Bruce McCullough writes,

The probability of getting brain cancer is determined by the number of younger siblings. So claim some scientists, according to an article published in the current issue of The Economist.

I have ordered your book so that I can read more about controlling for intermediate outcomes, but I am not yet confident enough to tackle it myself. Perhaps you might blog this?

I’ll give my thoughts, but first here’s the scientific paper (by Altieri et al. in the journal Neurology), and here are the key parts of the news article that Bruce forwarded:

Younger siblings increase the chance of brain cancer

IT IS well known that many sorts of cancer run in families; in other words you get them (or, at least, a genetic predisposition towards them) from your parents. . . . Dr Altieri was looking for evidence to support the idea that at least some brain cancers are triggered by viruses and that children in large families are therefore at greater risk, because they are more likely to be exposed to childhood viral infections. . . .

Dr Altieri describes what he discovered when he analysed the records of the Swedish Family Cancer Database. This includes everyone born in Sweden since 1931, together with their parents even if born before that date.

More than 13,600 Swedes have developed brain tumours in the intervening decades. In small families there was no relationship between an individual’s risk of brain cancer and the number of siblings he had. However, children in families with five or more offspring had twice the average chance of developing brain cancer over the course of their lives compared with those who had no brothers and sisters at all.

Digging deeper, Dr Altieri found a more startling result. When he looked at those people who had had their cancer as children or young teenagers he found the rate was even higher–and that it was particularly high for those with many younger siblings. Under-15s with three or more younger siblings were 3.7 times more likely than only children to develop a common type of brain cancer called a meningioma, and at significantly higher risk of every other form of the disease that the researchers considered. . . . the mechanisms by which younger siblings have more influence than elder ones are speculative. . . . An alternative theory is that a first child may experience a period when his immune system is particularly sensitive to certain infections at about the age when third and fourth children are typically born. . . .

OK, now my thoughts. There are two issues to address here: first, what exactly did Altieri et al. find in their data analysis, and, second, how can we think about causal inference for birth order and the number of siblings?

What did Altieri et al. find?

The main results in the paper appear to be in Table 2, where the brain cancer risk is slightly higher among people with more siblings. The overall risk ratios, normalized at 1 for only children, are 1.03, 1.06, 1.10, and 1.06 for people with 1, 2, 3, or 4+ siblings, respectively. The table gives a p value for the trend as 0.005, but I think they made a mistake, because, in R:

> x <- 0:4 > y <- c(1,1.03,1.06,1.10,1.06) > summary (lm (y~x))

Call:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.012000 0.019950 50.727 1.69e-05 ***
x 0.019000 0.008145 2.333 0.102

Residual standard error: 0.02576 on 3 degrees of freedom
Multiple R-Squared: 0.6446, Adjusted R-squared: 0.5262
F-statistic: 5.442 on 1 and 3 DF, p-value: 0.1019

The p-value seems to be 0.10, not 0.005.

Stronger results appear in Tables T-1, T-2, and T-3 (referred to in the paper and included in the supplementary material at the article’s webpage). Risk ratios for brain cancer are quite a bit higher for kids with 3 or more younger siblings, and lower for kids with 3 or more older siblings.

In all these tables, results are broken down by type of cancer, but sample sizes are small enough that I don’t really put much trust into these subset analyses. A multilevel model would help, I suppose.

Causal inference for birth order

How to think about this causally? We can think about the number of younger siblings as a causal treatment: if littel Billy’s parents have more kids, how does this affect the probability that Billy gets brain cancer? But how do we think about older siblings? I’m a little stuck here: if I try to compare Billy as an only child to Billy as the youngest of three children, it’s hard to think of a corresponding causal “treatment.”

Thinking forward from treatments, suppose a couple has a kid and is considering to have another. One could imagine the effect of this on the first child’s probability of brain cancer. One can also consider the probability that the second child has brain cancer, but the comparison of the two kids would not be “causal” (in the Rubin sense). This is not to dismiss the comparison–I’m just laying out my struggle with thinking about these things. Similar issues arise in other noncausal comparisons (for example, comparing boys to girls).

The reluctant debunker

Finally, I’m sensitive to Andrew Oswald’s comment that I’m too critical of innovative research–even if there are methodological flaws in a paper, it’s conclusions could still be correct. My only defense is that I’m responding to Bruce’s request: I wasn’t going out looking for papers to debunk.

In any case, I’m not “debunking” this paper at all. I don’t see major statistical problems with their comparisons; I’m just struggling to understand it all.