Final nanoparticle size distribution under unusual parameter regimes.

We explore the large-scale behavior of a stochastic model for nanoparticle growth in an unusual parameter regime. This model encompasses two types of reactions: nucleation, where n monomers aggregate to form a nanoparticle, and growth, where a nanoparticle increases its size by consuming a monomer. Reverse reactions are disregarded.

An Application of Maximal Exponential Models to Duality Theory.

We use maximal exponential models to characterize a suitable polar cone in a mathematical convex optimization framework. A financial application of this result is provided, leading to a duality minimax theorem related to portfolio exponential utility maximization.

Time to first relapse as an endpoint in multiple sclerosis clinical trials.

Background: The increasing number of effective therapies to treat multiple sclerosis (MS) raises ethical concerns for the use of placebo in clinical trials, suggesting that new clinical trial design strategies are needed.

Objectives: To evaluate time to first relapse as an endpoint for MS clinical trials.

Methods: A recently-developed model fitting the distribution of time to first relapse in MS was used for simulations estimating the sample sizes of trials using this as an outcome, and for comparison with the size of trials using the annualized relapse rate (ARR) as the primary outcome.

A parametric model fitting time to first event for overdispersed data: application to time to relapse in multiple sclerosis.

In this article, we propose a parametric model for the distribution of time to first event when events are overdispersed and can be properly fitted by a Negative Binomial distribution. This is a very common situation in medical statistics, when the occurrence of events is summarized as a count for each patient and the simple Poisson model is not adequate to account for overdispersion of data. In this situation, studying the time of occurrence of the first event can be of interest.