Shu Wang of the Department of Biostatistics defends her dissertation on "Clustering Methods with Variable Selection for Data with Mixed Variable Types of Limits of Detection".
Committee Chairpersons: Jonathan Yabes, PhD and Joyce Chang, PhD, Department of Medicine
Stewart Anderson, PhD, Department of Biostatistics
Qi Mi, PhD, Department of Sports Medicine and Nutrition
Christopher Seymour, MD, MSc, Department of Critical Care Medicine
Graduate faculty of the University and all other interested parties are invited to attend
Clustering has emerged as one of the most essential and popular techniques for discovering patterns in data. Although clustering methods continue to be developed and adapted to cope with increasing complexity in data, certain features in datasets could limit the utilization of the existing approaches. First, many of the existing clustering methods are only useful for data with a single variable type – either all continuous or all categorical – despite the abundance of data with mixed variable types especially in the biomedical field. Second, standard cluster analyses typically assume that variables were collected completely and accurately. However, measurements for clinical biomarker data are often subject to limits of detection (LOD). In addition to these limitations, researchers are recently getting more interest in variable importance due to the increasing number of variables that become available for clustering. To achieve the goal of variable selection, and overcome aforementioned challenges, this dissertation proposes a non-parametric clustering method with variable selection for datasets with mixed types of variables, as well as a Bayesian framework for model-based clustering method with variable selection and the ability to handle censored biomarker variables.
In the first section, we propose a hybrid density- and partition-based (HyDaP) algorithm for mixed variable types to simultaneously find the clusters and the variables that are most important for clustering. The HyDaP algorithm involves two steps: variable selection step and clustering step. In the variable filtration step, we first identify the data clustering structure formed by continuous variables. We propose and define three cluster structures to aid in understanding the contribution of continuous variables to clustering. We then implemented variable filtration procedures tailored to the specific cluster structure in selecting relevant variables. The selected variables are used in the clustering step where we apply our proposed novel dissimilarity measure for mixed data type together with an existing clustering algorithm (e.g. K-medoids) to find the clusters. Simulations across various scenarios and cluster structures were conducted to examine the performance of our proposed method compared to commonly used clustering algorithms.
In the second section, we propose a finite mixture model under the Bayesian framework to simultaneously conduct variable selection, account for biomarker LOD and obtain clustering results. Finite mixture models for clustering perform well when parametric assumptions are met. However, it typically relies on the EM algorithm which could be sensitive to the choice of initial values. Thus, we took a Bayesian approach to obtain parameter estimates and the cluster membership. In addition, we put a spike-and-slab type of prior on each variable to obtain variable importance. To account for LOD, we added one more step in Gibbs sampling that iteratively fills in biomarker values below or above LODs. The performance of this method was examined under the same simulation settings in the first section.
PUBLIC HEALTH SIGNIFICANCE: Uncovering subgroups and patterns in the data play an important role in precision medicine. Cluster analysis is an essential tool to accomplish this. However clustering methods need to evolve to cope with increasing amount and complexity of data being collected. Our proposed clustering algorithms can be applied to electronic health record (EHR) data that may include mixed types of variables and biomarkers with limit of detection. It allows to discover patient subgroups and identify important variables for clustering at the same time.