Causal Inference with Compositional Data: Using directed acyclic graphs and data simulations to understand and model robust causal effects in nutritional and time-use epidemiology

The estimation of causal effects from observational data is complicated by various challenges. One of these is the analysis of data that are compositional. Compositional data comprise the parts of a whole (or total) which together sum to that whole. Although compositional data may arise in any setting, they are particularly common in nutritional and time-use epidemiology; for example, total energy intake is the sum of energy from all nutritional sources, and total time in a day is the sum of time spent in different activity behaviours. Compositional data bring many challenges for analysis and interpretation, but these have not been sufficiently explored in a causal inference framework.

This PhD thesis uses directed acyclic graphs and data simulations to study several challenges in the analysis of compositional data for causal inference in nutritional and time-use epidemiology. First, it explores the different approaches to energy intake adjustment, clarifying the causal estimand targeted by each approach, and investigating the performance in the presence of confounding. A model including separate terms for all sources of energy is found to be the most robust. Second, it examines the performance of substitution models in nutrition, with a focus on the range of estimands that may be considered. In general, the more well-defined the substitution, the more accurate the relative causal effect estimate will be. Finally, moving on from considering the target estimands that may be of interest, this thesis compares the performance of different parametric methods for estimating relative effects in compositional data, extending the context to both nutritional and physical activity, as examples of compositional data with variable and fixed totals. All existing approaches are shown to have utility, but the parametric relationship must be explored and modelled appropriately.