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Contraceptive failure
This point came up in a conversation over on ![[livejournal.com profile]](https://www.dreamwidth.org/img/external/lj-userinfo.gif)
steerpikelet's LJ, and I thought it bore repeating here. Partly because it's important, but mostly because it allows me to talk about one of my favourite bits of maths, namely probability theory.
The failure rates of contraceptives are invariably quoted per year, rather than per use. So when people say that condoms have a breakage rate of 3%, this does not mean that for every 100 condoms you use, you can expect 3 to split: it means that for every 100 couples who have been using condoms for a year, 3 couples will have had at least one condom split on them. The difference is dramatic; let's see what would have happened if 3% of condoms split. In that case, every time you use a condom, it has a 97% chance of not splitting. So if you use, say, 100 condoms, the chance you won't experience any breaks at all is the product of the probabilities of each condom not breaking, i.e. 0.97 x 0.97 x ... x 0.97 = 0.97^100 = 0.047... . Which is to say that if 3% of condoms split, and you had sex 100 times in a year, you'd have only a 5% chance of not experiencing at least one broken "condom". And you'd have more than an 80% chance of experiencing two or more condom breakages in that year: the probability of exactly one condom breaking is 0.03 (for the broken condom) x 0.97^99 (for the 99 unbroken ones) x 100 (choices for which condom is the broken one) = 0.147, so the probability of two or more breaking is 1 - P(none break) - P(exactly one breaks) = 1 - 0.047 - 0.147 =~ 0.806. Such a "contraceptive" would be effectively useless.
"Blimey, guv'nor," I hear you say, "100 times a year? Are you avin' a laugh? It's all right for you layabout students with your peace marches and your LSD, but some of us have got to work for a livin'." Well, OK, suppose you have sex 20 times a year and use special fundie condoms that break in 3% of uses. Your chance of not experiencing any breaks would be 1 - 0.97^20 = 0.456..., which is to say that you've only got a bit better than a 45% chance of not seeing a broken "condom". Like I said, effectively useless.
Let's return to reality, and try to work out the actual per-use failure rate of real condoms. Suppose, again, that the couples in the studies had sex on average 100 times a year (adjust up or down as you prefer). Then the probability of a given condom not breaking is the 100th root of 0.97, which is 0.999695. So the chance of it breaking is actually 0.03%. If the couples had sex on average 200 times a year, we'd get 1 - (0.97^(1/200)) = 0.015%.
This is important to know about, because the less-scrupulous opponents of contraception will frequently quote per-year failure rates as if they were per-use rates (when they don't just lie outright, that is). And they're right: if condoms did fail on 3% of occasions, there wouldn't be much point in bothering with them. But they're actually much, much better than that. So if anyone ever says "condoms are useless, they fail 3% of the time", now you know what to say to them.
[Beware also the difference between breakage rate (interesting for STD protection) and conception rate (interesting for, well, contraception). Also, according to the site linked above, about half of breakages occur when you're putting the condom on, and are therefore harmless. Assuming you don't do something stupid like say "oh bugger, that was the last one, we'll just have to carry on without one." Mathematics is powerless against such stupidity.]
steerpikelet's LJ, and I thought it bore repeating here. Partly because it's important, but mostly because it allows me to talk about one of my favourite bits of maths, namely probability theory.The failure rates of contraceptives are invariably quoted per year, rather than per use. So when people say that condoms have a breakage rate of 3%, this does not mean that for every 100 condoms you use, you can expect 3 to split: it means that for every 100 couples who have been using condoms for a year, 3 couples will have had at least one condom split on them. The difference is dramatic; let's see what would have happened if 3% of condoms split. In that case, every time you use a condom, it has a 97% chance of not splitting. So if you use, say, 100 condoms, the chance you won't experience any breaks at all is the product of the probabilities of each condom not breaking, i.e. 0.97 x 0.97 x ... x 0.97 = 0.97^100 = 0.047... . Which is to say that if 3% of condoms split, and you had sex 100 times in a year, you'd have only a 5% chance of not experiencing at least one broken "condom". And you'd have more than an 80% chance of experiencing two or more condom breakages in that year: the probability of exactly one condom breaking is 0.03 (for the broken condom) x 0.97^99 (for the 99 unbroken ones) x 100 (choices for which condom is the broken one) = 0.147, so the probability of two or more breaking is 1 - P(none break) - P(exactly one breaks) = 1 - 0.047 - 0.147 =~ 0.806. Such a "contraceptive" would be effectively useless.
"Blimey, guv'nor," I hear you say, "100 times a year? Are you avin' a laugh? It's all right for you layabout students with your peace marches and your LSD, but some of us have got to work for a livin'." Well, OK, suppose you have sex 20 times a year and use special fundie condoms that break in 3% of uses. Your chance of not experiencing any breaks would be 1 - 0.97^20 = 0.456..., which is to say that you've only got a bit better than a 45% chance of not seeing a broken "condom". Like I said, effectively useless.
Let's return to reality, and try to work out the actual per-use failure rate of real condoms. Suppose, again, that the couples in the studies had sex on average 100 times a year (adjust up or down as you prefer). Then the probability of a given condom not breaking is the 100th root of 0.97, which is 0.999695. So the chance of it breaking is actually 0.03%. If the couples had sex on average 200 times a year, we'd get 1 - (0.97^(1/200)) = 0.015%.
This is important to know about, because the less-scrupulous opponents of contraception will frequently quote per-year failure rates as if they were per-use rates (when they don't just lie outright, that is). And they're right: if condoms did fail on 3% of occasions, there wouldn't be much point in bothering with them. But they're actually much, much better than that. So if anyone ever says "condoms are useless, they fail 3% of the time", now you know what to say to them.
[Beware also the difference between breakage rate (interesting for STD protection) and conception rate (interesting for, well, contraception). Also, according to the site linked above, about half of breakages occur when you're putting the condom on, and are therefore harmless. Assuming you don't do something stupid like say "oh bugger, that was the last one, we'll just have to carry on without one." Mathematics is powerless against such stupidity.]
Hmmmm
How would you measure condom split rate? You could ask people randomly on the street (but who actually keeps records?), but I can't imagine you getting 1000 couples together and running an experiment (I would love to see the ethics board approve that one). Or you could do a simulated machine pumping test. Also, sometimes condoms do split but nobody notices- which is the most dangerous part!
Presumably independence doesn't quite work in the way you describe. There are some people who are good with condoms. There are some that are bad. (There are some that remember to take their pills. Some that don't.) More 15 year olds will probably have problems with condoms than 25 year olds. So because of that, the condom failure rate over a year is almost certain for some, and almost zero for others, certainly if you discard pre-use splittage. Also, if one does split, you're more careful next time so...
Anyway, yes, I think the main point is that it's a silly thing to measure, as you can't get good data, and to look at it on a case by case basis is misleading, as people in general have nookie more than once a year, and that's what you're actually concerned with.
Ben xxx
Re: Hmmmm
Re: Hmmmm
Re: Hmmmm
With STIs as well as pregnancy, measuring the actual tranmission rates is more helpful than measuring condom breaks. This has been done: HIV, HPV. It would seem that condoms are actually more effective at preventing HIV transmission than they are at preventing pregnancy. Condom break figures are just estimates based on one thing or another.
Also, on lying outright (warning: may inspire more tears).
Re: Hmmmm
TBH, I've always thought of condoms as an STD prevention measure rather than a pregnancy-prevention measure: I feel rather happier if there's something else providing a backup on the latter.
Re: Hmmmm
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I don't know why but that strikes me as hilarious...
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Similarly while The Pill is reported to be 98% effective in reality the end-users aren't anywhere near strict enough in administering it to achieve this figure. I can't remember what the actual use value is but it was somewhere around 85%.
The most effective contraceptive is the Mirena coil at 99.5%, a form of IUD, as you can do very little to interfere with its functioning short of removing it. The reported failures were also in very specific circumstances, one of which I believe was a woman who had 2 wombs and it hadn't been diagnosed before insertion. Unfortunately it doesnt offer anything in the way of protection against STDs and pelvic infections which still remains the only benefit of using condoms. It has been suggested that its use should be promoted more than The Pill due to its effectiveness and low side effect profile, but funnily enough guess which is cheaper to give out on a large scale?
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At this point in the conversation I usually plug the injection of depo-provera, which has nasty side effects for some but is perfectly safe and healthy for many. And it stops your periods! I also think it's a similar price to the pill. However it isn't a good idea to promote it to teens because it interferes with laying down bone density (which is more or less done by the time you're 22ish).
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Sure, the majority of women get on fine with Implanon. I didn't see scars from any other contraception method though.
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When compared to Depoprovera the Mirena coil beats it on effectiveness and side effect profile in independent studies. The Mirena coil can however be painful to insert in women who have never had a child and that is what puts many women off having it done. Once you've had a kid your cervix is a bit wider and more easily accepts the Mirena going through.
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And can I thank you for injecting some sanity into that thread? I would normally, but I didn't have the stamina to get involved in it around then.
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This last bit however refers to the rather frightening 'typical use' failure rate of 15% (15 pregnancies per year per 100 couples), mostly result from people only putting condoms on halfway through sex or not using them every time. The 2-3% failure rate you quoted is what happens when people are doing everything right, sadly it's not really representative of how people use them in the real world.
So Now You Know.
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When an argument degenerates that far, as they often seem to on Reddit, I find it best to swallow my pride and walk away - not always easy to do, mind. You're both too entrenched for either of you to win, and it's not worth the hassle.
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