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Bayesian Causal Inference for Epidemiological and Clinical Studies.

[PhD] Patrick J Graham, 2001

This thesis addresses the problem of causal inference using the potential responses or counterfactual approach to defining causal relations and the Bayesian approach to statistical inference. The distinguishing feature of the potential responses framework for causality is the notion of multiple potential response variables, one corresponding to each possible exposure level. Causal effects are defined in terms of contrasts between potential responses. The fundamental problem of causal inference relates to our inability to simultaneously observe more than one potential response for each individual and causal inference can be viewed as the process of using observable data to make inferential statements concerning causal relations, defined in terms of potential response variables.

A key insight of the potential responses framework is that causal inference is not inherently concerned with inference from a sample to a population and, as pointed out by Rubin, when viewed from a Bayesian perspective, inference for causal effects follows from the posterior distribution for the unobserved potential responses. Methodological details required for practical implementation

For finite populations causal inferences are potentially sensitive to prior assumptions concerning the association between potential responses because observable data is uninformative with respect to this association. However, I demonstrate that there are situations in which finite population inference for certain causal effects is practically independent of assumptions concerning the association between potential responses. On the other hand, it is demonstrated that posterior inferences for causal effects are sensitive to ignorability assumptions. These assumptions are characterised via selection effects which are associated with actual exposure but represent the impact of actual exposure status on outcome distributions over and above the true biological, psychological or sociological effect of exposure.

Using a causal adaptation of generalised linear models, the selection effects are identified with a model parameter, and prior uncertainty concerning selection effects can therefore be accommodated via the prior distribution for the model parameters. Within the causal generalised linear model framework the fundamental problem of causal inference manifests itself as a problem of identifiability which can be resolved only via information from beyond the data at hand. Knowledge that exposure levels were assigned at random provides an irrefutable source of identifying information.
Motivated by the realisation that knowledge of causal relations is of practical importance because it facilitates the development of intervention strategies, I develop a predictive approach to causal inference in which inferential activities are concerned with the posterior predictive distribution for future observable responses under different assumptions concerning the future exposure distribution. The potential responses framework proves invaluable in deriving the required predictive distributions.

A unique feature of the predictive approach to causal inference is the requirement to specify a prior model which links model parameters for the future cohort to model parameters for the observable cohort. This prior model can be used to reflect prior knowledge regarding the likely impact of exposure modifying interventions on future cohort exposure distributions. As with inference for causal effects, it is shown that predictive causal inference is considerably simplified when ignorability assumptions for observable cohort exposure levels can be justified. It is argued that predictive causal inferences are more directly policy relevant than inferences for causal effects.

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