Predictive causal inference
by
Patrick Graham
Christchurch School of Medicine

Causality and causal inference are topics receiving increasing attention in biostatistics. Particularly influential has been the potential outcomes or counterfactual framework for defining causal relations, associated with the work of Rubin in statistics and Greenland and Robins in epidemiology. Within the potential outcomes framework the notion of a single response variable is replaced by a vector of potential response variables, one corresponding to each possible level of exposure. Causal effects can then be defined in terms of contrasts between potential responses. Because it is generally possible to observe only a single response for each individual in a study, causal effects are, in general, unobservable. Methods of causal inference developed within the potential outcomes framework have to date concentrated on these unobservable causal effects. However, in the health sciences interest in causality is ultimately justified in terms of identifying appropriate interventions aimed at improving future health outcomes. Consequently it can be argued that our inferential methods should support the ultimate aim of health research by facilitating prediction of future, observable, outcomes under alternative intervention scenarios. This paper pursues this idea.

I present a general framework for predictive causal inference which, although based on the potential outcomes framework, emphasises prediction of future observables. Inferential issues are addressed from the Bayesian viewpoint and a feature of the analysis is the requirement to specify a prior model which links model parameters for the observable study cohort to model parameters for the future cohort. It is through this prior model that prior information concerning the impact of an intervention on the future exposure distribution is accommodated. In order to illustrate the main ideas and the style of inference I present a simplified example concerning the impact of improved participation in screening on breast cancer mortality. Predictive causal inferences seem more directly policy relevant than inferences for causal effects and, because they involve observable entities, offer more scope for empirical verification.

Date received: August 30, 2001