Does obesity shorten life? The importance of well-defined interventions to answer causal questions

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Abstract
Many observational studies have estimated a strong effect of obesity on mortality. In this paper, we explicitly define the causal question that is asked by these studies and discuss the problems associated with it. We argue that observational studies of obesity and mortality violate the condition of consistency of counterfactual (potential) outcomes, a necessary condition for meaningful causal inference, because (1) they do not explicitly specify the interventions on body mass index (BMI) that are being compared and (2) different methods to modify BMI may lead to different counterfactual mortality outcomes, even if they lead to the same BMI value in a given person. Besides precluding the estimation of unambiguous causal effects, this violation of consistency affects the ability to address two additional conditions that are also necessary for causal inference: exchangeability and positivity. We conclude that consistency violations not only preclude the estimation of well-defined causal effects but also compromise our ability to estimate ill-defined causal effects.

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