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使用停止负二项分布的临床试验设计

Clinical Trial Design Using A Stopped Negative Binomial Distribution.

作者信息

DeVeaux Michelle, Kane Michael J, Zelterman Daniel

机构信息

Regeneron Pharmaceuticals Inc., Tarrytown, NY,

Department of Biostatistics, School of Epidemiology and Public Health, Yale University, New Haven, CT,

出版信息

Stat Interface. 2018;11(4):699-707. doi: 10.4310/SII.2018.v11.n4.a13. Epub 2018 Sep 19.

DOI:10.4310/SII.2018.v11.n4.a13
PMID:30655933
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC6333309/
Abstract

We introduce a discrete distribution suggested by curtailed sampling rules common in early-stage clinical trials. We derive the distribution of the smallest number of independent and identically distributed Bernoulli trials needed to observe either successes or failures. This report provides a closed-form expression for the mass function, moment generating function, and provides connections to other, standard distributions.

摘要

我们引入了一种由早期临床试验中常见的截尾抽样规则所建议的离散分布。我们推导了观察到(r)次成功或(s)次失败所需的独立同分布伯努利试验的最小次数的分布。本报告给出了概率质量函数、矩生成函数的封闭形式表达式，并建立了与其他标准分布的联系。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7596/6333309/997aa6740a87/nihms-984670-f0008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7596/6333309/8f20019d2c4c/nihms-984670-f0001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7596/6333309/3aa5ee9427e4/nihms-984670-f0002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7596/6333309/aa85283e2b29/nihms-984670-f0003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7596/6333309/9eff5691380d/nihms-984670-f0004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7596/6333309/6528e039585c/nihms-984670-f0005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7596/6333309/775c53f7950b/nihms-984670-f0006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7596/6333309/aafbe5954b25/nihms-984670-f0007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7596/6333309/997aa6740a87/nihms-984670-f0008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7596/6333309/8f20019d2c4c/nihms-984670-f0001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7596/6333309/3aa5ee9427e4/nihms-984670-f0002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7596/6333309/aa85283e2b29/nihms-984670-f0003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7596/6333309/9eff5691380d/nihms-984670-f0004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7596/6333309/6528e039585c/nihms-984670-f0005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7596/6333309/775c53f7950b/nihms-984670-f0006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7596/6333309/aafbe5954b25/nihms-984670-f0007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7596/6333309/997aa6740a87/nihms-984670-f0008.jpg

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引用本文的文献

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本文引用的文献

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Approximations to distribution functions which are hypergeometric series.
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