My two cents Catherine on some great points your raised:

I don't know the evidence-base underlying the probabilities Juan Gérvas. But, in theory, the math can be simple.

Concerns reported in your first para -- i.e. selection bias -- can be taken care of in the design (e.g. RCTs) or analysis (e.g. appropriate probability weightings)

Concerns raised in your second para are about generalizability and absolute risk reductions -- might want to look at the control event rates in the evidence before suspecting they are incorrect. 

What is however important to know is the nature of the comparative effectiveness of the various interventions that is reported -- direct randomized comparison, direct nonrandomized comparison or indirect comparison.  

On Tue, Nov 3, 2015 at 6:57 AM, Aicken, Catherine <[log in to unmask]> wrote:

Interesting, and it seems obvious that using two methods would increase effectiveness.

 

However I’d be surprised if the maths worked out exactly as you explain, in practice. Contraceptive behaviour is more complicated than that! It’s possible that users of multiple methods are more motivated *not* to become pregnant (hence better pill-takers and better condom-users) than users of just one method. Or the effect could be the reverse: knowing that they are protected by taking the pill, a couple may use condoms less consistently (e.g. putting it on after some penetrative sex); a woman taking the pill may be less motivated to take her contraceptive pill consistently because she always uses condoms. To make matters even more complicated, women don’t always take contraceptive pills just for their contraceptive effect (e.g. for oligomenorrhoea, and some pills, for acne) nor condoms (to prevent STIs).

 

Also (and please correct me if I’m wrong) even if 100 women were to have heterosexual sex for a year, not all of them would become pregnant. So the apparent ‘effectiveness’ of any method is affected by infertility and subfertility in women and their male partner/s (which may be undiagnosed). So even assuming perfect use, with unknown (and unquantified?) effects of infertility and subfertility, perfect use of 2 methods would further reduce the risk of pregnancy, but the maths can’t be quite that simple.

 

Best wishes

Catherine

 

From: Evidence based health (EBH) [mailto:[log in to unmask]] On Behalf Of Juan Gérvas
Sent: 03 November 2015 10:26
To: [log in to unmask]
Subject: EBM and maths: one/two contraceptive methods

 

¿Embarazo indeseado? Evítelo con los mejores métodos: DIU e implantes hormonales.
Unwanted pregnancies? Avoid it with reversible contraception: IUDs and hormonal implants.
http://well.blogs.nytimes.com/2015/10/26/iuds-and-hormonal-implants-remain-underused-contraceptives/?ref=health&_r=1 …
Embarazos por 100 mujeres, anual. Espermicida 28%, condón varón 18%, píldora 9%, inyección 6%, DIU 0,8%, implante 0,05%.
Pregnacies per 100 women in a year. Spermicide 28%, male condom 18%, pill 9%, injection 6%, IUD 0.8%, implant 0.05%
http://www.acog.org/Resources-And-Publications/Committee-Opinions/Committee-on-Gynecologic-Practice/Increasing-Access-to-Contraceptive-Implants-and-Intrauterine-Devices-to-Reduce-Unintended-Pregnancy

-sometimes, patients/friends/relatives ask you about the combined use of the pill and the male condom:

Thanks to the laws of probability, using two contraceptive methods at the same time boosts their effectiveness. Remember, if two events A and B are independent, the probability of both occurring is P(A and B) = P(A) x P(B). If you use both a condom and the pill they work independently, because if one method fails it has no impact on the other. That means the failure rate of the combined condom and pill method is the product of their separate failure rates. For perfect use of the male condom and pill, that's 0.02 x 0.003 = 0.00006, or 0.006%. In other words, the combined method is over 99.99% effective when used perfectly.

The figure for “typical” use of the combined method is also much higher than using either method on its own. With failure rates of 15% for the male condom and 8% for the pill it pays to use them together, since 0.15 x 0.08 = 0.012, or 1.2%. With this rating of 98.8% effectiveness, using the combined method is clearly much safer. No one expects you to get out a calculator before you have sex, but you should always understand the risks involved and choose the right contraceptive methods for you.

http://www.mathscareers.org.uk/article/statistically-safe-sex/

-un saludo juan gérvas