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Alzheimer's disease (AD) is associated with progressive cognitive decline leading to dementia. The atrophy/loss of brain structure as seen on Magnetic Resonance Imaging (MRI) is strongly correlated with the severity of the cognitive impairment in AD. In this paper, we set out to find associations between predefined regions of the brain (regions of interest; ROIs) and the severity of the disease. Specifically, we use these associations to address two important issues in AD: (i) typical versus atypical atrophy patterns and (ii) the origin and direction of progression of atrophy, which is currently under debate.We observed that each AD-related ROI is associated with a wide range of severity and that the difference between ROIs is merely a difference in severity distribution. To model differences between the severity distribution of a subpopulation (with significant atrophy in certain ROIs) and the severity distribution of the entire population, we developed the concept of Distributional Association Rules. Using the Distributional Association Rules, we clustered ROIs into disease subsystems. We define a disease subsystem as a contiguous set of ROIs that are collectively implicated in AD. AD is known to be heterogeneous in the sense that multiple sets of ROIs may be related to the disease in a population. We proposed an enhancement to the association rule mining where the algorithm only discovers association rules with ROIs that form an approximately contiguous volume. Next, we applied these association rules to infer the direction of disease progression based on the support measures of the association rules. We also developed a novel statistical test to determine the statistical significance of the discovered direction.We evaluated the proposed method on the Mayo Clinic Alzheimer's Disease Research Center (ADRC) prospective patient cohorts. The key achievements of the methodology is that it accurately identified larger disease subsystems implicated in typical and atypical AD and it successfully mapped the directions of disease progression.The wealth of data available in Radiology gives rise to opportunities for applying this methodology to map out the trajectory of several other diseases, e.g. other neuro-degenerative diseases and cancers, most notably, breast cancer. The applicability of this method is not limited to image data, as associating predictors with severity provides valuable information in most areas of medicine as well as other industries.

Associative classification is a predictive modeling technique that constructs a classifier based on class association rules (also known as predictive association rules; PARs). PARs are association rules where the consequence of the rule is a class label. Associative classification has gained substantial research attention because it successfully joins the benefits of association rule mining with classification. These benefits include the inherent ability of association rule mining to extract high-order interactions among the predictors--an ability that many modern classifiers lack--and also the natural interpretability of the individual PARs.Associative classification is not without its caveats. Association rule mining often discovers a combinatorially large number of association rules, eroding the interpretability of the rule set. Extensive effort has been directed towards developing interestingness measures, which filter (predictive) association rules after they have been generated. These interestingness measures, albeit very successful at selecting interesting rules, lack two features that are highly valuable in the context of classification. First, only few of the interestingness measures are rooted in a statistical model. Given the distinction between a training and a test data set in the classification setting, the ability to make statistical inferences about the performance of the predictive classification rules on the test set is highly desirable. Second, the unfiltered set of predictive assocation rules (PARs) are often redundant, we can prove that certain PARs will not be used to construct a classification model given the presence of other PARs.In this paper, we propose a simple statistical model towards making inferences on the test set about the various performance metrics of predictive association rules. We also derive three filtering criteria based on hypothesis testing, which are very selective (reduce the number of PARs to be considered by the classifier by several orders of magnitude), yet do not effect the performance of the classification adversely. In the case, where the classification model is constructed as a logistic model on top of the PARs, we can mathematically prove, that the filtering criteria do not significantly effect the classifier's performance. We also demonstrate empirically on three publicly available data sets that the vast reduction in the number of PARs indeed did not come at the cost of reducing the predictive performance.