Statistics and Its Interface
Volume 11 (2018)
Clinical trial design using a stopped negative binomial distribution
Pages: 699 – 707
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.
discrete distributions, stopped negative binomial distribution, early-stage clinical trials, curtailed clinical trials
2010 Mathematics Subject Classification
Primary 62E15. Secondary 62P10.
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