{"id":3233,"date":"2024-06-10T11:22:36","date_gmt":"2024-06-10T15:22:36","guid":{"rendered":"https:\/\/cytel.agencyukdev.com\/perspectives\/negative-binomial-distribution-in-group-sequential-designs\/"},"modified":"2024-08-22T05:54:46","modified_gmt":"2024-08-22T09:54:46","slug":"negative-binomial-distribution-in-group-sequential-designs","status":"publish","type":"perspectives","link":"https:\/\/cytel.agencyukdev.com\/fr\/perspectives\/negative-binomial-distribution-in-group-sequential-designs\/","title":{"rendered":"Negative Binomial Distribution in Group Sequential Designs"},"content":{"rendered":"<p>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 \u2014 for example, the number of migraines, seizures, recurrent infections, hospitalizations, episodes of diarrhea, and so on.<\/p>\n<p>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.<\/p>\n<p><!--more--><\/p>\n<h2>Negative binomial distribution: A brief overview<\/h2>\n<p>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\u2019s 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\u00a0<a href=\"https:\/\/stats.stackexchange.com\/questions\/169109\/why-is-a-negative-binomial-random-variable-called-that\" target=\"_blank\" rel=\"noopener\">negative numbers<\/a>.<\/p>\n<p>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 \u2014 many times as a primary or key secondary endpoint.<\/p>\n<p>&nbsp;<\/p>\n<h2>Application of negative binomial distribution in group sequential designs<\/h2>\n<p>In the context of group sequential designed trials \u2014 a type of adaptive trial design that includes pre-planned interim analyses that potentially allow for stopping for efficacy or futility \u2014 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).<\/p>\n<p>&nbsp;<\/p>\n<h2>Designing clinical trials with Solara\u00ae extends the capabilities of EAST\u00ae<\/h2>\n<p>EAST, Cytel\u2019s 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\u2019s clinical trial design simulation software does account for these design and operational features.<\/p>\n<p>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\u2019s implementation of the negative binomial distribution can be used for either of these distributions.<\/p>\n<p>&nbsp;<\/p>\n<p>Interested in learning more? <a href=\"https:\/\/cytel.agencyukdev.com\/fr\/resource\/advanced-statistical-methodologies-negative-binomial-for-group-sequential-designs-in-solara\/\">Watch<\/a> our on-demand webinar \u201cAdvanced Statistical Methodologies: Negative Binomial for Group Sequential Designs in Solara\u201d<\/p>\n<p>&nbsp;<\/p>","protected":false},"featured_media":3105,"parent":0,"template":"","meta":{"_acf_changed":false},"tags":[76],"by-topic":[457,500,435],"by-year":[74],"class_list":["post-3233","perspectives","type-perspectives","status-publish","has-post-thumbnail","hentry","tag-blog","by-topic-clinical-trial-design","by-topic-group-sequential-designs","by-topic-software","by-year-74"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Negative Binomial Distribution in Group Sequential Designs - Clinical Trial Software &amp; 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