Modelling MRI enhancing lesion counts in multiple sclerosis using a negative binomial model: implications for clinical trials

Abstract

In multiple sclerosis (MS) the number of new enhancing lesions seen on monthly magnetic resonance imaging (MRI) scans is the most widely used response variable in MRI-monitored studies of experimental treatments. However, no statistical model has been proposed to describe the distribution of the number of such lesions across MS patients. This article briefly summarizes the statistical models for counted data. The negative binomial (NB) model is proposed to fit the number of new enhancing lesions counted in a set of 56 untreated MS patients followed for 9 months. It is shown that the large variability present in this data set is better addressed by the NB model (residual deviance=66.6, 54 degrees of freedom) than by the Poisson model (residual deviance=1830.1, 55 degrees of freedom). Applications of the parametrization of lesion counts are discussed, and an example related to computer simulations for the sample size estimation is presented.