Causality and counterfactual analysis

Transcription

1 Chapter 6.4 Causality and counterfactual analysis Daniel M. Hausman 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 multidimensional 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 causation 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

2 310 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 X had had a different value, x 0 (and everything else at that time and place were the same), one can only observe how the outcome in fact differs when X = x 0 at a different time, and when there is no assurance that everything else is just the same. In this way, in Greenland s terminology, a measure of association is obtained, from which the measure of effect is inferred. As more is known about the functional relation between X, Y, and other variables, for which measures of association constitute evidence, a better answer will be possible to the counterfactual question about what the value of Y would have been if the value of X had been x 0. Although Greenland uses causal language, he is concerned with counterfactuals rather than causation. Greenland insists that the counterfactual question is well defined only when values of X are actions. When the values of X are not actions, the question: What would the value of Y have been if the value of X had been x 0? cannot be answered, because it is not known how the value of X became x 0 instead of x 1. If a heavy smoker, P, had not died of lung cancer at age 50 years because (counterfactually) P had never smoked, then P s life expectancy would be much longer than if P had not died of lung cancer because of a successful chemotherapy treatment. There is no answer to the question: How long would P have lived if P had not died of lung cancer until one specifies the action or intervention that would have brought it about that P had not died of lung cancer. Calculations of health gaps or years of life lost, such as the number of years of life lost to AIDS, pose exactly such allegedly ill-formed questions. It is unknown how long individuals with AIDS would live if they were not infected with AIDS, because there are different ways in which they might not have had AIDS, and their life expectancies would depend on how they were not infected. Health gaps are thus not well defined and the whole attempt to measure DALYs may be an irretrievable muddle. Why doesn t this difficulty apply equally to all counterfactuals? How does insisting that the values of X be actions circumvent the problems? Consider Greenland s own example: x 1 is the revocation of Kosovo s autonomy in 1988 and Y is mortality in Kosovo in The actual value of Y can, in principle, be observed. One then asks the counterfactual question: What would mortality in 1999 have been if Kosovo s autonomy had not been revoked in 1988 (if the value of X were x 0 )? The answer cannot be determined by observation, because no one can observe a counterfactual mortality rate. However, it could be assumed that the counterfactual mortality in 1999 would be the same as the actual mortality in 1988, subject to corrections for factors that are independent of

3 Causality and counterfactual analysis 311 whether autonomy was revoked. In this way, estimates of what mortality would have been in 1999 if Kosovo s autonomy had not been revoked can be obtained and one can offer a fallible answer to the counterfactual question. Notice that the increased mortality in 1999 was due to the fact that Kosovo s autonomy was revoked in just the way it was. If its autonomy were revoked by a Yugoslav government dominated by ethnic Albanians, as part of an effort to impose Kosovo s culture and interests on the whole of Yugoslavia, its effects would presumably have been very different. Consequently, it matters a great deal how x 0, the non-revocation, is specified. A non-revocation is not of course any specific kind of action, although a specific non-revocation could be identical to some particular action (or actions). The hypothetical non-revocation Greenland refers to, x 0, is presumably a specific complicated set of actions that differs from the actions the Yugoslav government took in 1988 as little as possible, apart from not revoking Kosovo s autonomy. According to Lewis theory (Lewis 1973b), a counterfactual such as: If Yugoslavia had not revoked Kosovo s autonomy in 1988, ethnic cleansing would not have occurred in Kosovo in 1999, is true if and only if some possible world without the revocation and without ethnic cleansing is more similar to the actual world than any possible world without revocation and with the ethnic cleansing. Notice that Lewis does not rely on causal knowledge to evaluate the truth of the counterfactual. This is important, because Lewis hopes to define causation in terms of chains of counterfactual dependence (Lewis 1973a). Lewis account of counterfactuals depends on a theory of similarity among possible worlds (Lewis 1979). In its simplest outline, the possible worlds in which Kosovo s autonomy is not revoked that are most similar to the actual world will be identical to the actual world until shortly before the moment in 1988 when Yugoslavia revoked Kosovo s autonomy. Then, despite the occurrence of the causal antecedents for the revocation, the revocation miraculously fails to occur. Apart from lacking the revocation, the closest possible worlds will differ very little from the actual world at the moment when Kosovo s autonomy was in fact revoked. History then runs on, according to the same laws as those that govern the actual world. One relies on those laws to predict what the result would be if Yugoslavia had not revoked Kosovo s autonomy when it did. Several quite different possible worlds may be equally similar to the actual world, and the counterfactual will not be true, unless ethnic cleansing does not occur in any of those worlds. Although Greenland does not explicitly talk about similarity between possible worlds, he relies implicitly on some such notion in specifying what action x 0, the non-revocation, is. What then of counterfactuals like those Greenland criticizes, such as: If P had not died of lung cancer at age 50 years, then P would have lived for at least 20 years more. According to Lewis, this counterfactual is no more difficult to evaluate than the counterfactual concerning what would

4 312 Summary Measures of Population Health have been the case if the Yugoslavs had not revoked Kosovo s autonomy. Are possible worlds in which P lives for at least 20 years after not dying of lung cancer at age 50 more similar to the actual world than possible worlds in which P does not die of lung cancer and dies before age 70? Possible worlds in which P never smoked are less similar to the actual world than possible worlds in which P lives just the same life until age 50, contracts lung cancer, but fails to die of it because of a spontaneous remission. We have data on the general life expectancy of people who have lung cancers resembling P s, yet who do not die of them in circumstances like those in which P does in fact die of lung cancer. Thus we have some basis to judge whether it is true that if P had not died of lung cancer at age 50, then P would have lived at least 20 years more. Since a possible world in which P never smoked would be very unlike the actual world, one does not examine such a world to determine what would be the case if P had not died of lung cancer. In addition, Lewis framework permits one to consider counterfactuals with more complicated antecedents. For example, consider a counterfactual such as: If P had not died of lung cancer at age 50 years because P never smoked and never got lung cancer, then P would have lived to age 90. In evaluating this counterfactual, possible worlds that diverged from the actual world long ago when P in fact began smoking are considered. Whatever counterfactual is considered, the indeterminacy that concerns Greenland evaporates. Lewis views on similarity among possible worlds and his views of the evaluation of counterfactuals have been questioned elsewhere (Hausman 1998). When the consequence of some counterfactual antecedent depends on how it comes about, it is not always justifiable to suppose that it comes about in just one special way, as if by a miracle or intervention. When it is asked, for example, what is the average number of years of life lost owing to lung cancer, it is necessary to specify the possible state of affairs in which individuals no longer died of lung cancer. For example, do people not die of lung cancer because of interventions designed to stop causes of lung cancer, such as smoking or air pollution; or because of an intervention that interferes with the mechanisms by which these cause lung cancer; or because of improvements in treating lung cancer? Without some such specification, the question: How much longer (on average) would people live if they did not die of lung cancer? has no correct answer. There are, however, two reasons to doubt whether this is a serious problem in practice. First, in some cases the consequence of the non-occurrence of some health state (or some cause of death) will not be so sensitive to the way the health state or cause of death might be prevented. Although the calculation of the health gap caused by malaria will depend on whether one supposes malaria is eliminated by vaccination, by mosquito eradication, or by an effective treatment, the differences are not so large as to make the calculation meaningless. Second, I would conjecture that in assessing health gaps, health analysts typically assume that the

5 Causality and counterfactual analysis 313 counterfactual alternative to the death or disability resulting from a particular disease involves a last-minute intervention of the sort Lewis discusses. For example, one would naturally take the health gap caused by malaria to be the difference between the current state of health where malaria is prevalent and the state of health that would obtain in much the same conditions if there were a vaccine without side-effects or if there were a successful mosquito eradication programme. It is obvious that the benefits of an actual anti-malarial medication might be much less. Greenland s indeterminacy still exists, but at least in cases such as this one the indeterminacy is mild, and ignoring it would not be the greatest of the simplifications and idealizations required in order to define a summary measure of population health. References Hausman D (1998) Causal asymmetries. Cambridge University Press, New York. Lewis D (1973a) Causation. Journal of Philosophy, 70: Lewis D (1973b) Counterfactuals. Harvard University Press, Cambridge, MA. Lewis D (1979) Counterfactual dependence and time s arrow. Noûs, 13: Pearl J (2000) Causality: models, reasoning and inference. Cambridge University Press, Cambridge.

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