Statistical and simulation-based modelling approaches for causal inference in longitudinal data: Integrating counterfactual thinking into established methods for longitudinal data analysis

The counterfactual framework represents the dominant paradigm for testing and evaluating causal claims within epidemiology. What began as a philosophical framework has been formalised mathematically in the language of directed acyclic graphs (DAGs), whose underpinning theory provides a rigorous mathematical framework for the identification and estimation of causal effects. Moreover, DAGs provide a conceptual framework for thinking though causal processes and explicating causal assumptions. Advances in DAG-based methods are invaluable in the era of ‘big data’, since we are increasingly awash with large, complex – and frequently longitudinal – datasets. However, the relative recentness of such developments means that many established methods for analysing observational data have not been considered within a robust causal framework. This PhD thesis explores how counterfactual thinking, encoded in the language of DAGs, may be integrated into established methods for longitudinal data analysis, and illustrates several advantages of doing so. Three statistical- and simulation-based methods are considered: (1) the analysis of change, (2) regression with ‘unexplained residuals’, and (3) microsimulation modelling. For each method, DAGs are specifically employed to consider causal structures and to explore potential problems and/or biases that might arise when these methods are applied without sufficient consideration for such structures. In (1), DAGs are used to demonstrate that ‘change scores’ do not in general represent exogenous change; alternate analytical strategies for isolating change are identified. In (2), DAGs are employed to illustrate why the method works and how it may be extended to adjust for confounding. In (3), DAGs are used to explicitly consider data-generating processes, and to demonstrate some of the unique challenges faced by simulation approaches. DAGs are demonstrated to be useful tools for informing causal analyses across a wide variety of longitudinal scenarios, thereby providing a basis for integrating counterfactual thinking into other methods for longitudinal data analysis