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

Clinical Trial Design Using A Stopped Negative Binomial Distribution.

Author information

1
Regeneron Pharmaceuticals Inc., Tarrytown, NY, michelle.deveaux@regeneron.com.
2
Department of Biostatistics, School of Epidemiology and Public Health, Yale University, New Haven, CT, michael.kane@yale.edu.
3
Department of Biostatistics, School of Epidemiology and Public Health, Yale University, New Haven, CT, daniel.zelterman@yale.edu.

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 s successes or t failures. This report provides a closed-form expression for the mass function, moment generating function, and provides connections to other, standard distributions.

KEYWORDS:

curtailed clinical trials; discrete distributions; early-stage clinical trials; stopped negative binomial distribution

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