Some aspects of propensity score-based estimators for causal inference

Although most researchers would agree that the question "What is the effect of [...] on [...]?" is generally more interesting than "Are [...] and [...] associated?", traditionally, most statisticians have been reluctant to get into discussions about causality. Still, suppose we really would like to know the causal effect of an education policy on academic achievement or perhaps the causal effect of a vaccine on some disease. How should we proceed? A prerequisite is to have a clear understanding and a formal statistical formulation of what we mean by causation.

In this thesis causality is defined in terms of potential outcomes, as introduced by Neyman (1923) and extended by Rubin (1974). A potential outcome can be thought of as what would have happened to an individual if he or she received a different treatment than the one actually given. In reality we can only observe the outcome for that individual under the treatment actually received. Thus, causality in this context is reduced to thinking of how to observe outcomes that would have been if the individuals received a different treatment.