There is a New York Times article showing cumulative contraceptive failure rates over time, i.e., if you use a certain contraceptive method for five years, how likely is it that you would have become pregnant in that time? Here is how the values were calculated: “The probability that a woman doesn’t get pregnant at all over a given period of time is equal to the success rate of her contraceptive method, raised to the power of the number of years she uses that method.” By “success rate,” they mean percentage of women who avoid pregnancy in one year. However, it is important to remember that these rates are in fact only for the first year of use. The question becomes whether these rates can reasonably be applied to later years.
I have found a possible answer in a 2004 article by James Trussell, ‘Contraceptive failure in the United States’:
We confine attention to the first-year probabilities of pregnancy solely because probabilities for longer durations are generally not available. There are three main points to remember about the effectiveness of contraceptive methods over time. First, the risk of pregnancy during either perfect or typical use of a method should remain constant over time for an individual woman with a specific partner (providing that her underlying fecundity and frequency of intercourse do not change). Second, in contrast, the risk of pregnancy during typical use of a method will decline over time for a group of users, primarily because those users prone to fail do so early, leaving a pool of more diligent contraceptive users or those who are relatively infertile or who have lower coital frequency. This decline will be far less pronounced among users of those methods with little or no scope for imperfect use. Risk of pregnancy during perfect use for a group of users should decline as well, but this decline will not be as pronounced as that during typical use, because only the relatively more fecund and those with higher coital frequency are selected out early. For these reasons, the probability of becoming pregnant during the first year of use of a contraceptive method will be higher than the probability of becoming pregnant during the second year of use. Third, probabilities of pregnancy cumulate over time.
As the final sentence indicates, what the New York Times authors have done is mathematically correct. However, they should not have been so quick to take the first-year “success rate” and assume it is the same in the following years. The first-year rate includes women who, for one reason or another, were unsuited to use that kind of contraception (e.g., due to difficulty in regimen adherence, physiological reasons, etc.) and became pregnant and stopped using it. It follows that the second-year “success rate” will be greater, since it no longer includes these users. However, one might predict the reverse: perhaps the second-year “success rate” will actually be lower, since users who did not get pregnant in the first year might become more complacent about adherence.
Quickly searching, I was able to locate one study that measured non-injection hormonal contraceptive failure rate over three years (this category includes not just oral contraceptives, but also patches and rings). The cumulative failure rate was 4.8%, 7.8%, and 9.4%, after one, two, and three years, respectively. As one can see, the failure rates after two and three years were lower than what would be predicted based solely off the first year number (predicted: year 2, 9.3%; year 3, 13.7%). Although a look at the numbers for injectable (DMPA) contraception might give us caution: 0.1% after year 1, 0.7% after year 2, 0.7% after year 3. The number after the second year is in fact higher than the predicted value based on the failure rate after one year (predicted: 0.2%), but then after that, there were no additional contraceptive failures. I am not sure what the answer for this is, but it should give us pause about relying too much on this study. While I can admit that the study suggests that it’s common for contraceptive success rates to rise after one year of use, I cannot say this is certain. Finally, the cumulative failure rates for IUDs and implants over three years were: 0.3%, 0.6%, 0.9%. This matches up with the predicated values based off the first year (predicted: after year 2, 0.5991%; after year 3, 0.897%), probably because user adherence is hardly an issue here.
Cumulative contraception failure is an important area of research that seems neglected, given that “[t]he typical woman who uses reversible methods of contraception continuously from age 15 to age 45 would experience 1.8 contraceptive failures. If we consider both reversible methods and sterilization, the typical woman would experience only 1.3 contraceptive failures from age 15 to 45” (from the Trussell article). While it may be mentioned that there are much more effective methods (e.g., IUDs or implants) than what is commonly used, I find it very unfortunate that the one method with a perfect success rate often gets ignored or dismissed as impractical, especially given its role in developing certain virtues.