(Submitted by blog reader David Read)

About 9 months ago, my wife learned that she might need a kidney transplant. For most of her life she has endured reduced kidney function due to several infections suffered while she was a teenager. But in September, she learned that her kidney function (GFR) had dropped to 13 (out of 100). Usually, when someone’s GFR falls below 15, they become a transplant candidate. With this precipitous drop in function (her previous GFR had been in the 30’s), we thought we had only a few weeks before she would need to start dialysis.

We attended several day-long classes in which we learned about  the different types of dialysis and to get an understanding of the transplant process (getting on “the list”, looking for a living donor, awaiting a cadaver donor, etc). We learned that if we waited for a cadaver donor, it could be up to 7 years before she would make it to the top of the list and then would have to wait for a matched donor kidney to become available. Obviously, the solution would be to find a live (and willing) donor. In the class we learned that the best chance of finding a match would be with a sibling. Luckily, my wife has 2 – a brother and a sister.

The process of “matching” is fairly straightforward. First, the donor has to be the same blood type, in this case O. The Rh factor is not important. After the blood type is matched, samples of the donor’s and recipient’s blood are drawn and compared. There are 6 antigens that can determine whether a donated kidney will be accepted or not. A perfect match is when all 6 are compatible.

My wife’s siblings agreed to be tested but neither of them even knew their blood type. Surprisingly, neither did their doctors! My wife and I know our types because we have given blood and the Red Cross lets you know your type. We suggested that her sibs donate a pint of blood to 1) do a good deed and 2) learn their blood type for free. After much hand wringing and delays, we learned that both her sibs had blood type A – neither were a donor candidate.

In the meantime, our daughter determined that she was type O and she and my wife went in together to test for a match. During the matching process, only the donor is given the results. This is to protect the donor from any extra pressure from family members or the recipient. For instance, if after finding that they are a match a donor has a change of heart (no pun intended), they are the only ones who know that they matched in the first place. However, when our daughter received the news that she matched, she was ecstatic and called her mom right away.  She really wanted to be the one who helped her mom through this crisis.  However, there was one more hurtle to be cleared – the ultrasound.

After a match is found, the donor must undergo an ultrasound to determine the health, location and number of kidneys (yes, some people are born with one kidney, and some even with three!). Our daughter’s ultrasound results were devastating – for her. She had kidney stones and therefore could not be a donor. On the positive side, she learned of this issue long before it became a problem and has taken care of it. But, that didn’t help my wife.

However, our son-in-law decided that if his wife couldn’t donate, perhaps he could. After determining that he had the correct blood type , he went in for the compatibility tests. This was quite a decision for him because he has an aversion to seeing his own blood and these compatibility tests require that 6 – 8 vials of blood be drawn. But when the results came back – he was a match also! And the ultrasound found no irregularities. So the question is, what are the odds of BOTH a child AND their spouse being a matched kidney donor for a parent?

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 218.  Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own sarcastic and hilarious commentary. Also, visit Barbara’s blog.

First, there is a sticky problem of the probability that any donor will be healthy enough. I could not find a criterion or probability value for that, so I will have to leave it out of any calculation.

Second, the author discussed HLA matching as if it was an all-or-none deal according to several sources, including the LivingKidney Donors Network, it is no longer standard practice to use HLA matching as a factor to determine whether a donor is compatible. As it turns out, an exact match is best, but not necessary. Furthermore, there is little statistical difference in the survival rates among recipients with 5/6 and 0/6 matches, thanks to newer, better anti-rejection drugs (yeah science!).

For that reason, unless there is a perfect match, donor compatibility relies on the result of a number of tests of complex cell interactions to determine whether the recipient’s body will reject the organ.This is important, because the rest of what I will say here makes the prospect of finding a kidney donor look like finding Waldo in Santa’s workshop.

All of that said, the author suggested that both the daughter and son-in-law were perfect HLA matches, so we have enough information to at least estimate the odds, assuming that everyone involved is healthy.

The six antigens which have been identified as important for transplant are inherited from our parents, half from each. This makes a sibling the best possible chance for a perfect match, not a child, but a child is better than a stranger.

A perfect match with an unrelated donor carries odds of one in 100,000, or a probability of .00001. Since the daughter received half of hers from her mother, she is at least a 50% match, doubling the probability that she is a perfect match to .00002.So, the probability that both the daughter AND her husband would be “perfect matches” in terms of HLA compatibility is .00001 times .00002, or .00000000002 (5 million to one).