Vanessa Didelez has just moved to Germany from the University of Bristol, UK, to be Professor of Statistics and Causal Inference at the Leibniz Institute, University of Bremen. Her research focuses on graphical models and causal inference especially in time-dependent settings, and encompasses aspects of statistics, epidemiology, philosophy and computer science. She obtained her PhD in 2000 from the University of Dortmund under supervision of Iris Pigeot and was appointed Lecturer in Statistics at University College London where she started collaborating with Philip Dawid on a decision theoretic approach to causality. In 2006 she stayed at the Norwegian Centre for Advanced Study establishing an ongoing exchange with Odd Aalen and his group on continuous-time causality. She is known for her contributions to the understanding of Mendelian randomisation as an instrumental variable approach to causal inference in epidemiology. Vanessa’s lecture will be on Thursday, July 14 at the World Congress in Toronto.

Causal Reasoning for Events in Continuous Time

We often make statements such as event A was the cause of event B; most statistical causal inference literature would translate this into two binary random variables, and use structural equations, causal DAGs and/or potential outcomes in order to formalise the difference between causation and association. An aspect that is often only implicit is that of temporality: event A can only be a cause of B if it happens earlier—it therefore seems more natural to adopt a stochastic process approach instead. As a concrete example, a public health authority may want to know whether home visits by nurses to elderly patients should be more or less frequent with view to subsequent hospitalisation events and survival. If the frequency of visits is to be increased, with financial implications, then we certainly want to know whether they are causally affecting hospitalisation, and not just whether both are associated.

Dynamic associations among different types of events in continuous time can be represented by local independence graphs as developed by Didelez (2008). Intuitively we say that a process is locally independent of another one if its short-term prediction is not improved by using the past of the other process, similar to Granger non-causality; the graphical representation uses nodes for processes or events and the absence of a directed edge for local independence. Important independence properties can be read off these—possibly cyclic—graphs using delta-separation (Didelez, 2006) which generalises d-separation from DAGs. In related work, Røysland (2011, 2012) showed how causal inference based on inverse probability weighting (IPW), well known for longitudinal data (Robins et al., 2000), can be extended to the continuous-time situation using a martingale approach.

In the work that I will present at the Medallion lecture (joint work with Kjetil Røysland, Odd Aalen and Theis Lange), we start by defining causal validity of local independence graphs in terms of interventions, which in the context of events in time take the form of modifications to the intensities of specific processes, e.g. a treatment process; causal validity is given if the specification of the dynamic system is rich enough to model such an intervention. This is similar to what is known as ‘modularity’ for causal DAGs. We then combine the above previous developments to give graphical rules for the identifiability of the effect of such interventions via IPW; these rules can be regarded as characterising ‘unobserved confounding’. Re-weighting then simply replaces the observed intensity by the one given by the intervention of interest. For this to be meaningful, causal validity and identifiability are crucial assumptions. As an aside, we find that it is helpful to also use causal reasoning when faced with censoring as the target of inference can often be regarded as the population in which censoring is prevented, i.e. its intensity is set to zero. We apply our theoretical results to the example of cancer screening in Norway.

Our approach can be regarded as the time-continuous version of Dawid & Didelez (2010), who develop a decision theoretic approach for sequential decisions in longitudinal settings and use a graphical representation with influence diagrams that include decision nodes; specifically causal validity is analogous to the extended stability of Dawid & Didelez (2010). This provides an explicit representation of the target of inference as well as allowing us to use simple graphical rules to check identifiability. While it is common to phrase causal queries in terms of potential outcomes or counterfactuals, it is worth emphasising that the decision theoretic framework and the way we define causal validity for events and stochastic processes do not require these. The question at hand is simply phrased in terms of inference based on a system that is observed under certain conditions to a system under different conditions, namely such that the intensity for certain types of events are changed, which offers greater generality.

References:

Dawid and Didelez (2010). Identifying the consequences of dynamic treatment strategies: A decision theoretic overview, Statistics Surveys, 4, 184-231.

Didelez (2006). Asymmetric Separation for Local Independence Graphs, in: Proceedings of the 22nd Annual Conference on Uncertainty in Artificial Intelligence, 130-137

Didelez (2008). Graphical models for marked point processes based on local independence, JRSS(B), 70, 245-264.

Robins, Hernan, Brumback (2000). Marginal structural models & causal inference in epidemiology. Epidemiology, 11:550-560.

Røysland (2011). A martingale approach to continuous time marginal structural models. Bernoulli, 17, 895-915.

Røysland (2012). Counterfactual analyses with graphical models based on local independence. Ann. Statist., 40, 2162-2194.