January 31, 2007

silhouette3.JPG From the desk of Jane Galt:

Splain me, please?

Let me make clearer what I said in the last post about fertility and the effectiveness of Plan B.

An egg lives, on average, one day.

Sperm live, in a fertile woman, an average of 3-5 days.

Assume that rapes and accidents are randomly distributed throughout the menstrual cycle. (They probably aren't, but more on that later.) That means that, assuming you are going to have an unfortunate event, there is a 1/28 probability that it will occur on a given day of an average woman's menstrual cycle.

4-6 of those days will be "fertile" days on which it is possible to get pregnant: the day of ovulation, plus 3-5 days before that. Peak fertility occurs on the day before ovulation; you have a 26% chance of getting pregnant on that day. The day of ovulation, it drops to 15 percent (travel time is a killer), and then to basically nothing. On the other end, because sperm die off somewhat rapidly, fertility drops off the longer the gap between ejaculation and ovulation; by four days before ovulation, it's basically negligible.

By rough extrapolation from the the allegation on this fertility site that fertility goes from about 10% day O-5 to 33% on O-day itself (dropping to nothing almost immediately thereafter), I get the following:

5 days before ovulation: 10% chance of getting pregnant without Plan B
4 days before ovulation: 17% chance of getting pregnant without Plan B
3 days before ovulation: 24% chance of getting pregnant without Plan B
2 days before ovulation: 27% chance of getting pregnant without Plan B
1 day before ovulation: 30% chance of getting pregnant without Plan B
Ovulation day: 33% chance of getting pregnant without Plan B

So if 1,000 women have an unfortunate incident in an average 28 day cycle, that will be roughly 35 incidents per day.

On O-5, 3 pregnancies will result
On O -4, 6 pregnancies will result
On O-3, 8 pregnancies will result
On O-2, 9 pregnancies will result
On O-1 day, 10 pregnancies will result
On O day, 12 pregnancies will result


This makes for a total of 48 pregnancies. Assuming that ovulation comes at the beginning of O-day, 12 of them will come after ovulation.

Now, let's posit two things:

1) All the women take Plan B immediately (for maximium effectiveness)
2) Plan B does not prevent implantation, only ovulation

Even if Plan B were perfectly effective every single time it is taken right up to the moment of ovulation, it would still have a failure rate of 25%, higher than its quoted rate. So one of these things must be true:

1) It fails more than quoted
2) My probabilities are off
3) It suppresses implantation

Moreover, most women don't take it right away. Accidents aren't randomly distributed; they're undoubtedly concentrated in several ways. First, women seem to be more attractive when they are ovulating; second, accidents are almost certainly concentrated on weekends, when health clinics are harder to get to. Third, they will be concentrated at night. Unless they've been raped, women are unlikely to get out of bed and go to the emergency room, particularly if they've been drinking.

So now let's lag the fertility by 12 or 24 or 48 hours. It takes only a few hours for sperm to reach the fallopian tube. Suddenly, 17-31 out of 48 pregnancies prevented by Plan B involve already fertilised eggs.

Now, perhaps I'm missing something here. I'm sure my avidly pro-choice readers will be happy to explain it. But given the life of a sperm, I just don't see how it's possible that Plan B both noticeably affects pregnancy, and does nothing about implantation.

Now, personally, I don't think I care whether it does or not. But if it doesn't touch implantation, I'm puzzled.

Posted by Jane Galt at January 31, 2007 4:18 PM | TrackBack | Technorati inbound links
Comments
Posted by: Storkdoc on January 31, 2007 6:02 PM

From Uptodate.com, here is the mechansim of action for levonorgesteral the active ingredient in plan b

"MECHANISM OF ACTION — Pregnancy may be prevented through several mechanisms: Thickening of cervical mucus, which inhibits sperm passage through the uterus and sperm survival; inhibition of ovulation, from a negative feedback mechanism on the hypothalamus, leading to reduced secretion of follicle stimulating hormone (FSH) and luteinizing hormone (LH); inhibition of implantation. Levonorgestrel is not effective once the implantation process has begun."

So it can prevent implantation which typically occurs 5 to 7 days after conception.

Posted by: Brandon Berg on January 31, 2007 6:41 PM

That sounds to me like a 1.2% failure rate, not a 25% failure rate. I believe that failure rate is the ratio of pregnancies to uses, not the ratio of pregnancies that actually happen to pregnancies that would have happened.

Posted by: Jane Galt on January 31, 2007 6:46 PM

If that's true, Plan B doesn't work that well; the odds of becoming pregnant in any given month of unprotected sex are only like 25%. If Plan B knocks that down to 11% . . . well, it's better than nothing, but hardly a panacea. Especially since its side effects are apparently quite gnarly.

Posted by: Jane Galt on January 31, 2007 6:48 PM

In fact, since the odds of getting pregnant during any single act of intercourse are much less than 11%, it would seem that if Brandon is right, Plan B doesn't work at all.

Posted by: dorkafork on January 31, 2007 7:00 PM

You've got 35 rapes resulting in 48 pregnancies. I believe that is somewhat problematic.

Posted by: dorkafork on January 31, 2007 7:01 PM

Unless I'm reading that wrong.

Posted by: Jane Galt on January 31, 2007 7:05 PM

You're reading it wrong. That's 35 rapes/accidents a day.

Posted by: dorkafork on January 31, 2007 7:05 PM

Nevermind my first comment, my mistake.

Posted by: dorkafork on January 31, 2007 7:12 PM

To atone somewhat, here's a (rather provocatively titled) description by a biologist of how Plan B works. Short version: a spike in LH levels triggers ovulation and progesterone suppresses LH. Plan B is a large dose of progesterone and progesterone is produced by the body to maintain the uterine lining, and is produced after ovulation. Which would imply that it would not have a negative effect on implantation.

Posted by: dorkafork on January 31, 2007 7:14 PM

Which you already linked to. It's not my day. I give up.

Posted by: Ryan on January 31, 2007 7:23 PM

I realize Jane was trying to simplifly as much as possible. But I thought I'd include the following for reference;

It seems reasonable to infer that coitus also occasionally provokes or accelerates single ovulations, thus impugning some rhythm methods of contraception. But there seems no very good evidence that rape induces ovulation.

http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=6536139&query_hl=12&itool=pubmed_DocSum


Sexual abuse occurred during ovulation among 5 of the 11 victims who had reached menses, thus placing them at risk of pregnancy.
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=12289998&query_hl=12&itool=pubmed_docsum

Posted by: Karl Smith on January 31, 2007 8:21 PM

Unless, I am reading this wrong Jane it looks like you stats show that the probability of getting pregnant from a single incidence of unprotected sex are 4.8%

With Plan B that number potentially drops to 1.2% - thus your probability has been cut by 75%.

This is pretty effective, even without stoping implantation.

It also supports the notion that Plan B primarly works by supressing ovulation. There are only 1.2 percentage points left to get rid of.

Posted by: Karl Smith on January 31, 2007 8:31 PM

Actually, I just reread your post

You said day off ovulation 15%, 0 thereafter.

So suppose Plan B stops all ovulation immediately upon injestion. Then we have a very effect BC right here. There is only one way you can get pregnant - You had sex on the day you ovulated.

Anyday before and ovulation is prevented. Any day after and probability is by assumption 0.

On that day there is still only a 15% of pregnancy. So the total chance of becoming pregnant after taking Plan B is only about .5% (1/28 * .15).

Indeed, assuming the above is true - Plan B stops ovulation and no pregnancy with sex after obvulation - then there is only .5% that the implantion effect will even have a chance to work.

Posted by: Dr. T on January 31, 2007 8:44 PM

The Uptodate.com information about "Plan B" quoted by Storkdoc is incorrect. A quick search of will find multiple studies of levonorgestrel's mode of action. The drug blocks the mid-cycle surge in luteinizing hormone and inhibits ovulation. It has no measurable effects on implantation. Some authors speculate that the drug produces an unfavorable endometrial environment or a slowing of spermatocytes, but there is no reliable evidence for those claims. Those claims make little sense, because other progesterones are used to improve the uterine environment in early pregnancies in women who tend to miscarry due to autoimmune conditions.

Posted by: Brandon Berg on January 31, 2007 9:43 PM

Okay, you're right. You didn't say what the quoted effectiveness rate was in the original post, so I was assuming it was lower than 7%. They really do mean that 89% of expected pregnancies are prevented.

So...I don't know. But I assume that the 89% number is based on ideal usage, which probably means no more than 12 hours after sex.

Posted by: Brandon Berg on January 31, 2007 9:44 PM

I meant that I was assuming it was lower than 11%. I don't know where that 7% came from.

Posted by: Elizabeth Bauer on February 1, 2007 4:06 AM

Interesting -- the usual "effectiveness rate" is the probability that an average woman using the contraceptive method for a year, will get pregnant during that time. So I don't know what the "Plan B" effectiveness rate means, since no one expects a woman to use this as the primary contraceptive method. At any rate, the studies I've seen have shown no effect on actual unplanned pregnancies, meaning that it's either not very effective or women take more chances when it's available and cancel things out.

There's a pro-life blog (www.lti-blog.blogspot.com) which actually has a lot of data on the topic, coming from the opinion that Plan B does not work after ovulation. (They say that one of the reasons why the "establishment" says it has post-ovulatory effects is that some studies consider any conception after day 14 to be post-ovulatory.)

About rape and pregnancy, the likelihood of pregnancy isn't the same as ordinary sex. Stress can delay ovulation, so a rape on O-4 would be less likely to result in pregnancy that "regular" sex, but a very stressful event just before ovulation can speed it up, so I'm not sure of the ultimate effect.

Posted by: sasha on February 1, 2007 12:07 PM

ironically, if you don't like plan B because it sometimes prevents implantation (and you consider preventing implantation immoral), making it available over the counter might lower its "immoral" usage. You're absolutely right that most accidents happen on weekends and nights between consensual partners, so no one's about to jump up and run to the emergency room. However, even if you wouldn't get up to go to the emergency room, you might go over to the medicine cabinet to take a pill you bought at the drug store last month "just in case."

Posted by: tripp on February 1, 2007 12:11 PM

The effectiveness rate is the percentage of women who do not become pregnant while using protection who would have gotten pregnant without protection. If 25% (say) of the women who have sex twice per week would become pregnant in the course of a year, then a birth control method with a 95% effectiveness would prevent 95% of pregnancies of those 25% (so 0.24% of the women would be pregnant). If it was just how many women get pregnant with a year of use, you are saying that pregnancy is independent of sexual activity, which it obviously is not.

Posted by: Mark on February 1, 2007 6:08 PM

One explanation could be that Plan B has a significant spermicidal or sperm-motility-impairing effect. Literature on the drug actually cites this as a mechanism of action, as noted in the first comment.

If you assume Plan B is a perfect, instantaneous spermicide, then obviously, women who take it *immediately* following unprotected sex will *never* get pregnant.

Perhaps Plan B's effectiveness figures are from studies where it was administered near-immediately? If so, the real-life failure rate would seem very much tied to how quickly the drug is taken. If taken, say, 24 hours after sex, perhaps the failure rate could be as high as the 25% you suggest.

Posted by: Njorl on February 2, 2007 10:45 AM

"An egg lives, on average, one day."

That is actually not so. It is what people are told for purposes of birth control calculations. It makes them estimate more conservatively.

The egg usually is susceptible for 6-12 hours. Those fertility percentages you quote for O-day probably place ovulation at the middle of the day. This means that half of the incidents would still be before ovulation.

Posted by: Njorl on February 2, 2007 10:53 AM

Hit the button too soon.

I meant to point out that eliminating 1/2 of your O-day pregnancies brings down the rate to 12.5%. That is still higher than the data would suggest. We's expect a 87.5% cap on effectiveness, and the claim is 89%, but we are assuming all averages as gospel, and that the susceptibility of the egg is a step function. Also, if the efficiency is indeed 87%, a trial finding an 89% efficiency would not be surprising.

Posted by: Christina on February 2, 2007 12:18 PM

Pardon me, but isn't it pretty obvious that Plan B must prevent implantation of a fertilized egg if all other hormonal birth contol drugs do as well? It strikes me as silly that the regular BC I take would have such a property, but post-coital BC would not.

I shocked my pro-life mom when I told her once, "I don't know how many abortions I've had," before explaining that I was referring to the abortificant qualities of the birth control I'm on, not a plethora of D and Cs.

Posted by: Njorl on February 2, 2007 12:54 PM

"Pardon me, but isn't it pretty obvious that Plan B must prevent implantation of a fertilized egg if all other hormonal birth contol drugs do as well? "

Not necessarily. If they do not directly cause the thinning of the endometrium, but rather, the lack of ovulation causes the thinnning of the endometrium, then there is no chance that a fertilized egg will encounter an endometrium thinned by hormonal birth control. If the pill fails to prevent ovulation, the endometrium might well have thickened. This has not been studied to my knowledge.

Posted by: Christina on February 2, 2007 4:17 PM

You seem to have proven my point.

A. All hormonal birth control suppresses ovulation.

B. Lack of ovulation causes thinning of endometrium.

C. Thin endometrium won't support fertilized egg.

D. Plan B fulfills all those.

Posted by: Njorl on February 2, 2007 4:56 PM

But if there is no ovulation, the thin endometrium does not prevent implantation.

A woman's endometrium thins and thickens each month if she is not on the pill. Thinning is not exclusively a response to taking the pill.

The point of contention is:
a)Does the endometrium thin because there is no ovulation?
b)Does the same stimulus that prevents ovulation cause the thinning of the endometrium?

If the answer to a) is yes, the pills will never prevent the implantation of a fertilized egg. If there is an egg, the endometrium will not be thinned.

If the answer to b) is yes, then it is possible that the hormones would successfully thin the endometrium, but fail to prevent ovulation. In this instance, a fertilized egg that would otherwise have emplanted would fail to do so.

As I stated, I do not believe this matter has been addressed by research.

Posted by: Greg D on February 7, 2007 9:12 PM

Does Plan B block ovulation for that month? Or does it just delay it until later in the month? If the later, how much later? 2 days? 5 days?

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