Probability of Ectopic Pregnancy: The Math Behind Atypical Implantation

Use math to calculate your risk of ectopic pregnancy, but if you have symptoms put down your calculator and call your doctor. Image by Decoded Pregnancy

Use math to calculate your risk of ectopic pregnancy, but if you have symptoms put down your calculator and call your doctor. Image by Decoded Pregnancy

When an egg is fertilized, if the embryo implants someplace other than the uterus, then the condition is an “ectopic pregnancy.” Most ectopic pregnancies are implanted in the fallopian tubes; these are “tubal pregnancies.” Other locations, such as the cervix, are also possible. What are the statistics associated with these atypical pregnancy outcomes, and what do the numbers mean?

Chances of Ectopic Pregnancy

The online American Family Physician (AFP) reports that “Ectopic pregnancy occurs at a rate of 19.7 cases per 1,000 pregnancies in North America.” That is close to 2%; but your own personal chances depend on several risk factors. Do you use an IUD? Have you had an ectopic pregnancy before? If you answered yes to either question, you are at an increased risk of atypical pregnancy implantation.

IUD and Ectopic Pregnancy

According to Medicine Net, you are very unlikely to become pregnant while using an IUD. However, if you do get pregnant while an IUD is in use, your chance of ectopic pregnancy is about 50% – that’s one out of every two women who get pregnant with an IUD in place.

This is an important example of “conditional probability.” The risk of pregnancy while using the IUD for birth control is very low; and the overall risk of ectopic pregnancy is also low. It’s only the risk of ectopic implantation in the unlikely event that you become pregnant while using an IUD that may reach the 50% mark. How can we take some comfort from these statistics?

Let’s do some math. The formula for conditional probability is “P(E|U) = P(E ∩ U) / P(U)”, where:


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  • P(something) means “the Probability that something occurs”. Let’s look at the three parts of this equation.
  • P(E|U) means “the Probability of Ectopic pregnancy given (that’s the ‘|’ symbol) pregnancy while Using an IUD“.
  • P(E ∩ U) means “the Probability of Ectopic pregnancy and also (that’s the ‘∩’ symbol, “intersection”) pregnancy while Using an IUD“.
  • P(U) means “the Probability of pregnancy while Using an IUD“.

Can we put some numbers into this equation? According to Planned Parenthood, fewer than one woman in one hundred will become pregnant in a year of using an IUD. Let’s assume that each of those hundred women averted becoming pregnant ten times in that year. Then P(U) = 1/(100 * 10) = 1/1000 = 0.001.

Earlier we noted that P(E|U) = 50% = 0.5. So “P(E|U) = P(E ∩ U) / P(U)”; and we have “0.5 = P(E ∩ U) / 0.001”.

Therefore P(E ∩ U) = 0.5 *  0.001 = 0.0005 = 0.05%. By this calculation, the probability of using an IUD and becoming pregnant, and also having an ectopic pregnancy at that time, is 0.05%.

Uterine Pregnancy after Ectopic Pregnancy

Having one ectopic pregnancy does increase the odds of having another.

Medicine Net states that one previous ectopic pregnancy indicates a 15% chance of a second; and a second ectopic pregnancy increases the risk of a third to 30%.

Let’s put that report from Medicine Net into a positive light. After one ectopic pregnancy, 85 out of 100 women will have a normal pregnancy. Even after two, 70 out of 100 women will have a normal pregnancy.

The National Center for Biotechnology Information (NCBI) is less hopeful. “One out of three women who have had one ectopic pregnancy are later able to have a baby.” It’s not clear whether their data is skewed by the women who decide to not attempt another pregnancy.

Calculating Your Chances of an Ectopic Pregnancy

Although the math clearly indicates that you’re more likely to experience an ectopic pregnancy if you have already had one, or if you get pregnant while using an IUD, any woman who gets pregnant may have an atypical pregnancy. In this case, math isn’t enough – if you have symptoms of an ectopic pregnancy, forget the numbers and call your doctor.

Disclaimer: The information contained in this article is for educational purposes only and should not be used for diagnosis or to guide treatment without the opinion of a health professional. Any reader concerned about her health should contact a doctor for advice.

References for Risks of Ectopic Pregnancy

Betrán, et al. “Maternal and perinatal health“. World Health Organization. Referenced Sept. 9, 2013.

Stöppler, Melissa Conrad, MD. “Ectopic pregnancy“. MedicineNet. Referenced Sept. 9, 2013.

Reviewed by Storck, Susan, MD. “Ectopic pregnancy“. National Center for Biotechnology Information of NIH. (2/8/2013). Referenced Sept. 9, 2013.

Tenore, Josie L., MD, SM. “Ectopic Pregnancy“. American Family Physician (Am Fam Physician. 2000 Feb 15;61(4):1080-1088). Referenced Sept. 9, 2013.

© Copyright 2013 Mike DeHaan: Math, All rights Reserved. Written For: Decoded Pregnancy
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