Artificial contraceptives are not a hundred percent effective. Each method has its own failure rate. Given the such a failure rate and a starting population size, what is the effect on population growth?

For this quick study, I chose condoms because they're the most popular, because they're not permanent, and they don't have any side effects, barring latex allergies. I ran the numbers through a spreadsheet and came up with surprising results.

Condoms have a typical use failure rate of 14% and a perfect use failure rate of 2%. Perfect use means that they are used correctly each and every time a couple has sex; usually this means laboratory conditions. Typical use means that they are used, but sometimes incorrectly, as happens in real-world conditions.

Given a starting population of 100,000 fertile women, assuming they have sex once a month, assuming no gaps between delivery and subsequent pregnancy (women who have delivered babies are immediately reintroduced into the sexually active population, i.e., after nine months), assuming all pregnancies come to term, and taking a five year period, I came up with the following figures:

Month | Fertile women | Pregnancies |

1 | 100,000 | 14,000 |

2 | 86,000 | 12,040 |

3 | 73,960 | 10,354 |

4 | 63,606 | 8,905 |

5 | 54,701 | 7,658 |

6 | 47,043 | 6,586 |

7 | 40,457 | 5,664 |

8 | 34,793 | 4,871 |

9 | 29,922 | 4,189 |

10 | 39,733 | 5,563 |

11 | 46,210 | 6,469 |

12 | 50,095 | 7,013 |

13 | 51,987 | 7,278 |

14 | 52,367 | 7,331 |

15 | 51,621 | 7,227 |

16 | 50,058 | 7,008 |

17 | 47,921 | 6,709 |

18 | 45,401 | 6,356 |

19 | 44,608 | 6,245 |

20 | 44,832 | 6,276 |

21 | 45,569 | 6,380 |

22 | 46,467 | 6,505 |

23 | 47,293 | 6,621 |

24 | 47,899 | 6,706 |

25 | 48,201 | 6,748 |

26 | 48,162 | 6,743 |

27 | 47,776 | 6,689 |

28 | 47,332 | 6,626 |

29 | 46,982 | 6,577 |

30 | 46,784 | 6,550 |

31 | 46,740 | 6,544 |

32 | 46,817 | 6,554 |

33 | 46,969 | 6,576 |

34 | 47,141 | 6,600 |

35 | 47,284 | 6,620 |

36 | 47,353 | 6,629 |

37 | 47,350 | 6,629 |

38 | 47,299 | 6,622 |

39 | 47,227 | 6,612 |

40 | 47,158 | 6,602 |

41 | 47,111 | 6,595 |

42 | 47,091 | 6,593 |

43 | 47,098 | 6,594 |

44 | 47,124 | 6,597 |

45 | 47,156 | 6,602 |

46 | 47,183 | 6,606 |

47 | 47,199 | 6,608 |

48 | 47,203 | 6,608 |

49 | 47,197 | 6,608 |

50 | 47,185 | 6,606 |

51 | 47,172 | 6,604 |

52 | 47,161 | 6,603 |

53 | 47,156 | 6,602 |

54 | 47,156 | 6,602 |

55 | 47,160 | 6,602 |

56 | 47,165 | 6,603 |

57 | 47,171 | 6,604 |

58 | 47,174 | 6,604 |

59 | 47,176 | 6,605 |

60 | 47,175 | 6,605 |

This shows that the number of pregnancies per month eventually normalizes at 6,600 somewhere in the middle of the third year. This also shows that in any given population of typical condom users, more than half will eventually be in the pregnant state.

The sum total of children to be born -- given typical condom use -- in this sexually active population of 100,000 women over this five year period is over 400,000. This corresponds to about 4 children per family, or a 200% increase in population.

Total cost of birth control for 100,000 women over the five years,at P10 per condom: about P30-M.

Using the "perfect use" scenario of a 2% failure rate, all other assumptions held constant, the number of pregnancies per month normalizes at 1,700 a little after the end of the first year. This corresponds to 14,000 pregnant women at any given time. Over a five year period, the number of children to be born is 100,000, or a 30% increase in the population.

Total cost of birth control for 100,000 women over the five years, at P10 per condom: about P52-M.

Please review my computations to see if the figures are correct.

Hi Dom, just thought I'd share something amusing. There's some idiot on Wikipedia who's basically contributing garbage. Several people have tried to give him stern warnings and it's escalated quite a bit. Anyway, the part that I thought might amuse you is that said idiot started internet detectiving me and other people who were against him, and now he believes that I am you, posting a bunch of stuff about you and telling everyone that my blog is at villageidiotsavant.blogspot.com. Haha. :P

ReplyDeleteOh, dear. I feel like Jean Valjean, so wrongly accused. :-)

ReplyDeleteHi Dom,

ReplyDeleteIt seems the failure rates are per year (more precisely first year of use).

http://www.contraceptivetechnology.com/table.html

Bdul

Hi, Bdul,

ReplyDeleteThanks for the feedback.

The table you reference would be more useful if it showed the failure rate in succeeding years (in which case I could adjust my figures), but it does not. Besides, the table header says: "% of Women Experiencing an Unintended Pregnancy..." so I believe my approach still holds.

Your table yields an interesting column, though: the percentage who continue to use a particular method for one year. More than half of condom users discontinue its use.

What's even more interesting is that the Church-approved Family-Awareness methods are 25% effective under typical use, and almost as effective as male condoms in perfect use.

So, thank you for the table!

Hi Dom,

ReplyDeleteI don't want to argue but it seems the failure rate numbers you used IS == the percentage of unintended pregnancies during the first year of use. (Failure nga!)

It would be nice if you could refer us to data that shows that the number you used is indeed the failure rate per use/incident.

Bdul

Hi, Bdul,

ReplyDeleteI see your point now. Sorry for the misunderstanding earlier.

Using the percent failure per year statistic yields a much simpler equation as the number of unwanted pregnancies becomes 12,000-14,000 per year, depending on which number you choose to use. Over 5 years, this yields 72,000-84,000 unwanted pregnancies, which is consistent with a 2% probability of failure per use.

According to an article by the Bandolier (http://www.medicine.ox.ac.uk/bandolier/band64/b64-4.html), the average probability for condom failure is at 5%. Their comment:

It seems that the reported rate of condom failure through slippage and breakage is significant. While 95% effectiveness of a contraceptive method sounds good, actually it leaves a woman with a chance of pregnancy which may be considered unacceptable. At 95% it is 7:1 against in any one year, rising to 33:1 against at 99%. As any follower of the turf could tell us, outsiders at 33:1 win races every day.Thanks for pointing out the error in how I used the data.