A Stopped Negative Binomial Distribution
Statistics Theory
2018-02-16 v8 Statistics Theory
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.
Cite
@article{arxiv.1508.01264,
title = {A Stopped Negative Binomial Distribution},
author = {Michelle DeVeaux and Michael J. Kane and Daniel Zelterman},
journal= {arXiv preprint arXiv:1508.01264},
year = {2018}
}