Causality: Statistical Perspectives and Applications
Many statistical analyses aim at a causal explanation of the data. The early observational studies on the risks of smoking (Cornfield et al., 1959), for example, aimed at something deeper than to show the poorer prognosis of a smoker. The hoped-for interpretation was causal: those who smoked would, on average, have had a better health had they not done so and, consequently, any future intervention against smoking will, at least in a similar population, have a positive impact on health. Causal interpretations and questions are the focus of this present book. They underpin many statistical studies in a variety of empirical disciplines, including natural and social sciences, psychology, and economics. The case of epidemiology and biostatistics is noted for a traditionally cautious attitude towards causality. Early researchers in these areas did not feel the need to use the word ‘causal’. Emphasis was on the requirement that the study be ‘secure’: that its conclusions should not rely on special assumptions about the nature of uncontrolled variation, something that is ideally only achieved in experimental studies. In the work of Fisher (1935), security was achieved largely by using randomization within an experimental context. This ensures that, when we form contrasts between the treatment groups, we are comparing ‘like with like’, and thus there are no systematic pre-existing differences between the treatment groups that might be alternative explanations of the observed difference in response.
Another idea originated by Fisher (1932) and later developed by Cochran (1957), Cox (1960), and Cox and McCullagh (1982) is the use of supplementary variables to improve the efficiency of estimators and of instrumental variables to make a causal effect of interest identifiable. The use of supplementary and instrumental variables in causal inference is discussed in Chapter 16 of this book, ‘Supplementary variables for causal estimation’ by Roland Ramsahai.
Early advances in the theory of experimental design, largely contributed by Rothamsted researchers, are discussed in Chapter 1, ‘Statistical causality: some historical remarks’, by David Cox. Also discussed in this chapter are some implications of the ‘Rothamsted view’ (and of the controversies that arose around it) for the current discussion on causal inference. A technical discussion of the problems of causal inference in randomized experiments in medicine is given in Chapter 21,‘Causal inference in clinical trials’, by Krista Fischer and Ian White.
The 1960s witnessed the early development of a theory of causal inference in observational studies, a notable example being the work of Bradford Hill (1965). Hill proposed a set of guidelines to strengthen the case for a causal interpretation of the results of a given observational study. One of these guidelines, the presence of a dose–response relationship, is discussed in depth in Chapter 19, ‘Nonreactive and purely reactive doses in observational studies’, by Paul Rosenbaum. Hill’s guidelines are informal, and they do not provide a definition of ‘causal’. During the 1990s, a wider community of researchers, gathered from such disciplines as statistics, philosophy, economics, social science, machine learning, and artificial intelligence, proposed a more aggressive approach to causality, reminiscent of the long philosophers’ struggle to reduce causality to probabilities. These researchers transformed cause–effect relationships into objects that can be manipulated mathematically (Pearl, 2000). They attempted to formalize concepts such as confounding and to set up various formal frameworks for causal inference from observational and experimental studies. In a given application, such frameworks allow us (i) to define the target causal effects, (ii) to express the causal assumptions in a clear way, and determine whether they are sufficient to allow estimation of the target effects from the available data, (iii) to identify analysis modalities and algorithms that render the estimate feasible, and (iv) to identify observations and experiments that would render the estimate feasible, or assumptions under which the conclusions of the analysis have a causal interpretation.
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