The analysis of curves can be claimed to be the core of most scientific ventures. In this dissertation, we focus on the statistical aspect of this type of analysis. Here, the curves originate from health and food-related areas and include improvements in blood glucose measurements, classification of moles, measurements of parameters during liver transplants in pigs, and data from the monitoring of the quality of fish. More specifically, the statistical curve analysis consists of several perspectives were all have some kind of in- trinsic comparison effort. However, the main approaches in these studies are related to regression and the problem of finding suitable critical regions. The regression part consists of robust nonlinear regression and linear mixed models while the critical regions are found through classification and hypothesis testing in scale-space. By improving the critical decision boundaries through e.g. the Bonferroni correction of scale-space maps in Paper I, and developing features to improve decisions regarding the classification of moles in Paper II, we were able to obtain high sensitivity and specificity in the developed systems. Re- gression was an integral part of the classification effort in Paper II, the improvement of blood glucose measurements in Paper III, and the statistical analysis of parameters measured during liver transplantation in pigs in Paper IV.
Paper I is focused on maximizing sensitivity and specificity when detecting a significant change in the data. Here as in Paper II hyperspectral images are the source of data. The developed method produces a scale-space, where significant changes can be detected.
Paper II aims to maximize sensitivity, specificity, and precision in the classification of moles. This is accomplished through curves from subimages obtained from each channel of the hyperspectral images. These curves show characteristic features from three important classes of moles. By using these features through the regression of these curves, we accomplish high sensitivity, specificity, and precision in the classification pursuit.
In Paper III, we introduce a novel method for improving blood glucose estimation from continuous glucose measurements by using deconvolution. First, regression is used to estimate the parameters in the convolution kernel. Thereafter this response function was deconvolved through regression. In this way, we can estimate blood glucose from subcutaneous measurements. This gives a new method for controlling blood glucose levels which is of great importance for type 1 diabetes patients during and after exercise to avoid hypoglycemia.
Testing two different methods in liver transplantation of pigs, where the statistical analysis of curves was done through the application of linear mixed models, is the focus of Paper IV. An important output of this work is that the two treatments can be statistically distinguished through the use of linear mixed models
