An article in the New York Times describes research that supposedly linked a rare gene mutation to autism:
Dr. Matthew W. State, a professor of genetics and child psychiatry at Yale, led a team that looked for de novo mutations [= mutations that are not in the parents] in 200 people who had been given an autism diagnosis, as well as in parents and siblings who showed no signs of the disorder. The team found that two unrelated children with autism in the study had de novo mutations in the same gene — and nothing similar in those without a diagnosis.
“That is like throwing a dart at a dart board with 21,000 spots and hitting the same one twice,” Dr. State said. “The chances that this gene is related to autism risk is something like 99.9999 percent.”
It is like throwing 200 darts at a dart board with 21,000 spots (the number of genes) and hitting the same one twice. (Each person has about 1 de novo mutation.) What are the odds of that? If all spots are equally likely to be hit, then the probability is about 0.6. More likely than not. (Dr. State seems to think it is extremely unlikely.) This is a variation on the birthday paradox. If there are 23 people in a room, it is 50/50 that two of them will share a birthday.
When Dr. State says, “The chances that this gene is related to autism risk is something like 99.9999 percent,” he is making an elementary mistake. He has taken a very low p value (maybe 0.000001) from a statistical test to indicate the likelihood that the null hypothesis (no association with autism) is true. P values indicate strength of evidence, not probability of truth.
One way to look at the evidence is that there is a group of 200 people (with an autism diagnosis) among whom two have a certain mutation and another group of about 600 people (their parents and siblings) none of whom have that mutation. If two instances of the mutation were randomly distributed among 800 people what are the odds that both instances would be in any pre-defined group of 200 of the 800 people (defined, say, by the letters in their first name)? The chance of this happening is 1/16. Not strong evidence of an association between the mutation and the actual pre-defined group (autism diagnosis).
Another study published at the same time found an link between autism and a mutation in the same gene identified by Dr. State’s group but again the association was weak. It may be a more subtle example of the birthday paradox: If twenty groups of genetics researchers are looking for a gene linked to autism, what are the odds that two of them will happen upon the same gene by chance?
If the gene with the de novo mutations is actually linked to autism, then we will have insight into the cause of 1% of the 200 autism cases Dr. Smart’s group studied. When genetics researchers try so hard and come up with so little, it increases my belief that the main causes of autism are environmental.
Thanks to Bryan Castañeda.