Statistics and Its Interface

Volume 11 (2018)

Number 4

Clinical trial design using a stopped negative binomial distribution

Pages: 699 – 707

DOI: http://dx.doi.org/10.4310/SII.2018.v11.n4.a13

Authors

Michelle Deveaux (Regeneron Pharmaceuticals Inc., Tarrytown, New York, U.S.A.)

Michael J. Kane (Department of Biostatistics, School of Epidemiology and Public Health, Yale University, New Haven, Connecticut, U.S.A.)

Daniel Zelterman (Department of Biostatistics, School of Epidemiology and Public Health, Yale University, New Haven, Connecticut, U.S.A.)

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

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

2010 Mathematics Subject Classification

Primary 62E15. Secondary 62P10.

Full Text (PDF format)

This research was supported by National Cancer Institute grants R01CA131301, R01CA157749, R01CA148996, R01CA168733, and PC50CA196530, by the Yale Comprehensive Cancer Center, and by the Yale Center for Outcomes Research.

Received 10 August 2017

Published 19 September 2018