Running the Numbers on Rape and Pregnancy

The Math Seems Implausible Because It Is

I read arstechnica most days because it often has computer/IT related articles that are valuable for work. It also has other articles that cover popular science, cars and other things. These latter are all very much of a sort that lean heavily in one political direction. For example, it had an article I saw this weekend which claims that over 64,000 additional pregnancies have occurred in the US since the Dobbs decision pushed abortion back to the states and 14 of them more or less made it illegal.

This seemed extraordinarily high.

So I went and followed the link to the scientific paper they based the article on.

Rape-Related Pregnancies in the 14 US States With Total Abortion Bans

Many US women report experiencing sexual violence, and many seek abortion for rape-related pregnancies. Following the US Supreme Court’s 2022 Dobbs v Jackson Women’s Health Organization (Dobbs) decision overturning Roe v Wade, 14 states have outlawed abortion at any gestational duration. Although 5 of these states allow exceptions for rape-related pregnancies, stringent gestational duration limits apply, and survivors must report the rape to law enforcement, a requirement likely to disqualify most survivors of rape, of whom only 21% report their rape to police.

Post Dobbs, 10 or fewer legal abortions occurred monthly in each of the total abortion ban states. We estimated rape-related pregnancies by state to assess how abortion bans affected survivors of rape.

The key finding is this table which has a number problems that stand out when you look at them for more than a few seconds

The Pregnancies

The first thing to observe is that they estimate that there is a per-vaginal rape pregnancy rate of 12.4%. Right there you see this is looking like junk. Just the basic 12.4% pregnancy rate appears to be crud because it suggests that, unless rapes are inherently more likely to lead to pregnancy that regular non-rape sex, one in eight sexual encounters results in pregnancy. Even when couples are deliberately trying to make babies and therefore there is no contraception, the pregnancy rate per sexual event is lower than that as in at least an order of magnitude lower, perhaps two. Places like WebMD claim that fertile 20 year olds only have a 25% chance of conceiving per menstrual cycle when trying to do so (i.e. multiple sexual encounters) and note that fertility drops significantly as women age. And course the likelihood in the US is that many (most?) fertile women will be on the pill or similar when raped - unless the claim is that rapes only happen to catholics and other devout religious sorts.

So that number is obviously wrong. But they derive it using a calculation they explain in the eMethods supplement.

Rape-related pregnancy (incidence) during abortion ban period = CVR * a * b

CVR = Completed vaginal rape incidence during abortion ban period (calculated as above)

a = Lifetime rape-related pregnancy rate, 14.9% (CDC 2016/17)

b = Ratio of per-rape pregnancy rate to lifetime rape-related pregnancy rate (Holmes et al, 1996)

Specifically, Holmes et al found a per-rape pregnancy rate of 5% and a lifetime rape-related pregnancy rate of 6%; hence we estimate the per-rape:lifetime ratio as 5.0/6.0 = 83%.

And we look at those numbers and realize that 14.9%*5/6=12.4% and that all three of those numbers are being abused.

The 14.9% number appears to come from the science behind this CDC page which summarizes the findings as:

• Almost 3 million women in the U.S. experienced RRP during their lifetime.

• About 18 million women have experienced vaginal rape in their lifetime.

What that says is that about a sixth of the women raped in the US became pregnant at least one time. As I read the notes it seems clear that in many cases (probably a large proportion of the 3 million) this is multiple rapes within a household. That 3 million number is pretty horrific but it is talking about a lifetime (say 30 years of fertility). If we just take that number and work it back it says that there are about 100,000 RRPs in the whole of the US per year or 150,000 for 18 months. Yes some women will have mutiple RRPs in their lifetime and some will die before they have had 30 years of fertility and some other number will be fertile for more than 30 years but it’s close enough.

Right there we see another problem because it implies that in just 14 states over 64,000 RRPs occur in some period between 12 months and 18 months while 100-150k occur in the entire country in the same period.

Because I like checking these things I went to the US Census website and queried the populations of the 14 states and the US for 2023. The fourteen states comprise just under 50 million (49,892,502) population. The US total is just under 335 million (334,914,895). So some simple sums tells us that the 14 states are just under 15% of the US population.

49,892,502/334,914,895=14.9%

If we assume 18 months total for every state (which is an over-estimate - about 60% of the population is Texas and Texas was just 16 months) then the number of RRPs expected in those states would be 14.9% of the number in the US, that is 14.9% of 150,000 which is 14.9%*150,000=22,345. We can probably round it down to 22,000 or even 20,000.

Even the unadjusted number is roughly ONE THIRD of the number in the article.

So that’s rubbish.

Update: I just realized after reading WMBrigg’s critique¹ and then re-reading the above that they know the pregnancy rate per rape. It is quoted above:

Holmes et al found a per-rape pregnancy rate of 5%

Since it is possible that some percentage of women will be raped more than once in 18 months it is perhaps acceptable to increase that number slightly - to say 5.5% or maybe 6% as a worst case estimate. 12.4% is laughably wrong and contradicted by their own source.

The Rapes

But we can also look at some of the other statistics. The total number of rapes in their 14 states is estimated to be just under 520,000.

The female population (and in this case since we’re concerned with pregnancy and vaginal rape, we can ignore the male population) of the 15 states is about 25 million.

To cut them some slack lets assume we’re talking one year instead of between 1-1.5 years. If in one year some 500,000 rapes are estimated to have occurred in a population of 25 million that works out at 2% of the (female) population being raped. That’s one woman in 50 or put it another way 20 women per thousand.

This is roughly TEN times the number (1.9/thousand) in the most recent estimate of the U.S. Department of Justice’s Bureau of Justice Statistics and its National Crime Victimization Survey (NCVS). I should note that the authors cite this estimate although they note that it is believed to undercount the number of rapes. But the 2014 research they refer to makes no claim that the number in the BJS is undercounting rapes by a factor of ten.

Also if one in 50 women are being raped each year then nationally that’s over 3 million rapes nationally a year. In order to match that with the the CDC (see above) which says that 18 million women experience rape over their lifetime then most of those 18 million women would need to be raped several times over their lifetime.

So that number doesn’t come close to passing the smell test.

What might be reasonable numbers?

OK lets take the official numbers and work forward.

25 million women

1.9/thousand rapes

round the numbers and we can expect about 50,000 rapes in the 14 states a year or 75,000 in 18 months. Given that Texas is 60% of the population and had 16 months instead of 18, I’m going to say the total for the period under study is less than 70,000 and probably more like 65,000 but I can’t be bothered to figure out the precise maths

So 70,000 instead of 520,000 or about 13% of the original claim.

Assume that half of that number are on women that are infertile for one reason or another (age, contraception …) giving us 35,000 rapes that could potentially lead to pregnancy.

If we assume that women not on contraception etc. are on average fertile 2 days out of 28, that they are raped on a random day in their cycle and that if raped when fertile then they will become pregnant then that gives us an RRP of about 7% (this is also probably an over estimate…)

35,000 x 0.07 = 2,450

So instead of 64,000 RRPs a more reasonable maximum is 2,500 or about 4% of the headline number. It is works out at about 1 in 10,000 for women in the 14 states.

Update: Based on the Holmes number quoted above that 5% of rapes lead to pregnancy the number of pregnancies would be

70,000 x 0.05 = 3,500

If we assume the reported rapes number is lower and do some other jiggling I could see getting towards a ballpark of 6,400 i.e. 10% of the number claimed. But I would considr that number to be very much on the high side.

Summary

Article says 520,000 rapes and 64,000+ pregnancies.

Quick worst case back of the envelope calculations say 70,000 rapes and 2,500 pregnancies.

The study overestimates the number of expected rapes by a factor of 7-8

The study overestimates the number of expected pregnancies by at least a factor of 25.

I am prepared to believe that rapes are under-reported, even using victim surveys in part because I know women who have been raped who haven’t told anyone in authority. Despite that I find it hard to believe that one woman in 50 is raped each year. I find it impossible to believe that one in 400 is raped and becomes pregnant as a result each year which is what the article implies.

Who are the Authors?

The authors of this toilet paper are

• Samuel L. Dickman, MD - Planned Parenthood of Montana, Billings, Montana

• Kari White, PhD - Resound Research for Reproductive Health, Austin, Texas

• David U. Himmelstein, MD - Hunter College, City University of New York, New York

• Emily Lupez, MD - Department of Medicine, Cambridge Health Alliance, Cambridge, Massachusett

• Elizabeth Schrier, MD - Department of Medicine, University of California, San Francisco

• Steffie Woolhandler, MD, MPH - Hunter College, City University of New York, New York

You will be entirely unsurprised to note that the lead author has a relevant disclosure to make

Dr Dickman reported that he is a plaintiff in several lawsuits challenging abortion restrictions in Montana.

I hope that the defendants in Dr Dickman’s cases are aware of this paper and can pay someone to do the sums a bit better than I have so as debunk Dr Dickman’s scientific credentials.

Why Publish?

The article is published in JAMA (Journal of the American Medical Association) Internal Medicine as a Research Letter on the topic of “Health and the 2024 US Election” and the journal has a related editorial that uses this article to bitch about abortion restrictions

In this issue of JAMA Internal Medicine, Dickman et al¹ demonstrate the scope of the problem. In the 14 states that have made abortion highly restrictive,² the estimated number of rapes resulting in pregnancy is exponentially larger than the number of persons having legal abortions, even in those states that have an exception for rape. Whether these survivors of rape had illegal abortions, received medication abortion through the mail, traveled to other states, or carried the child to birth is unknown.

Now I have a lot of sympathy for women who have been raped and I can certainly understand why they would want an abortion. But I have very little sympathy for the JAMA editors who appear to have approved this shoddy study in order to help them make the case that abortion should not be limited by states.

The editors write unquestioningly that “the estimated number of rapes resulting in pregnancy is exponentially larger than the number of persons having legal abortions” and fail to consider whether the estimated number of rapes resulting in pregnancy is actually plausible. Something that affects a maximum of one woman in a ten thousand each year is very different to one that affects one in 400 which is roughly what the authors claim.

PS “exponentially larger” - David Friedman has thoughts²

1. Dickman Cries "Rape!": On The Bizarre New Rape-Pregnancy Paper

2. Abused Words