Causal Inference in Survival Analysis for Personalised Health Care

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Copyright: Zhu, Elliott
The central aim of this thesis is concerned with the elucidation of cause-effect relationships from observational data among variables or events in the context of personalised healthcare. Appropriate methodology for extracting such relationships has been developed and discussed within the scope of longitudinal survival analysis. The thesis rethinks two fundamental questions of causality: (1) What empirical evidence is required for legitimate inference of cause-effect relationships? (2) Given that we are willing to accept causal information about a phenomenon, how can we draw inferences from such information? These questions have been without satisfactory answers in the light of observational healthcare, in part because we have not had clear definitions for the causal effect given the ever complex data structure and clinical questions on the unobserved outcome of survival probability, and in part because we have not had effective mathematical tools for deriving individualised causal answers to these questions. In the last decade, owing partly to advances in machine learning models, causality has undergone a major transformation: from a concept shrouded in properly designed randomised experiments into a mathematical object with well-defined semantics which can potentially be identified from observational data. This development has significantly brought down the cost of personalised healthcare in both medication discovery and evaluation. This thesis provides a systematic account of this causal transformation, addressed primarily to epidemiologists, particularly the pharmacoepidemiologist. Following a description of the conceptual and mathematical languages used in causal inference, this thesis emphasizes the development of practical methods for elucidating potentially causal relationships from (longitudinal) observational data, estimating the effects of treatment, and providing recommendations of treatments based on observed scenarios. I have tried in this thesis to present machine learning tools that handle causal relationships side by side with statistical probability theory. The prerequisites are startlingly simple, the results are straightforward. No more than basic skills in probability theory and some familiarity with machine learning are needed for the reader to begin solving causal problems that are too complex for the unaided intellect. The sequence of discussion follows more or less the chronological order by which I have tackled these topics, thus recreating for the reader the sense of progress that accompanied these developments. Following the introductory chapter (Chapter 1), I start with the formal description and review of the mathematical language of causal inference, in particular, how one can go about discovering cause-effect relationships using observational data (Chapter 2). I then proceed to the question of the definition of treatment effect on time-to-event outcomes. In particular, a framework of heterogeneous treatment effect estimation in survival analysis is provided to estimate the effects of static binary treatment conditions on a range of time-to-event outcomes encountered in the healthcare context (Chapters 3 and 4). The framework is then discussed in Chapters 5 and 6 with a more complex data stream, first in the case of time-varying confounders and exposures and then in the contingency of stochastic treatment options, where I examine the concepts of survival treatment effect given longitudinal confounding as well as the contour of time-varying survival dose response function. Chapter 7 offers an application of treatment effect estimation models in a recommendation system, where I used extensive simulations and case studies to demonstrate the advantage of an explanatory model over a predictive model in providing optimal treatment recommendations to patients. I end this thesis with the pursuit of the viability of causal exploration in public health management in Chapter 8, where a case study aiming to answer the question of the effect of public health interventions during the recent SARS-COV-2 pandemic is presented. The work shows that when there is a lack of quality observational data, approaches based on the potential outcomes theory (including the projects presented in Chapters 3 to 7) may fail to make a valid inference and additional assumptions have to be made on the functional form of the causal process. Together, my thesis bridges studies in causal inference theory and machine learning methods in the context of observational healthcare. Significant progress has been made in the development of estimation frameworks for individualised treatment effects subject to longitudinal data with informative censoring. I aim to provide pragmatic insights on the applications and limitations of advanced machine learning models in relation to empirical evidence and draw a clear distinction between causal discovery and conventional predictive learning in the realm of public health and epidemiology.
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PhD Doctorate
UNSW Faculty
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