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Modelling Spatial Medical Data
Abstract
Models are sometimes incomplete, especially in scaling data where other information of large regions needs to be predicted by smaller ones. Uncertainty analysis is the process of assessing uncertainty in modelling or scaling to identify major uncertainty sources, quantify their degree and relative importance, examine their effects on model output under different scenarios, and determine prediction accuracy. Especially for large dimensional data where spatial process in regional investigation are difficult to applied due to incompleteness leading us to spatial heterogeneity and non-linearity of our data. Modelling the uncertainty particular in scaling data starts with a general structure (linear most of the time) that explains as accurate as it is the real data and the model is built through adding variables, which are significant or which aid in prediction (hierarchical modelling). Parameter estimation is an important issue for the evaluation of these proposed models. Statistical techniques based on the spatial modelling could be proposed to overcome the problem of dimensionality and the spatial homogeneity between different grains levels based on the neighbourhood structure of the regions with similar characteristics. Investigation of the neighbourhood structure analysis could be applied using kriging or variogram techniques. In this work, we introduce and analyse methodologies for scaling data under uncertainty where incomplete data can be explained by spatial modelling at different scales. Incomplete data of uncertainties in regions involve spatial homogeneity upon neighbourhood structure between regions. The last could be illustrated by using spatial modelling techniques (like spatial autocorrelation, partition functions, and multilevel models). Parameter estimation of these models could be achieved by using stochastic (spatial hierarchical models, kriging, auto-correlation) methods. Comparison between different models could be achieved by considering statistical measures like log-likelihood ratio test. The best model is the one, which explains better the real data.
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