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The primary efficacy endpoint of this clinical trial in a rare disease is based on count data to compare an event rate between placebo and active arm. Since the prospective population is expected to vary widely with respect to the event rate, the use of negative binomial model seems appropriate.
There is lower prevalence of subjects with more severe disease who have higher chance of experiencing the event. In order to complete the clinical trial in a reasonable timeframe, more subjects with less severity have to be included which requires the evaluation of sample size and power for the mixture of subpopulations with different severity of the disease. To accomplish this task, we derived closed-form expressions for sample size for the mixture of negative binomial subpopulations and performed extensive simulations to validate the results.
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