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Negative Binomial Distribution in Group Sequential Designs

In clinical trials based on count data, the aim is to compare independent treatment groups in terms of the rate of occurrence of a particular outcome, such as number of times a subject responds to a therapy, develops a certain adverse experience, requires specialized care, or takes medication to achieve a particular response — for example, the number of migraines, seizures, recurrent infections, hospitalizations, episodes of diarrhea, and so on.

Negative binomial probability distribution can be used to model the number of times a particular outcome occurs during a clinical trial. Here, I explain this statistical methodology and its application in adaptive group sequential clinical trial designs.

Negative binomial distribution: A brief overview

The negative binomial distribution is a probability distribution that describes the number of trials required for a specified number of successes to occur. In other words, it models the number of failures that occur before a pre-determined number of successes is reached. It’s called negative binomial distribution as a reference to the fact that a certain binomial coefficient that appears in the formula can be written more simply with negative numbers.

The negative binomial distribution is commonly used to model situations where the number of trials needed to achieve a certain number of successes is variable and not fixed. However, in clinical trials, it is mostly used to model the number of events observed during a given duration of study treatment — many times as a primary or key secondary endpoint.


Application of negative binomial distribution in group sequential designs

In the context of group sequential designed trials — a type of adaptive trial design that includes pre-planned interim analyses that potentially allow for stopping for efficacy or futility — a negative binomial endpoint is handled similarly as a continuous, binary, or time-to-event endpoint would be handled. That is, the overall type 1 error is apportioned at interim analyses timed as portions of the statistical information (inverse of variance).


Designing clinical trials with Solara® extends the capabilities of EAST®

EAST, Cytel’s flagship clinical trial design software, can be used to calculate the required sample size for a clinical trial with a particular power based on a negative binomial endpoint. However, the application of group sequential design for early efficacy and/or futility stoppage, and accounting for rates of enrollment and dropout are not available in EAST. Solara, Cytel’s clinical trial design simulation software does account for these design and operational features.

Solara supports the design of clinical trials based on ratio of event rates assuming a Poisson or negative binomial distribution. Recall from mathematical statistics that the Poisson distribution is a special case of the negative binomial distribution with dispersion parameter 1. Hence, Solara’s implementation of the negative binomial distribution can be used for either of these distributions.


Interested in learning more? Register today for our on-demand webinar “Advanced Statistical Methodologies: Negative Binomial for Group Sequential Designs in Solara”:


Register for the Webinar



JimBolognese_cropAbout Jim Bolognese

Jim Bolognese is a Senior Research Fellow at Cytel. He is a highly experienced biostatistician with a career spanning over four decades. Previously, at Merck, he played a crucial role as a biostatistician in all phases of drug development across various therapeutic areas. At Cytel, Jim has served as a biostatistical consultant to biotech companies, providing strategic insights into drug development challenges. He has also contributed significantly to biostatistical software development, offering a unique end-user perspective.


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