Modelli statistici per lo studio della Fibrillazione Atriale

This work involves the analysis of a dataset consisting of the RR intervals, an ECG feature, of ten different patients before, during and after an event of Atrial Fibrillation (AF), a cardiac arrhythmia relatively common among the population. More precisely, in Chapter 1 we study the problem of AF from a medical point of view and we describe in detail the dataset available. In Chapter 2 we deepen the theory of time series analysis. In particular we have analyzed the ARIMA (Auto-Regressive Integrated Moving Average) class processes. Within Chapter 3, after the identification of a suitable model to describe the evolution of the series of RR intervals during AF, we propose an innovative method to identify the phenomenon of AF by studying certain statistical parameters of the chosen model. Then we evaluate the performance of the proposed method in terms of timeliness. Chapter 4 focuses its attention on control charts, a special tool used in SPC (Statistical Process Control). In Chapter 5, we present the results obtained by applying the tools described in Chapter 4 to the series of RR intervals before, during and after AF. Then we illustrate the strengths and weaknesses of the analysis (also in respect of the results presented in Chapter 3). In the end there are two appendices: the first contains two tables of the control charts and the second presents the codes used in data analysis. The purpose of this thesis is to find one or more methods to quickly detect both the onset and the end of AF by monitoring the time series of RR intervals. Moreover, the work in this paper, besides providing a deeper understanding of the clinical problem and more effective results through a statistical analysis, also led to innovative contributions by adapting to this case models belonging to a very different research area (SPC).