A Stopped Negative Binomial Distribution
Michelle DeVeaux, Michael J. Kane, and Daniel Zelterman

TL;DR
This paper introduces the stopped negative binomial distribution, a new discrete distribution modeling the number of Bernoulli trials until s successes or t failures, with applications in clinical trial monitoring.
Contribution
It derives the distribution's closed form, explores its properties, and demonstrates its use in clinical trial sequential monitoring and post-hoc analysis.
Findings
Distribution derived in closed form
Properties of the distribution analyzed
Applied to clinical trial monitoring
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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Taxonomy
TopicsStatistical Methods in Clinical Trials · Statistical Distribution Estimation and Applications · Bayesian Methods and Mixture Models
