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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/997| Statistical Analysis of OGTT Results | |
| NICOLAS ELIO KUSCHINSKI KATHMANN | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| Estadística bayesiana | |
| Type 2 diabetes is a serious health condition that has only become more prevalent in recent years. One tool frequently used to help in its diagnosis is the oral glucose tolerance test, or OGTT. The methods currently in use for studying OGTT data, however, are basic, and do not take full advantage of the structure of the data created in an OGTT test. This work proposes a model for the mathematical analysis of OGTT data using Bayesian statistics on inverse problems. The main focus of the thesis is rst to propose the model, and then to investigate various potential ramications and improvements on it. A model for OGTT data analysis is proposed, and tested on data from real OGTT tests with results that t data well and closely match the intuition of medical collaborators. A second test for diabetes has recently been proposed by researchers in Cuernavaca and Mexico City. Variable selection methodology is developed to study the ability of this tool to predict OGTT results. The results are unpromising. However, as a result of this analysis, a new technique for variable selection is proposed. This technique is christened FATSO and is useful for likelihood regularization in situations where intuitive parameter tuning is desirable. This is generally useful enough to give an importance to the new test which extends beyond merely OGTT analysis. A potential improvement on the OGTT protocol is considered which would change the times at which OGTT data is collected. This modication is treated as a problem in the Bayesian design of experiments, and a new algorithm is developed for this purpose. Another modication to the OGTT protocol is also considered which changes the method used for collecting samples, replacing it with one that is cheaper and which reduces patient discomfort. Although this method was thought to be too imprecise for the purposes of an OGTT, the mathematical | |
| 05-08-2019 | |
| Tesis de doctorado | |
| ESTADÍSTICA | |
| Versión aceptada | |
| acceptedVersion - Versión aceptada | |
| Aparece en las colecciones: | Tesis del CIMAT |
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| TE 718.pdf | 2.59 MB | Adobe PDF | Visualizar/Abrir |