Sammendrag
An important problem in epidemiology is to determine the true effect of public health related interventions or medical treatments. The randomized controlled trial is the gold standard for establishing such effects. It is simple, however, to imagine scenarios where such trials are not feasible; either because it would require too much time or resources or because it would impose treatments that were known to be harmful for particular patients. Many individuals are routinely excluded from such trials because of the potential risk involved. Experiments on children and pregnant women are for instance rarely done. This means that we typically obtain only limited knowledge of treatment effects based on randomized controlled trials in such cases.
It is tempting to take advantage of registry data or observational studies if a relevant controlled trial is not at hand. There is for instance an increasing desire to use health registries for quality assessment of the various treatments that are offered by national health systems. However, simple descriptive statistics will often fall short of determining true treatment effects.
We will discuss statistical analysis of counterfactual interventions with graphical models based on local independence. The idea is to treat the counterfactual scenario as just another probability measure on the underlying sample space. Short-term predictions provide dynamical characterizations of the various involved factors. A hypothetical direct intervention on a factor would change its dynamics. The non-directly intervened factors, on the other hand, should have the same dynamical characterization as in the observational scenario. We claim that any probability measure on sample space that is compatible with these characteristics yields a reasonable model for the counterfactual scenario. Any probability measure that may govern the frequencies of the "counterfactual observations" is characterized in terms of a given martingale problem. This provides a wealth of tools from stochastic analysis that have previously not been considered in causal inference.
We show that important techniques in causal inference such as the do-calculus on Bayesian networks, due to Judea Pearl, and the Marginal Structural Models, due to James Robins, can be understood very well, and can also be generalized within our framework.