# 2 UBC Statistics MSc Student Talks

Thursday, August 21, 2014 - 11:00
UBC Statistics MSc Students Mahsin MD (11:00am) and Peijun Sang (11:30am)
Statistics Seminar
Room 4192, Earth Sciences Building (2207 Main Mall)

Determination of Sample Size for Phase II Clinical Trials in Multiple Sclerosis using Lesional Recovery as an Outcome Measure

Speaker:  Md Mahsin

Multiple sclerosis (MS) is an inflammatory demyelinating disease of the central nervous system. The hallmark feature of the disease is the formation of focal demyelinating lesions accompanied by myelin destruction in the white matter (WM). Magnetic resonance imaging (MRI) is used identify and visualize these lesions. Repeated MRI scanning of patients (most often monthly) over period of months has become a standard protocol for Phase II trials of experimental treatment in MS. The formation of WM lesions in MS is characterized by inflammatory demyelination and then remyelination usually occurs over several months after lesion formation. Hence, a measure reflecting lesional recovery is a promising outcome for phase II clinical trials that assess the eff ect of therapies intended to induce remyelination. Our objective is to provide sample sizes required to detect such an experimental treatment e ffect with certain statistical power. We consider a parallel group design with two arms of equal number of subjects. The study design is considered as a three level hierarchical data structure where lesions are nested within subjects and are assessed repeatedly over the study period. Variable numbers of new enhancing lesions per subject and variable numbers of measurements at before and after enhancement (depends on the time of the lesion's appearance) are also considered. The numbers of subjects in each treatment arm necessary to obtain statistical powers of 80% or 90% are determined for di erent numbers (6; 9; 12) of monthly follow-up scans. A mixed-e ffects linear regression model is used for this sample size determination.

Copula Models from Combining Sub-models for Different Groups

Speaker:  Peijun Sang

The multivariate Student t copula is widely used in modeling the dependence structure of financial return data. However, it is subject to tail symmetry. The existence of tail asymmetry, particularly skewed to the joint lower tail, has been shown in a variety of situations. I will talk about how to employ skew-t distributions to allow for tail dependence and asymmetry.  Another interesting research topic I want to discuss is how to combine distributions of variables from different non-overlapping groups. Structured factor copula models proposed by Krupskii and Joe consist of one approach. I will introduce another method to handle this problem. Applications to financial return data will be included to make a comparison of these two methods.