Sample size calculation for clinical trials with correlated count measurements based on the negative binomial distribution

Statistical inference based on correlated count measurements are frequently performed in biomedical studies. Most of existing sample size calculation methods for count outcomes are developed under the Poisson model. Deviation from the Poisson assumption (equality of mean and variance) has been widely documented in practice, which indicates urgent needs of sample size methods with more realistic assumptions to ensure valid experimental design. In this study, we investigate sample size calculation for clinical trials with correlated count measurements based on the negative binomial distribution. This approach is flexible to accommodate overdispersion and unequal measurement intervals, as well as arbitrary randomization ratios, missing data patterns, and correlation structures. Importantly, the derived sample size formulas have closed forms both for the comparison of slopes and for the comparison of time-averaged responses, which greatly reduces the burden of implementation in practice. We conducted extensive simulation to demonstrate that the proposed method maintains the nominal levels of power and type I error over a wide range of design configurations. We illustrate the application of this approach using a real epileptic trial.