A longitudinal model for magnetic resonance imaging lesion count data in multiple sclerosis patients

Magnetic resonance imaging (MRI) data are routinely collected at multiple time points during phase 2 clinical trials in multiple sclerosis. However, these data are typically summarized into a single response for each patient before analysis. Models based on these summary statistics do not allow the exploration of the trade-off between numbers of patients and numbers of scans per patient or the development of optimal schedules for MRI scanning. To address these limitations, in this paper, we develop a longitudinal model to describe one MRI outcome: the number of lesions observed on an individual MRI scan. We motivate our choice of a mixed hidden Markov model based both on novel graphical diagnostic methods applied to five real data sets and on conceptual considerations. Using this model, we compare the performance of a number of different tests of treatment effect. These include standard parametric and nonparametric tests, as well as tests based on the new model. We conduct an extensive simulation study using data generated from the longitudinal model to investigate the parameters that affect test performance and to assess size and power. We determine that the parameters of the hidden Markov chain do not substantially affect the performance of the tests. Furthermore, we describe conditions under which likelihood ratio tests based on the longitudinal model appreciably outperform the standard tests based on summary statistics. These results establish that the new model is a valuable practical tool for designing and analyzing multiple sclerosis clinical trials.