So to remind you, the low birthweight paradox-- again, babies of smokers are more likely to be low birthweight . Low birthweight is bad. It has higher mortality.
So the heroes of this story are Hernandez-Diaz, Schisterman, and Hernan, who published this paper in 2006 that explains the low birthweight paradox. They used data from the National Center for Health Statistics.
If you use a collider to select your sample, as we did with the SAT scores and as people did with low birthweight , or if you add a collider as a control variable in a regression model, you are going to induce a biased view of what those relationships are. And I should say, biased in this case does not mean oh, it might be off by a little bit.
So in this diagram, an arrow means that A causes B. So the arrow here from smoking to mortality means that smoking is a cause of mortality. It is also a cause of low birthweight . And then there are other unknown risk factors, which potentially also cause low birthweight and also cause mortality.
And so they replicated Yerushalmi's study from 1971. Looking at the distribution of birthweights , we can see the blue line there. Those are babies of smokers.
It has consequences for lives. So I'm going to start with the "Low Birthweight Paradox," which is one of the first examples. This comes from a paper in 1971.
And a few of their results, one of them was that the babies of mothers who smoke tend to be lighter by about 6%, and they are more likely to be classified as low birthweight , meaning that they fall below a particular threshold. And that was no surprise at the time.
That was known to be true. They also found that if a baby is classified as low birthweight , it has higher mortality by quite a lot. So the background rate was about 8 per 1,000 at the time.
And babies of smokers do, in fact have higher mortality. But then the weird part is that if you select low birthweight babies, the babies of smokers have lower mortality. The reason is there are two ways that a baby might be low birthweight .
Imagine you're a doctor. You're treating a patient who is low birthweight , and you find out that the mother is a smoker, you might be relieved because that explains it. And it provides a relatively benign explanation that's better than the alternatives.
They are, in fact, lighter on average and more likely to fall below that threshold and be classified as low birthweight . And if we look at mortality here as a function of birthweight , you can see the crossover point that is Berkson's paradox. So above, let's say, 2,000 grams at birth, the mortality rate is higher for children of smokers, which is what we expect.
And so this sampling process, if we select based on low birthweight status, this is an example of collider bias. That is a possible explanation of the low birthweight paradox. The obesity paradox lived a little bit longer.
This was in the '70s. It's better now. But for low birthweight babies, it was substantially higher, about 170 per 1,000. And again, that effect was known.
And again, that effect was known. But the thing that was surprising is that if you are researching low birthweight babies, so you select just those babies, what you find is that the babies of non-smokers are actually healthier.
And that two ways is the key to those examples that I gave from epidemiology. So to remind you, the low birthweight paradox-- again, babies of smokers are more likely to be low birthweight . Low birthweight is bad.
But then the weird part is that if you select low birthweight babies, the babies of smokers have lower mortality. The reason is there are two ways that a baby might be low birthweight . One possible cause is maternal smoking.
It is also a cause of low birthweight . And then there are other unknown risk factors, which potentially also cause low birthweight and also cause mortality. So this diagram is a graphical representation of those hypotheses.
arrows are colliding with each other. And so this sampling process, if we select based on low birthweight status, this is an example of collider bias. That is a possible explanation of the low birthweight paradox.
Those are babies of smokers. They are, in fact, lighter on average and more likely to fall below that threshold and be classified as low birthweight . And if we look at mortality here as a function of birthweight , you can see the crossover point that is Berkson's paradox.
and not just a correlation, but causal in the sense of a counterfactual, like if that had not happened, the outcome would not have happened. And here we can see that two ways to get in effect, which is that there are two causes of low birthweight . And so, again, if we know that one of the causes exists, the probability of that other cause goes down.