## Wednesday, June 5, 2013

### Twins, or In which newspapers mess up odds calculations (again)

This BBC piece interviews a couple who've been 'blessed' with three sets of twins (rather you than me).   The caption states that
Doctors told them the chances of having three sets of twins was 500,000-1.
Doctors that don't know much about genetics, perhaps.

Our old friend the Daily Mail managed to imply that this happened for the first time in Britain last year:

Obviously they don't read the Telegraph, which has an example from 2001. (The DM article has since been changed but they forgot to change the title of the web-page, which is why it appears like this on Google; the correction is not acknowledged, naturally.)  And if three sets of twins are unlucky, feel for this poor woman, who has six!

The Telegraph helpfully details the mathematics involved in their calculation.  For natural births, in white European women, approximately 1 in 80 result in twins (or triplets, or more, if one is even luckier).  Therefore if you take three births at random, there's about a one in $80 \times 80 \times 80 = 512,000$ chance they'll all be twins.

Except, obviously, these births were not selected 'at random' because they're all from the same mother.  Which is sort of the point.

Like many things, there are genetic factors which predispose people to have twins, generally (as far as my research tells me) because the mother is prone to hyper-ovulate.  So if you pick a mother who has already had twins, they're more likely to be someone prone to hyper-ovulation, and therefore it's more likely that they'll have a second set.  If they've already had two sets, well you can be pretty darn sure they hyper-ovulate.

Other factors are also important.  If you're of Nigerian ancestry, then your chances of having twins in the first place are considerably higher.  Older mothers are also more likely to have multiple births.

I haven't been able to find anything terribly concrete quantifying the observed proportions of multiple sets of twins, but it seems to be about four times as likely that you'll have a second set of twins if you've already had one.  This reduces our highly unlikely 1 in 500,000 to a mere 1 in $80 \times 20 \times 20 = 32,000$.

Quite a lot of families are out there who have gone through three pregnancies.  Third births within marriages and civil partnerships in England and Wales (outside marriage the order isn't recorded) represented about 7.5% of the 720,000 in 2010.  That's about 50,000 or so per year, so we can expect one of these stories to come around about every... oh nine months or so?

Actually that's probably not true, 'cos if people with two sets of twins already have any sense they'll start being a little bit more careful...

#### 1 comment:

1. The BBC gets there eventually :)

http://www.bbc.co.uk/news/magazine-22813345