Causal model selection in epidemiology

Abstract

In this thesis, I investigate two related types of causal model selection: confounder selection and constraint-based causal discovery.

The aim of confounder selection is to determine a valid adjustment set when the interest lies in the causal effect of an exposure or treatment X on an outcome Y. Ideally, this is based on a causal graph representing relevant domain knowledge. Alternative strategies range from simple knowledge-based rules to complex data-driven algorithms. In this thesis, I investigate popular strategies from a graphical perspective. Main results are that structural assumptions cannot be avoided even if no causal graph is drawn, and that `outcome-oriented' strategies often lead to more precise estimates than other methods.

The efficiency aspect in then further investigated for the case that the underlying causal graph is known or has been estimated, and the variables jointly follow a multivariate Gaussian distribution. I show that the `optimal' adjustment set yielding the smallest asymptotic variance can be read off using graphical rules and does not depend on the parameters of the distribution. It has an intuitive interpretation in terms of a graphical projection I propose and can be viewed as the target set of backward regression selection.

Instead of focussing on a single treatment-outcome pair and its confounding factors, the aim of causal discovery is to infer the causal structure among several variables simultaneously. I propose a modified version of the PC-algorithm for causal discovery that takes temporal background knowledge into account, and show that the new algorithm is sound and complete and has certain stability properties. Further, I formally investigate two recently suggested methods for handling missing values in causal discovery: test-wise deletion and multiple imputation. Finally, I discuss chances and challenges of causal discovery and causal graphical modelling in general.