The Birth-Weight Paradox


"In the mid-1960s, Jacob Yerushalmy pointed out that a mother’s smoking during pregnancy seemed to benefit the health of her newborn baby, if the baby happened to be born underweight."

Pearl, Judea. The Book of Why: The New Science of Cause and Effect (p. 183). Basic Books. Kindle Edition.

The Paradox Illustrated

  • We implemented this counterintuitive example as a causal Bayesian network, which means the arcs represent causal relationships.
  • The birth-weight paradox can be highlighted with two observations:
    • Babies of smokers have a lower birth weight than babies of non-smokers. \

    • Low-birth-weight babies of smoking mothers have a higher survival rate compared to those of non-smokers.

The Paradox Resolved

"Smoking may be harmful in that it contributes to low birth weight, but certain other causes of low birth weight, such as serious or life-threatening genetic abnormalities, are much more harmful. There are two possible explanations for low birth weight in one particular baby: it might have a smoking mother, or it might be affected by one of those other causes." (Pearl, pp. 184–185)

  • In other words, Low-Birth-Weight is a collider in the structure Smoking Mother → Low-Birth-Weight ← Birth Defect.

  • By observing Low-Birth-Weight, we open a noncausal ("back-door") path between Smoking Mother and Mortality of Child, which gives rise to the paradox. Please see our discussion of the Back-Door Criterion for more details on noncausal paths.

  • In BayesiaLab, we can illustrate what happens by highlighting all information paths:

    • Set Mortality of Child as Target Node.
    • Set evidence on Low-Birth-Weight.
    • Select Smoking Mother. Then, run Menu > Analysis > Visual > Graph > Influence Paths to Target.
    • Now, all influence paths are visible.
  • If we observe Smoking Mother=False, this explains away Low-Birth Weight=True and reduces the probability of Birth Defect=True;

  • On the other hand, if we observe Smoking Mother=False, the probability of Birth Defect=True increases, and the probability of Mortality of Child=True increases, too.​​​

  • Alternatively, we can use the WebSimulator to replicate these two scenarios:

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