Graphs, Time and Causal Inference

In this presentation, I will address key aspects of statistical modelling of and causal inference for events in (continuous) time. This is for instance relevant when some events correspond to some "treatment" and others to important outcomes such as "relapse" or "death".

First we discuss the visual representation of multivariate dependence structures among events, building on a marked point processes framework, using the concept of local independence and associated graphs (Didelez, 2008). It will be shown how reasoning and inference for systems with latent processes can be facilitated using such graphical representation and a suitable notion of graph-separation, called delta-separation.

Secondly, I present a formal notion of causal relations between events (or processes) in time based on a decision theoretic approach (Dawid and Didelez, 2010; Didelez, 2015), and discuss the use of local independence graphs to decide the question of identifiability in systems with unmeasured processes. This will be illustrated with an application to cancer screening in Norway (Roysland et al., 2020).

Moreover, we will address the connection to recent developments in causal mediation and competing events in survival analyses (Didelez, 2019; Stensrud et al., 2020).

The presentation will focus on basic principles and concepts rather than technical details.
 
References:
Dawid and Didelez (2010). Identifying the consequences of dynamic treatment strategies: A decision theoretic overview, Statistics Surveys, 4, 184-231.
Didelez (2008). Graphical models for marked point processes based on local independence. JRSS(B), 70, 245-264.
Didelez (2015). Causal Reasoning for events in continuous time: a decision-theoretic approach. Proceedings of the 31st Annual Conference on Uncertainty in Artificial Intelligence - Causality Workshop (Invited Paper).
Didelez (2019). Defining causal mediation with a longitudinal mediator and a survival outcome. Lifetime Data Anal 25, 593–610.
Roysland, Ryalen, Nygard, Didelez (2020). Graphical criteria for identification in continuous-time marginal structural survival models. In preparation.
Stensrud, Young, Didelez, Robins & Hernán (2020) Separable Effects for Causal Inference in the Presence of Competing Events, JASA (online).