The Assumptions on Which Causal Inferences Rest

SUMMARY Statisticians commonly make causal inferences from the results of randomized experiments, but usually question causal inferences from observational studies on the grounds that untestable assumptions are required. This paper explains the basis for this situation and examines, within quite a general framework, various assumptions that appear in the literature. It is demonstrated how the role of each assumption is intimately related to the sort of causal inference being considered. Contrary to general belief, it is shown that neither ‘no confounding’ nor ‘randomization’ are sufficient assumptions for testing the fundamental causal hypothesis of ‘no causation’. They become sufficient, however, if supplemented by a ‘modelling’ assumption for how unobserved covariates affect potential responses. Without supplementary assumptions, no confounding and randomization allow testing of weaker but more important hypotheses, such as ‘no mean effect’. This follows from the sufficiency of an assumption of ‘ignorable treatment assignment’ for testing the hypothesis of ‘no distribution effect‘. It is argued that these ideas will have some operational relevance if we can quantify our beliefs about how closely assumptions hold. to illustrate, a novel form of sensitivity analysis is contrasted with an analysis presented by Rosenbaum and Rubin.