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Causality and counterfactual analysis

In chapter 6.2 of this book, Sander Greenland provides an introduction to contemporary views of causal inference (see also Pearl 2000) and makes two points relevant to summary measures of population health: i) that health gaps are not well-defined; and ii) that a multidimensional index of population health would be superior to a scalar measure. In theory, a multidimensional index of population health is attractive, because health itself is multidimensional. But the theoretical attractions of a multidimen-sional index have to be balanced against the practical dangers that those who make health policy would ignore most of the dimensions. Greenland and I are not particularly competent to judge these dangers, and I shall focus the remainder of my remarks on matters of causal inference. Greenland considers how investigators answer counterfactual questions concerning what the consequences would have been had some other action been taken. Such questions are closely related to questions about the consequences of proposed interventions. These are in part questions concerning the use of incomplete prior causal knowledge. I do not know how commonly accepted Greenland's views are among epidemiologists, but they are controversial among philosophers. Given the page constraints, contemporary philosophical controversies concerning the nature of counterfactuals and the relations between cau-sation and counterfactuals will not be discussed in depth. I can only sketch the most influential view, which is due to David Lewis (Lewis 1973a; 1973b; 1979), and explain how it is related to Greenland's position. I shall argue that even a qualified acceptance of Lewis' view undermines Greenland's critique of health gaps. I shall also show that Greenland's own philosophical premises do not support so strong a conclusion as the one he draws. The general problem is as follows. One begins with a suspicion that there is some relation between a variable, X, and some outcome variable, Y, though one also believes that Y depends on other variables, both known 310 Summary Measures of Population Health and unknown. The functional relation between X, Y and other variables may be probabilistic or deterministic, but it is never fully known. One can observe the actual value of X at some particular time, x 1 , and the actual value of Y that results, y 1 , but not the other values X could have had at that time, or other values that Y would have taken in response. Rather than observing how the outcome would have differed if …