Power Analyses for Negative Binomial Models with Application to Multiple Sclerosis Clinical Trials

We use negative binomial (NB) models for the magnetic resonance imaging (MRI)-based brain lesion count data from parallel group (PG) and baseline versus treatment (BVT) trials for relapsing remitting multiple sclerosis (RRMS) patients, and describe the associated likelihood ratio (LR), score, and Wald tests. We perform power analyses and sample size estimation using the simulated percentiles of the exact distribution of the test statistics for the PG and BVT trials. When compared to the corresponding nonparametric test, the LR test results in 30–45% reduction in sample sizes for the PG trials and 25–60% reduction for the BVT trials.