The distribution of new enhancing lesion counts in multiple sclerosis: further explorations

Background A statistical distribution describing the number of new enhancing lesions seen on MRI in patients with MS is of great importance for improving the statistical methodology of clinical trials using new enhancing lesions as outcome measure. We examined whether there are superior alternatives for the currently proposed negative binomial (NB) distribution. Objective To determine the optimal statistical distribution describing new enhancing lesion counts from a selection of six conceivable models, and to assess the effect on the distribution of a treatment effect, varying follow-up duration and selection for activity at baseline. Methods The statistical NB, Poisson-Inverse Gaussian (P-IG), Poisson- Lognormal (P-LN), Neyman type A (NtA), Pólya-Aeppli (PA) and Zero Inflated Poisson (ZIP) distribution were fitted on new enhancing lesion data derived from one treated and two untreated cohorts of RRMS and relapsing SPMS patients and on subgroups of varying follow-up duration and selection for baseline activity. Measure of comparison was Akaike's information criterion (AIC). Results Both the subgroup analyses as well as a treatment had a noticeable effect on the distributional characteristics of new enhancing lesion counts. The NB distribution generally provided the most optimal fit, closely followed by the P-IG distribution and the P-LN distribution. Fits of the PA and NtA distribution were suboptimal, while the ZIP distribution was the least adequate for modelling new enhancing lesion counts. Conclusion The NB distribution is the optimal distribution for modelling new enhancing lesion counts, irrespective of the effect of treatment, follow-up duration or a baseline activity selection criterion.