This paper (which is mainly expository) sets up graphical models for causation, having a bit less than the usual complement of hypothetical counterfactuals. Assuming the invariance of error distributions may be essential for causal inference, but the errors themselves need not be invariant. Graphs can be interpreted using conditional distributions, so that we can better address connections between the mathematical framework and causality in the world. The identification problem is posed in terms of conditionals. As will be seen, causal relationships cannot be inferred from a data set by running regressions unless there is substantial prior knowledge about the mechanisms that generated the data. There are few successful applications of graphical models, mainly because few causal pathways can be excluded on a priori grounds. The invariance conditions themselves remain to be assessed.

<F4.554e+05> Epidemiologic methods were developed to prove general causation: identifying exposures that increase the risk of particular diseases. Courts often are more interested in specific causation: on balance of probabilities, was the plainti#'s disease caused by exposure to the agent in question? Some authorities have suggested that a relative risk greater than 2.0 meets the standard of proof for specific causation. Such a definite criterion is appealing, but there are di#culties. Bias and confounding are familiar problems; individual di#erences must be considered too. The issues are explored in the context of the swine flu vaccine and Guillain-Barre syndrome. The conclusion: there is a considerable gap between relative risks and proof of specific causation.<F4.051e+05> 1. Introduction<F4.554e+05> In a toxic tort case, the plainti# is exposed to a toxic agent, su#ers injury, and sues. To win, the plainti# must prove (i) "general causation" (the agent is capable of producing th...

This paper will review the design of statistical studies, and comment on the difficulty of drawing causal inferences from non-experimental data. The most basic design is a comparison of rates for two groups of subjects. Subjects in one group get the treatment of interest; subjects in the other group are the controls. The difficulty is ensuring that the groups are similar, apart from the treatment. Experiments versus observational studies In a randomized controlled experiment, the investigators assign the subjects to treatment or control, for instance, by tossing a coin. In an observational study, the subjects assign themselves. The difference is crucial, because of confounding. Confounding means a difference between the treatment group and the control group, other than the causal factor of primary interest. The confounder may be responsible for some or all of the observed effect that is of interest. In a randomized controlled experiment, near enough, chance will balance the two groups. Thus, confounding is rarely a problem. In an observational study, however, there often are important differences between the treatment and control groups. That is why experiments provide a more secure basis for causal inference than observational studies. When there is a conflict, experiments

The "salt hypothesis" is that higher levels of salt in the diet lead to higher levels of blood pressure, with attendant risk of cardiovascular disease. Intersalt was designed to test the hypothesis, with a cross-sectional study of salt levels and blood pressures in 52 populations. The study is often cited to support the salt hypothesis, but the data are somewhat contradictory. Thus, four of the populations (Kenya, Papua, and two Indian tribes in Brazil) have very low levels of salt and blood pressure. Across the other 48 populations, however, blood pressures go down as salt levels go up---contradicting the salt hypothesis. Regressions of blood pressure on age indicate that for young people, blood pressure is inversely related to salt intake---another paradox. This paper discusses the Intersalt data and study design, looking at some of the statistical issues and identifying respects in which the study failed to follow its own protocol. Also considered are human experiments bearing on t...

Applications and graphics for propensity score analysis Methods for propensity score analysis (PSA) originated with Rosenbaum and Rubin (1983), as vehicles to sharpen and clarify treatment group comparisons in observational studies. Although highly recommended by many statisticians, and applied often in medical sciences, PSA has seen relatively few applications in the social and behavioral sciences. This paper aims to facilitate sound PSA applications in psychological and other social sciences, and to emphasize the role visualization can play in such contexts. Numerous references to the expanding PSA literature are also provided. 2 Applications and graphics for propensity score analysis

Views expressed in this report are not necessarily those of the Social Exclusion Task Force or any other government department. This report was funded by the Department for Communities and Local Government (DCLG) when the Social Exclusion Unit (the predecessor of the current Social Exclusion Task Force based at the Cabinet Office) was based at DCLG. 1 CONTENTS

From spurious correlation to misleading association: The nature and extent of spurious correlation and its implication for the philosophy of science with special emphasis on positivism

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Regression models are often used to infer causation from association. For instance, Yule [79] showed – or tried to show – that welfare was a cause of poverty. Path models and structural equation models are later

ions, formalized as statistical models, is critical for applied researchers. Freedman et al. are right about one point: If you can avoid making inferences about individuals from aggregate data, you should do so. And of course valid survey data make ecological inferences superfluous. Unfortunately, Freedman et al. do not consider the many researchers who must make ecological inferences, even when risky. This position is consistent with the low value David Freedman generally seems to put on model-based inference, such as in regression analysis for causal inference (Freedman, 1998) or sampling adjustments for the U.S. Census (Brown et al., 1998), and may explain why Freedman et al. sometimes appear ambivalent about making ecological inferences even with their own model (1991: 682, 806). As statisticians, if they feel uncomfortable with the assumptions, they can work on other problems, or conclude that "surveys offer a better approach" (p.701), but many applied researchers