Spatial analyses of nerve patterns and global testing approaches
Doktorsavhandling, 2024

This thesis consists of two parts: statistical analyses of and models for epidermal nerve fibers (ENFs), and extensions of global envelope tests. In the first part, the main goal was to improve our understanding of the ENF structure changes that occur as a result of nerve damage due to neurological disorders, such as diabetic neuropathy. For this purpose, different stochastic models were proposed. The ENF data were treated as point patterns in three-dimensional boxes, and samples from subjects suffering from diabetic neuropathy and healthy volunteers were considered. In Paper I, we introduced a new summary that measured the volume of the epidermis covered by the nerves and examined second-order properties of the underlying processes. Further, a three-dimensional point process model for the nerve structure was developed. The two-dimensional version of the model captured the planar spatial structure. However, the complete model could not capture the attraction between the nerve fiber endings in the data. Therefore, in Paper II a pairwise interaction Markov model allowing neighboring nerve endings to interact was proposed. In Paper III, we considered the two-dimensional projections of the ENF patterns and developed spatial thinning models to study the nerve death process. Insights from our analyses indicated that nerve mortality is guided by a biological process that favors the removal of isolated nerve trees. The goodness-of-fit of the models in Papers I-III was evaluated using global envelope tests. In the second part, we extended the global envelope tests for quantile regression and for comparison of distributions of $n$ samples. In Paper IV, we proposed non-parametric, permutation based global tests, that allowed for simultaneous inference of the quantile regression process. In Paper V, we proposed graphical $n$-sample tests for correspondence of distributions based on the global envelope testing framework. Further, we presented a detailed discussion regarding the graphical interpretation of the test results for each suggested test statistic.

epidermal nerve fibers

diabetic neuropathy

global quantile regression

death process

Anisotropy

permutation test

point processes.

Euler, Skeppsgränd 3
Opponent: Ute Hahn, Aarhus University, Denmark

Författare

Konstantinos Konstantinou

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Spatial modeling of epidermal nerve fiber patterns

Statistics in Medicine,;Vol. 40(2021)p. 6479-6500

Artikel i vetenskaplig tidskrift

Pairwise interaction Markov model for 3D epidermal nerve fibre endings

Journal of Microscopy,;Vol. 288(2022)p. 54-67

Artikel i vetenskaplig tidskrift

Statistical modeling of diabetic neuropathy: Exploring the dynamics of nerve mortality

Statistics in Medicine,;Vol. 42(2023)p. 4128-4146

Artikel i vetenskaplig tidskrift

Tomáš Mrkvička, Konstantinos Konstantinou, Mikko Kuronen, Mari Myllymäki. Global quantile regression.

Konstantinou Konstantinos, Tomáš Mrkvička, Mari Myllymäki.The power of visualizing distributional differences: Formal graphical $n$-sample tests

This thesis has two main parts: statistical analyses and models for nerve fiber patterns, and extensions of a particular non-parametric method for testing hypotheses involving functional data, called “global envelope tests”, to various statistical areas. In the first part, our aim was to understand how diabetic neuropathy affects nerve changes. Diabetic neuropathy is a medical condition that damages the nerves in the uppermost part of the skin. Symptoms of this condition can be treated with proper medical treatment if it is detected early, and therefore its diagnosis at the earliest possible stage is important. To this end, we compared data from people with earlystage neuropathy and healthy people, constructed stochastic models, and used spatial statistical methods to learn more about the nerve structure changes. To assess how well our statistical models captured the spatial structure of the observed nerve data, we considered summary functions from spatial statistics literature and used the so-called global envelope tests. In the second part, we further developed these tests to be used in other situations. To this end, we developed permutation strategies that allowed the application of these tests for quantile regression inference and for comparing distributions among two or more sample groups.

Ämneskategorier

Matematik

ISBN

978-91-8103-060-0

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 5518

Utgivare

Chalmers

Euler, Skeppsgränd 3

Opponent: Ute Hahn, Aarhus University, Denmark

Mer information

Senast uppdaterat

2024-07-29