Bad Math about Infertility in the WSJ

From the Wall Street Journal:

Infertility, defined as the inability to conceive after one year of unprotected sex, affects one in six couples of childbearing age in the U.S. In 40% of cases, the problem is with the man; in 40% it’s with the woman, and in 20%, something is amiss with both, say Zev Rosenwaks and Marc Goldstein, fertility experts at New York Presbyterian/Weill Cornell Medical College and co-authors of the 2010 book, “A Baby at Last!”

Probability is often confusing, but after running the numbers, I’m fairly certain this math is wrong. If we assume that infertility affects one in six couples, then 5/6 pairings are fertile. Assuming that people choose who they try to have children with independent of fertility, at least initially, and assuming the infertility can be equally due to either the man or the woman, the results follow quite clearly: only about 5% of cases of infertility are due to both members of the couple being infertile, while the other 95% of the time it’s either due to the man or woman only.

Anyone know how the WSJ numbers were calculated?

How my calculations were done: if 5/6 pairings are fertile, this means that the square root of 5/6, or about 91%, of the population is fertile. Of those pairings then that result in infertility (that remaining 1/6), the ones that are due to both the man and woman being infertile are only (1-0.91)^2/(1/6), or about 5%.

3 Responses to “Bad Math about Infertility in the WSJ”

  1. Joe B. June 28, 2011 at 5:05 pm Permalink

    I think it is a selection bias problem.

    A couple is only going to seek help if they can’t conceive. If an infertility problem in one partner simply makes conception unlikely, but the couple conceives despite it, then they won’t go to a specialist in the first place.

    If both the man and the woman have fertility issues, they are much more likely to need and seek help, and so they would be overrepresented in the numbers.

  2. Michael Lugo June 28, 2011 at 5:27 pm Permalink

    So you’ve assumed that the events “problem is due to the man” and “problem is due to the woman” are independent. But they might not be – fertility problems are correlated with age, and ages of the members of a
    couple tend to be close to each other. The effect of this is in the right direction: the WSJ arrive suggests that 10 percent of men and 10 percent of women have “something wrong”, so with random mating one percent of all couples should have something wrong with both of them. But the actual number is much higher, one out of thirty couples.

  3. Samuel Arbesman June 28, 2011 at 9:07 pm Permalink

    @ Joe B. I was viewing infertility as a binary condition, but you’re right that infertility might be a matter of conception simply being unlikely.

    @ Michael Lugo Agreed. But without knowing more, I simply used an independence assumption.