Exploring the topology of progressive disease data

Abstract

This thesis aims to investigate the crucial objective of improving the comprehension of clinical data structure, acknowledging its increasing importance. We initiate our investigation by exploring the historical context of topological data analysis, a fundamental approach that facilitates the extraction of the inherent topological structure of data. This methodology reveals discrete segments within the dataset, wherein specific segments may indicate the presence of diseases in their initial stages, while other segments may correspond to different subtypes of advanced diseases. The identification of areas has significant significance for clinicians as it enables a deeper understanding of patients' symptoms within the disease topology and facilitates the implementation of personalised treatments. In the following section, we will go into the domain of Pseudo Time techniques, which enable the creation of temporal models from non-temporal cross-sectional data. These approaches provide useful insights by deducing temporal aspects of diseases. Nevertheless, the effectiveness of these methods relies heavily on the selection of suitable distance measures and labelling schemes that may effectively direct the process of trajectory modelling. The utilisation of clinical staging data, namely the categorisation of patients into "early stage" and "advanced stage," plays a crucial role in limiting the potential biases of pseudo-time models, hence guaranteeing the accurate representation of disease progression patterns. The advancement of our inquiry involves the use of two separate methodologies in constructing temporal phenotypes using data topology analysis: topological data analysis and pseudo time-series. Using data on type 2 diabetes, we give evidence that topological data analysis can effectively identify trajectories that reflect various temporal phenotypes. Additionally, we show that pseudo-time series analysis can be used to infer a state space model that exhibits transitions between hidden states, each representing discrete temporal abnormalities. Significantly, both approaches emphasise the importance of lipid profiles in identifying these symptoms. Our research presents the innovative TDA-PTS algorithm, which combines pseudo temporal and topological data analysis. The efficacy of the combined method is assessed on three different datasets, namely simulated data, diabetic data, and genomic data. This evaluation demonstrates how the system effectively identifies unique temporal phenotypes in each disease by considering various trajectories throughout the progression of the disease. Moreover, we explore the use of clinical staging data in order to construct robust and realistic trajectories. In this study, we utilise simulated data to showcase the accuracy attained in estimating the fundamental transition parameters using limited pseudo time approaches, which effectively mitigate the occurrence of unrealistic transitions. In the context of breast cancer pseudo time models, the trajectories are constrained by using the uniformity of cell size as a proxy of disease staging. This constraint leads to the development of models that more accurately depict the progressive increase in symptoms over time. Finally, we employ these techniques to actual glaucoma data, therefore confirming the efficacy of the algorithm in accurately representing the advancement and categorisation of the condition. This study provides a thorough examination of illness dynamics within clinical datasets, presenting information in a chronological order that spans from background information to methods and outcomes. The findings of this research make a substantial contribution to the field, enhancing our comprehension and modelling of disease dynamics.