Advances In Cluster Correlated Data Analysis When Cluster Size Is Informative
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Advances in Cluster-Correlated Data Analysis when Cluster Size Is Informative
associated with the outcomes. We develop a rank-based statistic to test the marginal effect of the continuous covariate under this complex form of informativeness. Existing statistical methods based on ranks are inadequate in the presence of such informative latent groups. Through detailed simulation studies, we demonstrate the superior performance of our new test statistic compared to parametric or semiparametric methods. Collectively, these projects contribute to the understanding and handling of ICS in clustered data analysis. The proposed methodologies and guidelines provide valuable tools for researchers dealing with informative cluster sizes in the context of survival analysis and extend the applicability of existing techniques to more complex scenarios. The findings from this dissertation enhance the accuracy and reliability of statistical analyses in the presence of ICS, ultimately improving the validity of inferences drawn from clustered data.
Longitudinal Data Analysis
Although many books currently available describe statistical models and methods for analyzing longitudinal data, they do not highlight connections between various research threads in the statistical literature. Responding to this void, Longitudinal Data Analysis provides a clear, comprehensive, and unified overview of state-of-the-art theory
Correlation Clustering
Given a set of objects and a pairwise similarity measure between them, the goal of correlation clustering is to partition the objects in a set of clusters to maximize the similarity of the objects within the same cluster and minimize the similarity of the objects in different clusters. In most of the variants of correlation clustering, the number of clusters is not a given parameter; instead, the optimal number of clusters is automatically determined. Correlation clustering is perhaps the most natural formulation of clustering: as it just needs a definition of similarity, its broad generality makes it applicable to a wide range of problems in different contexts, and, particularly, makes it naturally suitable to clustering structured objects for which feature vectors can be difficult to obtain. Despite its simplicity, generality, and wide applicability, correlation clustering has so far received much more attention from an algorithmic-theory perspective than from the data-mining community. The goal of this lecture is to show how correlation clustering can be a powerful addition to the toolkit of a data-mining researcher and practitioner, and to encourage further research in the area.