Estimating causal effects.

Although one goal of aetiologic epidemiology is to estimate 'the true effect' of an exposure on disease occurrence, epidemio-logists usually do not precisely specify what 'true effect' they want to estimate. We describe how the counterfactual theory of causation, originally developed in philosophy and statistics, can be adapted to epidemiological studies to provide precise answers to the questions 'What is a cause?', 'How should we measure effects?' and 'What effect measure should epidemiologists estimate in aetiologic studies?' We also show that the theory of counterfactuals (1) provides a general framework for designing and analysing aetiologic studies; (2) shows that we must always depend on a substitution step when estimating effects, and therefore the validity of our estimate will always depend on the validity of the substitution; (3) leads to precise definitions of effect measure, confounding, confounder, and effect-measure modification; and (4) shows why effect measures should be expected to vary across populations whenever the distribution of causal factors varies across the populations. Introduction Imagine that the creator of the universe appears to you in a dream and grants you the answer to one public-health question. The conversation might go as follows: You: What is the true effect of (your exposure here, denoted by E) on the occurrence of (your disease here, denoted by D)? Creator: What do you mean by 'the true effect'? The true value of what parameter? You: The true relative risk. Creator: Epidemiologists use the term relative risk for several different parameters. Which do you mean? You: The ratio of average risk with and without exposure—what some call the risk ratio 1 and others call the incidence proportion ratio. 2