# identical or sororalFebruary 26, 2009 11:40 AM   Subscribe

Fetusfilter: what are the statistical chances that two female fetuses, 15 weeks, diamniotic/dichorionic ("di-di") are identical?

So evidently our twin girls (15 weeks) are diamniotic-dichorionic (di-di), meaning they each have a placenta and sac to themselves. This seems to mean that the chance of identicals (versus fraternals) is 11% (33% twins are identical, 33% of those are "di-di" so 1/3x1/3=1/9 or 11%).

HOWEVER, since we now know they are both girls, does that somehow affect the odds? It would seem to raise it again, but I have no idea by how much or where it would go in the calculation. Any ideas?
posted by whatgorilla to Science & Nature (14 answers total) 1 user marked this as a favorite

posted by dersins at 11:43 AM on February 26, 2009

Strictly mathematically: If 11/100 are identical, 44.5/100 are non-identical same gender, and 44.5/100 are non-identical different gender, then ruling out the different gender case gives you 11/44.5 = 25% chance of being identical.
posted by teki at 11:56 AM on February 26, 2009

... I mean 11/(11 + 45.5) = 20%.
posted by teki at 11:57 AM on February 26, 2009

33% twins are identical, 33% of those are "di-di" so 1/3x1/3=1/9 or 11%

This isn't the right way to calculate what you're trying to calculate. Just FYI.
posted by flug at 12:03 PM on February 26, 2009

Assuming your figures are correct (I'm not going to check), 1/3 of twins overall are identical, and 2/3 are fraternal. Identical twins are always same-sex. Fraternal twins are (I'm assuming) equally likely to be opposite-sex as same-sex. In other words, 1/3 of twins overall are identical, 1/3 of twins overall are same-sex fraternal, and 1/3 of twins overall are opposite-sex fraternal. Which means 2/3 of all twins are same-sex. Thus, half, i.e., (1/3)/(2/3) of all same-sex twins are identical.

However, this is incorrect:

So evidently our twin girls (15 weeks) are diamniotic-dichorionic (di-di), meaning they each have a placenta and sac to themselves. This seems to mean that the chance of identicals (versus fraternals) is 11% (33% twins are identical, 33% of those are "di-di" so 1/3x1/3=1/9 or 11%).

11% is the probability of a pair of twins—out of all twins—being both identical and di-di. It is not the probability of a pair of twins known to be di-di of being identical. To find that, we also need to note that all fraternal twins are di-di. So: 2/3 of all pairs of twins are fraternal and di-di; 1/9 of all pairs of twins are identical and di-di. 7/9 (2/3+1/9) of all twins are di-di. Given that a pair of twins are di-di, the probability that they are identical is (1/9)/(7/9) = 1/7.

So to your main question: given that a pair of twins is known to be both same-sex and di-di, what is the probability that they are identical? We know, as before, 1/9 of all pairs of twins are di-di and identical (and necessarily same sex). 1/3 of all pairs of twins are same-sex and fraternal (and necessarily di-di). Thus, 4/9 (1/9+1/3) of all twins are same-sex and di-di. The probability that a pair of twins known to be same-sex and di-di are identical twins is (1/9)/(4/9) = 1/4.

Google "conditional probability" for background on the calculations.
posted by DevilsAdvocate at 12:10 PM on February 26, 2009 [2 favorites]

Where did you come up with the fact that 33% of twins are identical? That seems way too high. A cursory glance at wikipedia suggests that though the rate of dizgotic (DZ) twins varies by ethnicity and age, and has been on the rise due to hyperovulation practices, a rough estimate is that 30/1000 births are DZ. Of these, 60% will have matched gender, so 18/1000 births are matched-gender DZ.

This is to be compared to about 3/1000 births that are monozygotic (MZ) or identical. Of the latter, approximately 18-36% will be di-di so let's say 33% to be conservative and make the math easier. That means 1/1000 births are di-di MZ.

By my math, that means among all di-di pregnancies with matched gender (19/1000), 1/1000 are di-di MZ. Which means that if one knows that their twins are of the same gender and di-di, the odds of an identical twin are 1:18 or just over 5%.

That is my final answer, and I pray that my advanced degree in biostatistics hasn't failed.
posted by drpynchon at 12:28 PM on February 26, 2009 [1 favorite]

Response by poster: Wow, there's a long way between 25% (devilsadvocate's answer) and 5% (drpynchon's answer). 1 in 4 or 1 in 20.

I've read in several places that "Fraternal twins are more common than identical twins and account for about 2/3 of twin pregnancies" (1). And I've read that monozygotic di-di's occur 18-36% of the time (2).

Of course, there are other factors that further complicate (decrease) the chances of identical. The mother is 30 and was on birth control (though it was most likely weakened by anti-biotics), both of which seem to increase the chances of fraternal.

I have no real preference, I just wanted to see if someone could help me calculate the probability.

(1) -- http://www.keepkidshealthy.com/twins/expecting_twins.html
(2) -- http://en.wikipedia.org/wiki/Identical_twins#Monozygotic_twins
posted by whatgorilla at 12:52 PM on February 26, 2009

Best answer: OK, I've made a bunch of assumptions but this at least gives a ballpark estimate of what you're looking for.

I divided into several categories and calculated the proportions that will be in each category. The categories are male/male vs female/female vs male/female; identical vs non-indentical; and diamniotic/dichorionic vs diamniotic/monochorionic vs monoamniotic/monochorionic.

With the "facts" I used and assumptions I made (see below), the only possible categories your twins can fit into are:

Female-Female, identical, diamniotic/dichorionic: 4.6% of all twin births
Female-Female, non-identical, diamnotic/dichorionic: 23.9% of all twin births

So it looks like you've got about 84% chance of non-identical and 16% chance of identical.

The main reason this is different than the overall rule-of-thumb ratio of identical to non-identical twin births (1/3 identical to 2/3 non-identical), is because we can rule your twins out from the largest group of identical twins (65-70% of identical twins are diamniotic/monochorionic, which your girls are not) whereas we *can't* rule them out from the non-identical category (essentially all non-identical twins are diamniotic/diachorionic as far as I know).

Keep in mind these are round numbers, ballpark estimates, and rule-of-thumb type numbers and then I've gone and **extrapolated** from those. So keep in mind this is a round-number ballpark estimate at best.

But I think we can say for sure that the chances of them being non-identical are quite a lot higher than being identical--and given the facts you know, chances of them being non-identical are higher than before you knew those facts.

And on the other hand--keep in mind that these are odds calculations and in reality, they are what they are. If they are identical twins, it doesn't really matter if compared with the general population there is 90% chance, 9% chance, or 0.00009% chance of them being that.

Here is the background on my calculation--read only if you are interested in mind-numbing details.

"Facts" used:

* 104.6 male births for each 100 female (the U.S. average as of 2007).
* 1/3 of all twin births are identical vs 2/3 non-identical
* 28.5% if identical twins are diamniotic/dichorionic, 68.5% are diamniotic/monochorionic, and 3% monoamniotic/monochorionic (From a table here: http://twinstwice.com/twins.html - but it lists ranges and for calculation purposes I chose an exact number within the range given.)
* All non-identical twins are diamniotic/dichorionic

I call them "facts" instead of just plain facts because all of these are population-based averages and the like that might vary based on your nationality, ethnicity, toxic chemicals you've been exposed to or whatever. They are round-number rule of thumb type guidelines rather than hard, precise numbers.

Assumptions used:

* Identical twin births follow this same male/female proportion (ie, 104.6 male/male for every 100 female/female). This is probably not true but on the other hand the difference it makes is so small it won't materially affect the estimates I've given above.

* Each particular type of identical twin birth (diamniotic/dichorionic, diamniotic/monochorionic, monoamniotic/monochorionic) follows the same male/female proportion. (Again this is probably not literally true but also likely to change the overall result by only a small amount.)

* Non-identical twin births follow the same male/female proportion (ie, 104.6 males to 100 female live births)

The method used was to use the above figures to calculate what percentage of all twin births fall into each of the above categories: identical twins, male/male, diamniotic/dichorionic vs identical twins, male/male, diamniotic/monochorionic vs identical twins, male/male, monoamniotic/monochorionic vs identical twins, female/femael, diamniotic/dichorionic, etc. etc. etc.

Then note which categories this birth may fall into (identical twins, female/female, diamniotic/dichorionic or non-identical twins, female/female, diamnotic/dichorionic) and the proportions between those two categories.
posted by flug at 1:02 PM on February 26, 2009 [1 favorite]

Response by poster: BTW--since both of the "best answers" seem more sophisticated than my ideas, I'll split the difference, call it 15% and take of 4% for the other aforementioned contigencies, and call it 11% (coincidentally, my original guesstimate) until another conditional probability biostatistician comes along and tells me whose answer is the correct "best answer".
posted by whatgorilla at 1:04 PM on February 26, 2009

Response by poster: Thanks flug--(question--What did math did you use for the final calculation estimate of 14%? I tried 4.6 / 23.9, but came up with 19.25% chance identical, xx, di-di's).
posted by whatgorilla at 1:11 PM on February 26, 2009

4.6/(23.9 +4.6), ie (ident and xx,di-di)/(all possible xx,di-di), yields flug's 16%.
posted by Westringia F. at 1:21 PM on February 26, 2009

Wow, there's a long way between 25% (devilsadvocate's answer) and 5% (drpynchon's answer). 1 in 4 or 1 in 20.

It's because we used different starting numbers. I took your "1/3 of all twins identical" at face value, while drpynchon suggests the value is much less. Also, I made the assumption that half of all pairs of fraternal twins were same-sex, while drpynchon uses a slightly higher figure. Aside from those starting numbers, though, our methodology is the same. If I had used drpynchon's starting figures I would have come up with his final answer, and vice versa.
posted by DevilsAdvocate at 1:30 PM on February 26, 2009

Yeah DevlisAdvocate and I use the same math here. The answer is really going to depend heavily on your estimate of the prevalence of dizygotic twins (or in other words the fraction of twins that are dizygotic as compared to identical). As I mentioned this varies a great deal depending on lots of factors and has a fair bit of variability. After a bit more research it looks like the number I used was in fact an overestimate. The best published study I could dig up reports an overall prevalence of dizygotic twins of 8/1000 births in the US in 1990, rising to about 10/1000 by 2001. So indeed that would suggest that your estimate of 2/3's of all twins being fraternal isn't too far off.

By my math if 8/1000 are dizygotic (I use this as the newer estimate is probably inflated by more hyperovulated octamoms these days), then the odds are closer to about 17% of an identical twin pregnancy in your case.
posted by drpynchon at 5:18 PM on February 26, 2009