Motivated by real-time monitoring of dialysis, we aim at detecting difference between groups of Raman spectra generated from dialyzates at different time in one session. Baseline correction being a critical procedure in use of Raman Spectra, existing methods may not perform well on dialysis spectra due to nature of dialyzates, which contain numerous chemicals compounds. We first developed a new baseline correction method, Iterative Smoothing-spline with Root Error Adjustment (ISREA), which automatically adjusts intensities and employs smoothing-spline to produce a baseline in each iteration, providing better performance on dialysis spectra than a popular method Goldindec, and better accuracy regardless of types of samples. We proposed a two sample hypothesis testing on groups of baseline-corrected Raman spectra with ISREA. The uniqueness of the test lies in nature of the tested data. Instead of using Raman spectra as curves, we also consider a vector whose elements are peak intensities of biomarkers, meaning the data is regarded as mixed data and that a spectrum curve and a vector compose one observation. Our method tests on equality of the means of the two groups of mixed data. This method is based on asymptotic properties of the covariance of mixed data and FPCA. Simulation studies shows that our method is applicable to small sample size with proper power and size control. Meanwhile, to locate regions that contribute most to significant difference between two groups of univariate functional data, we developed a method to estimate the a sparse coefficient function by using a L1 norm penalty in functional logistic regression, and compared its performance with other methods. / Doctor of Philosophy / In U.S., there are more than 709,501 patients with End-Stage Renal Disease (ESRD). For those patients, dialysis is a standard treatment. While dialysis is time-consuming, expensive, and uncomfortable, it requires patients to take three sessions every week in facilities, and each session lasts for four hours regardless of patients' condition. An affordable, fast, and widely-applied technique called Raman spectroscopy draws attention. Spectral data from used dialysate samples collected at different time in one session can give information on the dialysis process and thus make real-time monitoring possible. With spectral data, we want to develop a statistical method that helps real-time monitoring on dialysis. This method can provide physicians with statistical evidence on dialysis process to improve their decision making, therefore increases efficiency of dialysis and better serve patients. On the other hand, Raman spectroscopy demands preprocessing called baseline correction on the raw spectra. A baseline is generated because of the nature of Raman technique and its instrumentation, which adds complexity to the spectra and interfere with analysis. Despite popularity of this technique and many existing baseline correction method, we found performance on dialysate spectra under expectation. Hence, we proposed a baseline correction method called Iterative Smoothing-spline with Root Error Adjustment (ISREA) and ISREA can provide better performance than existing methods. In addition, we come up with a method that is able to detect difference between the two groups of ISREA baseline-corrected spectra from dialysate collected at different time. Furthermore, we proposed and applied sparse functional logistic regression on two groups to locate regions where the significant difference comes from.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/99037 |
| Date | 17 June 2020 |
| Creators | Xu, Yunnan |
| Contributors | Statistics, Du, Pang, Guo, Feng, Deng, Xinwei, Kim, Inyoung |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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