A flexible mixed-effect negative binomial regression model for detecting unusual increases in MRI lesion counts in individual multiple sclerosis patients

We develop a new modeling approach to enhance a recently proposed method to detect increases of contrast-enhancing lesions (CELs) on repeated magnetic resonance imaging, which have been used as an indicator for potential adverse events in multiple sclerosis clinical trials. The method signals patients with unusual increases in CEL activity by estimating the probability of observing CEL counts as large as those observed on a patient's recent scans conditional on the patient's CEL counts on previous scans. This conditional probability index (CPI), computed based on a mixed-effect negative binomial regression model, can vary substantially depending on the choice of distribution for the patient-specific random effects. Therefore, we relax this parametric assumption to model the random effects with an infinite mixture of beta distributions, using the Dirichlet process, which effectively allows any form of distribution. To our knowledge, no previous literature considers a mixed-effect regression for longitudinal count variables where the random effect is modeled with a Dirichlet process mixture. As our inference is in the Bayesian framework, we adopt a meta-analytic approach to develop an informative prior based on previous clinical trials. This is particularly helpful at the early stages of trials when less data are available. Our enhanced method is illustrated with CEL data from 10 previous multiple sclerosis clinical trials. Our simulation study shows that our procedure estimates the CPI more accurately than parametric alternatives when the patient-specific random effect distribution is misspecified and that an informative prior improves the accuracy of the CPI estimates. Copyright (c) 2015 John Wiley & Sons, Ltd.