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


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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We thank Sander Greenland, Sonia Hernández-Díaz and Karen Steinberg for their detailed comments and expert advice. This work was supported by NIH Grant R01 HL080644.

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Correspondence to M A Hernán.



Formal definitions

We say that a counterfactual outcome Ya is consistent with the actual or realized outcome Y if Ya=Y when the subject received exposure level A=a.

Exchangeability means that any counterfactual outcome under any treatment level a is independent of the treatment actually received A, which is written symbolically as YaA. Randomization of the treatment is expected to result in exchangeability. Stratified randomization, in which the probability of receiving treatment varies by levels of the variables in L, is expected to result in conditional exchangeability within levels L, which is written as YaAL.

For discrete treatment A and covariates L, the positivity condition is written as Pr[A=aL=l]>0 if Pr[L=l]≠0. In general, positivity is written as fAL(al)>0 if fL(l)≠0, where fXZ(xz) is the conditional density function of the random variable X evaluated at the value x given the random variable Z evaluated at the value z.

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Hernán, M., Taubman, S. Does obesity shorten life? The importance of well-defined interventions to answer causal questions. Int J Obes 32 (Suppl 3), S8–S14 (2008).

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