Wednesday, February 18, 2015

Wednesday Omphaloskepsis: Will combining two forms of birth control increase overall birth control effectiveness?

Screen capture taken from, which shows the first two of three rows of the interactive graphic from the NYTimes article "How Likely Is It That Birth Control Could Let You Down?"

A friend of mine posted a link to this article on the effectiveness rates of various forms of birth control, from highly ineffective methods, such as fertility awareness based methods (i.e., the rhythm method) and withdrawal (i.e., “pulling out”) shown above, to highly effective methods, such as female sterilization (i.e., a hysterectomy) and male sterilization (i.e., vasectomy), not seen in the graph above. All of these statistics were presented as increasing rates of getting pregnant over a 10 year period, so the reader could directly compare the cumulative rates of pregnancy over time. An interesting thing is that some of the graphs show the differences between the "optimal" and "typical" rates of getting pregnant. Some of the methods, such as "spermicides" and "sponge (after giving birth)," show optimum curves that are not that better than typical curves, while other methods, such as "Pill, Evra patch, NuvaRing" and "Depo-Provera" show major differences between the optimum and typical curves. This indicates that some methods are minimally impacted by "human error" (e.g., improper use of spermicide or improper placement of the sponge), while others heavily impacted by such errors (e.g., using the Pill irregularly).

(A note to my fellow pedants: Here, I will be only considering the final (i.e., 10 year) rate, and so instead of referring to a chance of “X in 100 over 10 years,” I will refer only to a chance of “0.0X.” Yes, I know that there is a difference between “X in 100 over 10 years” vs. “0.0X,” but I don’t want to write “X in 100 over 10 years” over and over in this entry, and I assume that the reader doesn’t want to read “X in 100 over 10 years” over and over in this entry, so let’s just recognize that when I write “0.0X” in this entry, I implicitly mean “X in 100 over 10 years.”)

Interestingly, the most effective method on their chart wasn’t sterilization (which had a rate of 0.05 for women, and a rate of 0.02 for men), but actually a hormonal implant (which has a rate of 0.01). This raised a question in my mind: would it be possible to combine birth control methods in order to diminish the overall chance of getting pregnant? It is quite alluring and – on the surface – seems to make perfect sense.

Well, the more I thought about it, the more the answer was: it depends.

Although it's been several years since I studied reproductive physiology, I suppose that there would be some increased effectiveness if a couple combined two or more methods. Statistics indicates that, if the two methods were truly independent, then you multiply the two rates together (much like the chance of rolling two sixes with two dice is 1/6*1/6=1/36 and not 1/6+1/6=1/3). Therefore, if the woman uses one method and the male uses another method, then we can assume that the two methods are independent of each other, thus allowing us to multiply the two effectiveness rates together. Therefore, if a woman is using only spermicide (0.94) and if her male partner uses only the withdrawal method (0.92), then the possibility of pregnancy IS lower than the use of one of those methods alone (0.94*0.92=0.88); slightly worse than male condom alone (0.86).

However, if the two methods are not independent (like withdrawal and male condom), then one cannot simply multiply the two rates; an additional correctional factor must be multiplied to account for the codependence inherent in the two methods. Two additional hitches: (1) we don’t know what that correctional factor is, and (2) it will likely be different for each combination of codependent methods. However, even though we don't know what any of these correctional factors are, we could make the assumption that no two birth control methods will be synergistic (i.e., no correctional factor would be >1), which means that multiplying the two rates together produces an indication of the best potential effectiveness for typical use. Therefore, if the male partner uses both withdrawal and a male condom, the best potential effectiveness for typical use is (0.92*0.86=) 0.79.

However, the major take-away (at least for me) is the worlds of difference seen in the comparison between the effective pregnancy rates shown in the first two rows when compared with the third row. It’s like night and day. If one of the partners is using a method from the third row, the improvements provided from the use of any of the methods shown in the first two rows is effectively negligible. For example, if we look at combining male condom use (0.86) with female sterilization (0.05), and assume that these two method were totally independent (which is – in my opinion – a safe assumption in this case), then the resulting chance of pregnancy over 10 years of using this combination of birth control measures is (0.86*0.05=) 0.04; a change of 0.01.

The only way to see a significant improvement within this bottom row is if they were combined with another method from the third row. In the case of combining male sterilization (0.02) and female sterilization (0.05), the resulting chance of pregnancy over 10 years would be 0.001 or a 50-fold increase over female sterilization alone.

Of course, the statistics presented in the article are rates garnered at a population level. Like so many things in life, when one looks at individual cases, the picture can appear quite different. After all, in order to get that number of “5 in 100 over 10 years” for female sterilization, there had to be some women who got sterilized and also got pregnant. Part of this is due to potential errors in the medical procedure or with the medical device. Part of this is due to individual physiology. But while one can’t really change the impacts of either of these two factors, there is one other factor that alters an individual’s chance of getting pregnant: their copulation rate.

If a person's copulation rate is really high, it will have a major effect on the possibility of that particular individual getting pregnant, even if the effectiveness of their birth control method doesn't change. Why? Well, let's assume we are looking at a woman who has been sterilized (0.05). If this woman has sex only one time without any additional birth control, that chance 0.05. If that woman has sex once every single day for 10 years, then each time she has sex, there is an additive 5-in-100-over-10-years' chance that she will get pregnant. (Why is it additive and not multiplicative here? It’s for the same reason that there is a 1/6+1/6=1/3 chance of rolling at least one 6 when you roll two dice.) Of course, the chance of a resulting pregnancy (in the case of female sterilization - as with all of the cases on the bottom row) remains vanishingly small, due to the effectiveness of the form of birth control, but - given enough sexual encounters - the rate of 5-in-100-over-10-years does imply that a pregnancy will occur. And indeed, it does happen:
[A] mother from Menden, North Rhine-Westphalia, decided to have the sterilization after the birth of her second child in 2006. ... But in 2008 she became pregnant again and gave birth in 2009.
The truth is that having a copulation rate of zero (i.e., never having sex at all) is the best preventative to getting pregnant. (Keep in mind that this also means that you don't try to get in vitro fertilization, either.) Indeed, this course of "abstinence only" pregnancy control is often the method preferred by religious organizations (at least in the United Stated). Of course, what with humans being the biological animals that we are, copulation (and resulting pregnancy) tends to happen, even to men and women sworn to clerical celibacy.

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