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arXiv · 1508.01264

A Stopped Negative Binomial Distribution

Michelle DeVeaux·Michael J. Kane·Daniel Zelterman
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Abstract

This paper introduces a new discrete distribution suggested by curtailed sampling rules common in early-stage clinical trials. We derive the distribution of the smallest number of independent Bernoulli(p) trials needed in order to observe either s successes or t failures. The closed form expression for the distribution as well as the compound distribution are derived. Properties of the distribution are shown and discussed. A case study is presented showing how the distribution can be used to monitor sequential enrollment of clinical trials with binary outcomes as well as providing post-hoc analysis of completed trials.

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Michelle DeVeaux, Michael J. Kane, Daniel Zelterman. 2015-08-06. A Stopped Negative Binomial Distribution. https://arxiv.org/abs/1508.01264

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