Inference for a Poisson-Inverse Gaussian Model with an Application to Multiple Sclerosis Clinical Trials

Abstract

Magnetic resonance imaging (MRI) based new brain lesion counts are widely used to monitor disease progression in relapsing remitting multiple sclerosis (RRMS) clinical trials. These data generally tend to be overdispersed with respect to a Poisson distribution. It has been shown that the Poisson-Inverse Gaussian (P-IG) distribution fits better than the negative binomial to MRI data in RRMS patients that have been selected for lesion activity during the baseline scan. In this paper we use the P-IG distribution to model MRI lesion count data from RRMS parallel group trials. We propose asymptotic and simulation based exact parametric tests for the treatment effect such as the likelihood ratio (LR), score and Wald tests. The exact tests maintain precise Type I error levels whereas the asymptotic tests fail to do so for small samples. The LR test remains empirically unbiased and results in 30–50 % reduction in sample sizes required when compared to the Wilcoxon rank sum (WRS) test. The Wald test has the highest power to detect a reduction in the number of lesion counts and provides a 40–57 % reduction in sample sizes when compared to the WRS test.