Chances of getting pregnant when using 2-3 contraceptives together. Just curious

[ashleyrc]

Ok, so I started Sprintec birth control pills a week ago, and the chances of getting pregnant while on it alone is 1% per year of use (a little less actually, but for the sake of simplicity, we’ll stick with 1%).
I also have condoms, the Today sponge, and can also use the withdrawal method.
According to the sprintec instructions, the chances of getting pregnant in a year for each of the other methods are:
Condoms alone = 14%
Today sponge= 30% (approximately, may be from 10-40%)
Withdrawal method= 20%
So I was just curious what my chances of getting pregnant are if I use:
-Sprintec and the Withdrawal method,
-Sprintec and the Today sponge,
-Sprintec and condoms,
-Sprintec, the Today sponge, and condoms,
-Sprintec, the Today sponge, and the Withdrawal method,
-Sprintec, the Today sponge, condoms, and the Withdrawal method,

So how should I go about figuring out these possibilities, and yes, I know they are only theoretical values, but I would like to know how all of these compare to one another. Thanks!

 

[HallsofIvy]

In order to do any kind of calculation, you would have to assume that those are independent.

Given that, the best way would be to calculate the probability that the methods used together, all failed, which is just the product of the probabilities that anyone alone will fail.
So "condoms, sponge, and withdrawal method together" would have a failure rate of (.14)(.30)(.20)= .0084= 0.84%.

 

[ashleyrc]

So I went through the calculations, and my chances of getting pregnant are the following if I use:
-Sprintec and the Withdrawal method, = .2% (So 1 out of every 500 women would get pregnant…)
-Sprintec and the Today sponge, = .3% (1/333 women get preggo…)
-Sprintec and condoms, = .14% (1/715 women get preggo…)
-Sprintec, the Today sponge, and condoms, = .042% (1/2,381 women get preggo…)
-Sprintec, the Today sponge, and the Withdrawal method, = .06% (1/1667 women get preggo…)
-Sprintec, the Today sponge, condoms, and the Withdrawal method, = .0084% (1/11,904 women get preggo…)
If I go off of birth control,
-Today sponge, and condoms, = 4.2% (1/23 women get preggo…)
-Today sponge, and the Withdrawal method, = 6.0% (1/16 women get preggo…)
-Today sponge, condoms, and the Withdrawal method, = .84% (1/119 women get preggo…)
So there is definitely a big difference between using birth control and not using it. Even if I used all other forms of contraceptives at my disposal together (Today sponge, condoms, and the Withdrawal method) they would be about as safe as taking the birth control alone... though now that I think of it, who uses condoms and the withdrawal method at the same time?
At least I now have a damn good reason to make sure my birth control is my first priority :p
To be honest, I thought that using condoms and the sponge would have been more effective than a 4.2% failure rate!
Thank you for the help, this was pretty interesting for me to find out!

 

[HallsofIvy]

You might add to this that the best way to avoid pregancy is to be celibate!

 

[lurflurf]

I believe for statistical purposes the failure rate of celibacy (dispite obvious drawbacks) when practiced without error is taken to be about 0.0001%, I can't find a reference though. The only problem with the above calculations other than the accuracy of the individual failure rates is a failure to account for the failure rate of the null method. That is failure rates for all methods include the failure rate when using no method, which is normally taken to be 85-90%. When combining methods no method should only be included one. Thus -Sprintec and condoms, = .14% (1/715 women get preggo…) should be 1*14/(85 or 90)=.16% (1/607 or 642 women get preggo…) instead of 1*14/100=.14%.
Comparison of birth control_methods from wikipedia

 

[ashleyrc]

Wait, how is it possible to have a failure rate for celibacy? I believe only one woman did that, and she is heralded for it! :)

I think I understand your logic for the Null Mehod, since it is incorporated in each of the percentages I originally gave in my problem. So what you are saying is that I should not count the Null method each time for each percent, since that chance only occurs once even if a combination of methods are used. I know that I was only doing this for fun and perhaps a little peace of mind, but I think I actually started thinking a bit deeper about this problem! Thanks for pointing that out, what a great observation!

So when I calculate one with three methods, how should it end up?

-Sprintec, the Today sponge, and the Withdrawal method, = .06% (1/1667 women get preggo…) should be? I’m not sure how to figure this out…

 

[flatmaster]

The only way to know these numbers are correct is to test them emperically.

 

[lurflurf]

Wait, how is it possible to have a failure rate for celibacy?
...So when I calculate one with three methods, how should it end up?

-Sprintec, the Today sponge, and the Withdrawal method, = .06% (1/1667 women get preggo…) should be? I’m not sure how to figure this out…

It is always good to allow a margin for error in statistical work.
So let's settle on a failure rate for the method no method of 85%
Then when computing the failure rate of a number of methods we multiply the null method by each method divided by the null.

-Sprintec, the Today sponge, and the Withdrawal method,
=85%*(1/85)(20/85)(30/85)= .08% (1/1204 women get preggo…)

 

[Borek]

Wait, how is it possible to have a failure rate for celibacy? I believe only one woman did that, and she is heralded for it! :)

Judging from how often woman claim they have no idea how they got pregnant when their husbands were off for prolonged periods of time, 0.0001% is definitely underrated.