Causality and Matching
Causality is a concept that statisticians and statistical science traditionally shy away from. Recently, however, many successful attempts have been made to include the concept of causality in the statistical theory and vocabulary. The concept of predictive causality is based on stochastic processes, and that a cause must precede an effect in time. The theory of counterfactuals tries to solve a dilemma by allowing each individual to be its own control. More precisely, for each individual, two hypothetical outcomes are defined; the outcome if treated and the outcome if not treated. The whole theory based on counterfactuals relies on the assumption that there are no unmeasured confounders. Unfortunately, this assumption is completely untestable, and even worse, it never holds in practice. In certain applications it may be reasonable to assume that risk factors acts additively rather than multiplicatively on hazards.