Abstract not found

Abstract: This review presents empirical researchers with recent advances in causal inference, and stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, the conditional nature of all causal and counterfactual claims, and the methods that have been developed for the assessment of such claims. These advances are illustrated using a general theory of causation based on the Structural Causal Model (SCM) described in Pearl (2000a), which subsumes and unifies other approaches to causation, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: (1) queries about the effects of potential interventions, (also called “causal effects ” or “policy evaluation”) (2) queries about probabilities of counterfactuals, (including assessment of “regret, ” “attribution” or “causes of effects”) and (3) queries about direct and indirect effects (also known as “mediation”). Finally, the paper defines the formal and conceptual relationships between the structural and potential-outcome frameworks and presents tools for a symbiosis analysis that uses the strong features of both.

This paper deals with the problem of estimating the probability of causation, that is, the probability that one event was the real cause of another, in a given scenario. Starting from structural-semantical definitions of the probabilities of necessary or sufficient causation (or both), we show how to bound these quantities from data obtained in experimental and observational studies, under general assumptions concerning the data-generating process. In particular, we strengthen the results of Pearl (1999) by presenting sharp bounds based on combined experimental and nonexperimental data under no process assumptions, as well as under the mild assumptions of exogeneity (no confounding) and monotonicity (no prevention). These results delineate more precisely the basic assumptions that must be made before statistical measures such as the excess-risk-ratio could be used for assessing attributional quantities such as the probability of causation. 1

The concept of attributable fraction (1-3) has grown in importance as epidemiologists and epidemiologic data have played a larger role in interventions, regulations, and lawsuits concerning hazardous exposures. For example, in a lawsuit, the court may wish to determine the likelihood that a particular case's illness was caused by the exposure at issue, and the attributable fraction has been interpreted as just this likelihood (e.g., see ref. 4, p. 164). While the concept is known by many names (including attributable risk (5), etiologic fraction (4, 6, 7), and attributable proportion (8)), we would think this variety would cause no problem as long as the conceptual and algebraic formulations were unambiguous. Unfortunately, at least three distinct concepts have been variously identified as the attributable fraction, although these concepts have usually not been distinguished in the literature. Furthermore, certain equations used to relate attributable 1

This paper aims at assisting empirical researchers benefit from recent advances in causal inference. The paper stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, and the conditional nature of causal claims inferred from nonexperimental studies. These emphases are illustrated through a brief survey of recent results, including the control of confounding, the assessment of causal effects, the interpretation of counterfactuals, and a symbiosis between counterfactual and graphical methods of analysis.

According to common judicial standard, judgment in favor of plaintiff should be made if and only if it is "more probable than not" that the defendant's action was the cause for the plaintiff's damage (or death). This paper provides formal semantics, based on structural models of counterfactuals, for the probability that event x was a necessary or sufficient cause (or both) of another event y. The paper then explicates conditions under which the probability of necessary (or sufficient) causation can be learned from statistical data, and shows how data from both experimental and nonexperimental studies can be combined to yield information that neither study alone can provide. Finally,weshow that necessity and sufficiency are two independent aspects of causation, and that both should be invoked in the construction of causal explanations for specific scenarios.

INTRODUCTION Statistical modelling of heterogeneity may be based on strati#cation according to factors, regression on covariates, or by assuming a probability distribution of the interindividual variation. In survival analysis Vaupel et al. coined the phrase #frailty" in connection with a particular version of such a stochastic model, in which individual i was assumed to have death intensity Z i ##a# at age a, where the random variable Z i #the #frailty"# is assumed to have a gamma distribution. The assumptions that the randomness is ageindependent and that it acts multiplicatively on an underlying intensity ##a# are in principle arbitrary but have been taken as the basis for much subsequent work on random heterogeneity in survival analysis. Useful surveys are by Andersen et al. , Chapter IX, Nielsen et al. , Klein et al. , Aalen Schumacher et al. and Hougaard . The frailty models are likely to be particularly useful for modelling multivariate survival times, whethe

<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 provides a conceptual introduction to causal inference, aimed to assist health services researchers benefit from recent advances in this area. The paper stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underlie all causal inferences, the languages used in formulating those assumptions, and the conditional nature of causal claims inferred from nonexperimental studies. These emphases are illustrated through a brief survey of recent results, including the control of confounding, corrections for noncompliance, and a symbiosis between counterfactual and graphical methods of analysis.

Principal stratification has recently become a popular tool to address certain causal inference questions particularly in dealing with post-randomization factors in randomized trials. Here we analyze the conceptual basis for this framework and invite response to clarify the value of principal stratification in estimating causal effects of interest.