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From Statistical Evidence to Evidence of Causality

While statisticians and quantitative social scientists typically study the "effects of causes" (EoC), Lawyers and the Courts are more concerned with understanding the "causes of effects" (CoE). EoC can be addressed using experimental design and statistical analysis, but it is less clear how to incorporate statistical or epidemiological evidence into CoE reasoning, as might be required for a case at Law. Some form of counterfactual reasoning, such as the "potential outcomes" approach championed by Rubin, appears unavoidable, but this typically yields "answers" that are sensitive to arbitrary and untestable assumptions. We must therefore recognise that a CoE question simply might not have a well-determined answer. It is nevertheless possible to use statistical data to set bounds within which any answer must lie. With less than perfect data these bounds will themselves be uncertain, leading to a compounding of different kinds of uncertainty. Still further care is required in the presence of possible confounding factors. In addition, even identifying the relevant "counterfactual contrast" may be a matter of Policy as much as of Science. Defining the question is as non-trivial a task as finding a route towards an answer. This paper develops some technical elaborations of these philosophical points, and illustrates them with an analysis of a case study in child protection. Keywords: benfluorex, causes of effects, counterfactual, child protection, effects of causes, Fre'chet bound, potential outcome, probability of causation