Statistical methods for early discovery of diabetic neuropathy using epidermal nerve fiber data

The main aim with the work in this thesis is to increase the understanding of the effects diabetic neuropathy has on the epidermal nerve fibers and thereby find methods to detect the disorder at an earlier stage. Epidermal nerve fibers (ENFs) are small sensory nerve fibers in the skin, sensing heat and pain. Earlier diagnosis of the disorder can help to slow down the progression and delay the symptoms. The data used are skin samples from a group of 32 healthy volunteers and 20 diabetic subjects with differently progressed diabetic neuropathy, in which the nerve fibers have been traced using confocal microscopy. One part of the work is based on methods from spatial statistics, considering the points where the nerve fibers enter the epidermis and where they terminate as realizations of point processes. The point patterns obtained from healthy subjects are compared to those of subjects at an early stage of the neuropathy, in terms of spatial summary statistics, including a new tool to quantify the area of the skin covered by a nerve, the \textit{reactive territory}. Significant differences between the groups are found, that has not previously been reported. Moreover, a point process model for the nerve fiber patterns is proposed, to help the understanding of the growth process of the nerve fibers. In the other part of the work, hierarchical models for the nerve fiber segments are proposed, and used to perform unsupervised classification. The results are evaluated in terms of how well the diabetic subjects are separated from the healthy ones. It is found that the results are considerably improved when including the information about the nerve fiber segments, compared to only using the number of nerve fibers