Optimization and Machine Learning Methods for Diagnostic Testing of Prostate Cancer

Technological advances in biomarkers and imaging tests are creating new avenues to advance precision health for early detection of cancer. These advances have resulted in multiple layers of information that can be used to make clinical decisions, but how to best use these multiple sources of information is a challenging engineering problem due to the high cost and imperfect sensitivity and specificity of these tests. Questions that need to be addressed include which diagnostic tests to choose and how to best integrate them, in order to optimally balance the competing goals of early disease detection and minimal cost and harm from unnecessary testing. To study these research questions, we present new optimization-based models and data-driven analytic methods in three parts to improve early detection of prostate cancer (PCa). In the first part, we develop and validate predictive models to assess individual PCa risk using known clinical risk factors. Because not all men with newly-diagnosed PCa received imaging at diagnosis, we use an established method to correct for verification bias to evaluate the accuracy of published imaging guidelines. In addition to the published guidelines, we implement advanced classification modeling techniques to develop accurate classification rules identifying which patients should receive imaging. We propose a new algorithm for a classification model that considers information of patients with unverified disease and the high cost of misclassifying a metastatic patient. We summarize our development and implementation of state-wide, evidence-based imaging criteria that weigh the benefits and harms of radiological imaging for detection of metastatic PCa. In the second part of this thesis, we combine optimization and machine learning approaches into a robust optimization framework to design imaging guidelines that can account for imperfect calibration of predictions. We investigate efficient and effective ways to combine multiple medical diagnostic tests where the result of one test may be used to predict the outcome of another. We analyze the properties of the proposed optimization models from the perspectives of multiple stakeholders, and we present the results of fast approximation methods that we show can be used to solve large-scale models. In the third and final part of this thesis, we investigate the optimal design of composite multi-biomarker tests to achieve early detection of prostate cancer. Biomarker tests vary significantly in cost, and cause false positive and false negative results, leading to serious health implications for patients. Since no single biomarker on its own is considered satisfactory, we utilize simulation and statistical methods to develop the optimal diagnosis procedure for early detection of PCa consisting of a sequence of biomarker tests, balancing the benefits of early detection, such as increased survival, with the harms of testing, such as unnecessary prostate biopsies. In this dissertation, we identify new principles and methods to guide the design of early detection protocols for PCa using new diagnostic technologies. We provide important clinical evidence that can be used to improve health outcomes of patients while reducing wasteful application of diagnostic tests to patients for whom they are not effective. Moreover, some of the findings of this dissertation have been implemented directly into clinical practice in the state of Michigan. The models and methodologies we present in this thesis are not limited to PCa, and can be applied to a broad range of chronic diseases for which diagnostic tests are available.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143976/1/smerdan_1.pd

Combining Exploration and Exploitation in Active Learning

This thesis investigates the active learning in the presence of model bias. State of the art approaches advocate combining exploration and exploitation in active learning. However, they suffer from premature exploitation or unnecessary exploration in the later stages of learning. We propose to combine exploration and exploitation in active learning by discarding instances outside a sampling window that is centered around the estimated decision boundary and uniformly draw sample from this window. Initially the window spans the entire feature space and is gradually constricted, where the rate of constriction models the exploration-exploitation tradeoff. The desired effect of this approach (CExp) is that we get an increasing sampling density in informative regions as active learning progresses, resulting in a continuous and natural transition from exploration to exploitation, limiting both premature exploitation and unnecessary exploration. We show that our approach outperforms state of the art on real world multiclass datasets. We also extend our approach to spatial mapping problems where the standard active learning assumption of uniform costs is violated. We show that we can take advantage of \emph{spatial continuity} in the data by geographically partitioning the instances in the sampling window and choosing a single partition (region) for sampling, as opposed to taking a random sample from the entire window, resulting in a novel spatial active learning algorithm that combines exploration and exploitation. We demonstrate that our approach (CExp-Spatial) can generate cost-effective sampling trajectories over baseline sampling methods. Finally, we present the real world problem of mapping benthic habitats where bathymetry derived features are typically not strong enough to discriminate the fine details between classes identified from high-resolution imagery, increasing the possiblity of model bias in active learning. We demonstrate, under such conditions, that CExp outperforms state of the art and that CExp-Spatial can generate more cost-effective sampling trajectories for an Autonomous Underwater Vehicle in contrast to baseline sampling strategies

Combining Exploration and Exploitation in Active Learning

This thesis investigates the active learning in the presence of model bias. State of the art approaches advocate combining exploration and exploitation in active learning. However, they suffer from premature exploitation or unnecessary exploration in the later stages of learning. We propose to combine exploration and exploitation in active learning by discarding instances outside a sampling window that is centered around the estimated decision boundary and uniformly draw sample from this window. Initially the window spans the entire feature space and is gradually constricted, where the rate of constriction models the exploration-exploitation tradeoff. The desired effect of this approach (CExp) is that we get an increasing sampling density in informative regions as active learning progresses, resulting in a continuous and natural transition from exploration to exploitation, limiting both premature exploitation and unnecessary exploration. We show that our approach outperforms state of the art on real world multiclass datasets. We also extend our approach to spatial mapping problems where the standard active learning assumption of uniform costs is violated. We show that we can take advantage of \emph{spatial continuity} in the data by geographically partitioning the instances in the sampling window and choosing a single partition (region) for sampling, as opposed to taking a random sample from the entire window, resulting in a novel spatial active learning algorithm that combines exploration and exploitation. We demonstrate that our approach (CExp-Spatial) can generate cost-effective sampling trajectories over baseline sampling methods. Finally, we present the real world problem of mapping benthic habitats where bathymetry derived features are typically not strong enough to discriminate the fine details between classes identified from high-resolution imagery, increasing the possiblity of model bias in active learning. We demonstrate, under such conditions, that CExp outperforms state of the art and that CExp-Spatial can generate more cost-effective sampling trajectories for an Autonomous Underwater Vehicle in contrast to baseline sampling strategies

Sensing Structured Signals with Active and Ensemble Methods

Modern problems in signal processing and machine learning involve the analysis of data that is high-volume, high-dimensional, or both. In one example, scientists studying the environment must choose their set of measurements from an infinite set of possible sample locations. In another, performing inference on high-resolution images involves operating on vectors whose dimensionality is on the order of tens of thousands. To combat the challenges presented by these and other applications, researchers rely on two key features intrinsic to many large datasets. First, large volumes of data can often be accurately represented by a few key points, allowing for efficient processing, summary, and collection of data. Second, high-dimensional data often has low-dimensional intrinsic structure that can be leveraged for processing and storage. This thesis leverages these facts to develop and analyze algorithms capable of handling the challenges presented by modern data. The first scenario considered in this thesis is that of monitoring regions of low oxygen concentration (hypoxia) in lakes via an autonomous robot. Tracking the spatial extent of such hypoxic regions is of great interest and importance to scientists studying the Great Lakes, but current systems rely heavily on hydrodynamic models and a very small number of measurements at predefined sample locations. Existing active learning algorithms minimize the samples required to determine the spatial extent but do not consider the distance traveled during the estimation procedure. We propose a novel active learning algorithm for tracking such regions that balances both the number of measurements taken and the distance traveled in estimating the boundary of the hypoxic zone. The second scenario considered is learning a union of subspaces (UoS) model that best fits a given collection of points. This model can be viewed as a generalization of principal components analysis (PCA) in which data vectors are drawn from one of several low-dimensional linear subspaces of the ambient space and has applications in image segmentation and object recognition. The problem of automatically sorting the data according to nearest subspace is known as subspace clustering, and existing unsupervised algorithms perform this task well in many situations. However, state-of-the-art algorithms do not fully leverage the problem geometry, and the resulting clustering errors are far from the best possible using the UoS model. We present two novel means of bridging this gap. We first present a method of incorporating semi-supervised information into existing unsupervised subspace clustering algorithms in the form of pairwise constraints between items. We next study an ensemble algorithm for unsupervised subspace clustering that functions by combining the outputs from many efficient but inaccurate base clusterings to achieve state-of- the-art performance. Finally, we perform the first principled study of model selection for subspace clustering, in which we define clustering quality metrics that do not rely on the ground truth and evaluate their ability to reliably predict clustering accuracy. The contributions of this thesis demonstrate the applicability of tools from signal processing and machine learning to problems ranging from scientific exploration to computer vision. By utilizing inherent structure in the data, we develop algorithms that are efficient in terms of computational complexity and other realistic costs, making them truly practical for modern problems in data science.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/140795/1/lipor_1.pd