Richard Mann said, I'm not sure independence is the key here: of course the NYT assumes that you use the same contraception over 10 years, so thats not independent. Perhaps people would get better at using it over time, reducing the failure rate, but I think another explanation could be sub-populations that use the contraceptive well or not.
e.g. You get a better fit to the Korst et al data if you assume the are two sub-populations that use the contraceptive with different efficacies. Heres the results for using male condoms
with ~97% using the contraceptive well (3% failure rate per 3 months) and 3% using it very badly (80% failure per 3 months).
James Herbert-Read said, Hi Richard, Thanks for your comments. Your point that different individuals could use contraception more effectively than others is exactly what we mean by non-independence. Say 18 out of 100 women using male condoms have an unexpected pregnancy in year one. Do the remaining 82 women still have an 0.18 chance each of having an unexpected pregnancy in year two? No - because of exactly the reason you say. Different individuals are likely to be more or less effective at using particular forms of contraception - the years are not independent. And the data show this. It's nice to see your simple model supports this claim!
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