by Olivia DeLane

Dear Olivia,

I am an Arapawa Island goat and my doe and I are having trouble conceiving. We have tried on our own for 3 years and are now considering a visit to a place like the Swiss Village Foundation to be able to have kids. We are wondering if fertility clinics are actually able to help us or if we should just adopt instead. What do you think?

Sincerely,
Disappointed
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Dear Ted,

This is a very serious issue you’re talking about, so let’s run some numbers to see how concerned you should be.

Let’s say a healthy couple trying to have a kid has a 10% chance per month of conceiving. (I am making this number up, but it is about the rate for a mid-30s human female.) So, at the end of one month, 10% of couples will have conceived and 90% will keep trying. At the end of two months, 19% of all healthy couples will be pregnant and at the end of three months, 27% will be pregnant, and so on.

Let’s also assume that 2% of all couples have a fertility problem – without medical help, they will not conceive a child. (Again, this number is for demonstration purposes only.)

Your question is effectively: If a couple tries unsuccessfully for 3 years (36 months) before going to a fertility clinic, what is the chance that they genuinely have a fertility problem?

Some arithmetic should help here: If my numbers are reasonable, for every 10,000 couples, 200 will have a genuine fertility problem and 9800 will not.

Of those 9800 who do not have a problem, 980 will get pregnant the first month (since 10% will get pregnant each month). Of the 8820 who remain, 882 will get pregnant the second month, and so on. Over the course of 36 months, 99.747% of the healthy couples should have had one pregnancy. But that means that 0.253% of healthy couples will not have conceived simply by flipping ‘tails’ 36 times in a row by chance.

That means 221 healthy couples will walk in the door of the clinic along with the 200 who genuinely have a problem. I have made a diagram that helps explain the math.

So, that means that (for the numbers I have picked), more than half of the couples seeking treatment will not need medical assistance at all. If only 1% of couples have a genuine fertility problem, then only about 1/3rd of couples who go to the clinic will actually need help. The rest just need more time.

One would hope that professional fertility clinics would understand that many of the people coming in their doors might not have a problem at all. But this might not be the case. A very similar question was asked to oncologists (cancer doctors): If 2% of people have a certain kind of cancer and a cancer test is right 90% of the time, if your test says you have cancer, what is the chance you actually do have cancer?
75% of medical doctors did not answer this question correctly.

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Olivia DeLane has a Master’s certificate in normative ethology from Gallus College, a non-accredited online institution. Her writings are for entertainment purposes only and should not be misconstrued as being for any other use. Her at-home exercise video ‘Strut Those Drumsticks!’ will soon be available at Amazon.com.

1. Normand Balch

Fertility clinics are really very useful these days as more and more older women wants to give birth. Older women have a harder time conceiving without medical intervention. *;`:”

2. Josh

Dear Olivia,
Looks like the probability you ACTUALLY have cancer is around 17%, or 0.02/(0.02*.9+0.98*.1).

My logic: the numerator is the probability of having this cancer. The denominator is the probability of getting a positive on the test, which could happen one of two ways: a true positive (0.02*0.9) or a false positive (0.98*0.1). Am I correct?

• Josh,

I think you are basically right. Here is my logic:

10,000 people take the test, of whom 200 actually have cancer.

Of these 200 unfortunate people, 180 test positive.

Of the 9800 who do not have cancer, 980 test (falsely) positive.

Therefore, 180 + 980 = 1160 test positive.

Of those who test positive, 180 / 1160 = 15.5% actually have cancer.

I could be wrong. But either way, if your commonly offered test for a rare form of cancer comes back positive, it seems to me that the odds are still likely in your favor that it is the test that is in trouble, not you.

3. Delighted

Just noticed (finally) that you answered my question…

So if I went into business as a fertility clinic and claimed a 50% success rate, I could really mint some money – for nothing. Good to know…

I am now no longer “disappointed”, but rather, “delighted” – Thanks!

4. Some additional statistics here that may be of interest on this topic Olivia:
http://www.nytimes.com/2015/12/23/health/with-in-vitro-fertilization-persistence-pays-off-study-suggests.html?_r=0

– DelighTED