The puzzle consists of two pieces. First, smoking during pregnancy is linked to lower birthweight. That link was already being reported in the 1950s; for example, Simpson (1957) Simpson, W. J. (1957). A preliminary report on cigarette smoking and the incidence of prematurity. American Journal of Obstetrics and Gynecology. found that smoking mothers were much more likely to have babies in the low-birthweight group, and later prospective work by Yerushalmy (1964) Yerushalmy, J. (1964). Mother's cigarette smoking and survival of infant. American Journal of Obstetrics and Gynecology. again found more low-birthweight births among smokers, with heavier smoking linked to a higher chance of low birthweight.

Second, low birthweight is strongly linked to worse survival. The World Health Organization notes that low-birthweight infants are about 20 times more likely to die than heavier infants.

Put those two facts together and you would expect babies of smoking mothers to do worse. But once researchers looked only at low-birthweight babies, the pattern seemed to flip: babies of smoking mothers sometimes appeared more likely to survive than low-birthweight babies of non-smokers. In later data summarized by Hernández-Díaz, Schisterman, and Hernán (2006) Hernández-Díaz, S., Schisterman, E. F., and Hernán, M. A. (2006). The birth weight “paradox” uncovered? American Journal of Epidemiology. low-birthweight infants born to smokers had lower infant mortality than low-birthweight infants born to non-smokers, even though smokers had higher risks of both low birthweight and infant mortality overall.

That is what made the result so strange. Yerushalmy himself basically said: this cannot be right in any simple biological sense. As he put it "It is difficult to propose a reasonable explanation for this phenomenon of relatively more, but apparently healthier, infants of "low birth weight" among smoking than nonsmoking mothers. "

Solution

So is it true, then? Are babies born to smoking mothers actually healthier? Should doctors start prescribing cigarettes to worried mothers?

Not quite. What is happening here is a statistical quirk — one that can appear in many kinds of data if we are not careful about what exactly we are comparing. The first thing to notice is that the surprising result appears only after we restrict attention to babies with low birthweight. But if the question is whether smoking is harmful for infant survival, then the more relevant comparison is much simpler: do babies of smoking mothers have higher or lower mortality overall?

That should be the starting point. And overall, smoking is not protective. The apparent benefit appears only inside a selected subgroup: babies who already have low birthweight.

The next step is to remember that low birthweight is not a single disease. It is more like a symptom, and different causes can lead to the same symptom. Some babies are small because their mothers smoked. Others are small because of serious underlying problems, such as congenital conditions, placental complications, or other forms of fetal distress. These causes do not carry the same risk.

So among low-birthweight babies, we are mixing together at least two very different groups. Some babies are low birthweight because of smoking. Others are low birthweight because something much more severe is going on. The second group is much more likely to die. This means that low-birthweight babies of non-smokers can look unusually fragile, not because non-smoking is dangerous, but because, in the absence of smoking, their low birthweight is more likely to signal a serious underlying problem.

This is the heart of the birthweight paradox.

The collider problem

More technically, the mistake is called collider bias. A collider is a variable that is caused by two other variables. In this case, low birthweight can be caused by smoking, but it can also be caused by serious underlying illness.

In a simple causal diagram, the structure looks like this:

Smoking → Low birthweight ← Underlying illness → Infant mortality

Low birthweight sits in the middle as a collider. Normally, smoking and underlying illness do not have to be related. But once we look only at low-birthweight babies, we condition on that collider. That creates a misleading relationship between smoking and underlying illness.

The intuition is simple. If a baby has low birthweight and the mother smoked, then smoking itself may explain why the baby is small. But if a baby has low birthweight and the mother did not smoke, then we start to suspect some other cause. And some of those other causes are very dangerous.

So, within the low-birthweight group, smoking becomes associated with a lower chance of severe underlying illness. That makes babies of smoking mothers appear healthier, even though smoking itself is not helping them. The comparison is distorted because we selected babies based on a variable that both smoking and illness can cause.

This is why the result feels paradoxical. The data are not showing that smoking saves babies. They are showing that conditioning on low birthweight changes the comparison. We are no longer asking, “What is the effect of smoking?” We are asking, “Among babies who are already small, are the babies of smokers different from the babies of non-smokers?” And the answer is yes — but not for the reason we first think.