored in the literature. Amongst methods based on the minimal sufficient statistic, we propose two exact methods that out‐perform Jennison and Turnbull's method across 10 selected designs. One of these we prefer and recommend for practical and theoretical reasons. We also investigate a method based on inverting Fisher's combination test, as well as a pure tie‐breaking variant of it. For the range of designs considered, neither of these methods result in large enough improvements in efficiency to justify violation of the sufficiency principle. For any nonadaptive sequential design, an R‐package is provided to select a method and compute the inference from a given realization.