Stochastické modelovaní a optimalizace rizik

Abstract

Doctoral thesis called Stochastic modeling and optimization of risks deals with stochastic modeling in two application areas of medicine, namely in the field of colorectal surgery, where the occurrence of anastomotic leakage in rectal surgery is investigated. The second investigated area is the treatment of critical limb ischemia by stem cells. The thesis show methods by which it is possible to mathematically describe these medical problems, compare the effectiveness of the methods used and predict the success of treatment.

The thesis contains eleven chapters. The introductory part defines the concept of stochastic modeling. The second chapter summarizes the objectives of the dissertation. In the chapter Introduction to Medical Issues there is a brief overview of two modeled application areas, colorectal surgery and treatment of critical limb ischemia using stem cells. The following chapters give an overview of mathematical theory. In the chapter 4 there is a passage devoted to the classical survival analysis. Chapter five give innovative approach in survival analysis called nonparametric predictive inference. Chapter six describes the principal component analysis, at chapter seven is description of bootstrap methods. Chapter eight contains logistical regression. In the chapters nine and ten is described modeling at applications areas. In the appendix is the overall conclusion with the application effect in medicine. Next follows list of used literature and an overview of the author's publications. The attachment provides brief summaries of some R-scripts used for implementation of the created stochastic models. The full version of the R-scripts is included on the attached CD.