Another great walk this morning with my pal Zeke, who is taking all this far better than I am. As people often do when confronted with bad news, I turned my mind to scripture as we walked, to see if there was some solace or, barring that, wisdom to be found.
And it can work if you pick the right scripture. The one I picked this morning was paleontologist Stephen Jay Gould’s essay The Median Isn’t the Message. Faced in 1982 with a diagnosis of mesothelioma, a cancer associated with exposure to asbestos, Gould went to the medical library to read up on his condition. He read that his cancer was incurable, with a median mortality of eight months after diagnosis. After a bit of thought, Gould was elated at the good news in those statistics.
Degenerative myelopathy, the incurable neuromuscular disease that has been suggested as a likely cause of the growing weakness in Zeke’s hindquarters, is a devastating and incurable illness that is, apparently, uniformly terminal. And incurable. Did I mention incurable?
The typical progression of the disease without treatment is diagnosis, then paralysis of the rear legs within three to six months, then at some point shortly thereafter a similar degeneration of the front leg muscles, with subsequent deterioration of the brain culminating in death. Treatment can significantlysomewhat extend the dog’s lifespan.
Once I’d thought about this for a while, I felt a slow relief spread through me. Joy followed.
Averages are tricky things, as Gould pointed out in the essay linked above. This is especially so when you’re reading medical information that hasn’t been (ahem) vetted through peer review. The “average dog” with DM lives for a year after the onset of muscle weakness, but what kind of average are we talking about here? More than likely, we’re talking a median, in which half the dogs studied died before a year had passed, and half after.
It’s possible, given the rarity of the disease and the informality of the sources, that we’re talking about a “mode” average. A mode is different from a median. Let’s say you, Bill Gates, and three Somali gradeschoolers are put in a room and asked to show how much cash you have in your pockets. Two of the kids have nothing, one has one cent. You have forty bucks, and Gates, embarrassed, confesses that he left the house in a hurry and only has what’s left over from his dinner tab last night: 800 dollars. You have a cumulative $840.02. Most people would compute the room’s average cash on hand at $168.00, by taking the total and dividing by the five people present. That’s an arithmetic mean. Arithmetic means are useful for figuring out how much each person on a road trip should put in for gasoline, and for not much else. They are seldom used in science.
The median is the amount greater than or equal to half the values in the range, so the median cash on hand in the room would be one cent. The mode is the most frequent value: the mode in the room is zero.
Whether it’s a median or (far less likely) a mode, that devastatingly swift average progression of the disease is good news for Zeke. Medians are generally used because natural phenomena, when reduced to numbers, display a wide range of variation. That “average dog with DM” in fact represents a lot of dogs, some living longer than two years, some dying tragically quickly. The short end of the scale has an obvious limit, at zero: no dog will die of the disease before it starts to exhibit symptoms. On the other hand, it is conceivable that some dog with DM might live a rather long time with the disease.
Thus the mortality graph of DM is what is known in the stats biz as a skewed distribution, with a wall at the zero end, a bell curve or plateau between six and eighteen months, and a long tail that stretches out conceivably to the limit of normal canine life expectancy. Half the dogs with DM will die before the median. But half will live past it.
Zeke has been scraping his back toenails while walking — one of the field marks of DM onset — for two years now. We noticed weakness in his hind legs almost a year ago. It has not gotten significantly worse since then. It has, in fact, gotten better for months at a time. According to what I’ve read, Zeke has already secured himself a spot well out on that long tail. So far, in fact, that I am wondering whether his ailment is DM at all. If it is, Zeke has already beaten the odds.
And so did Gould, who beat his mesothelioma and lived for twenty years past that day in the library, at last dying of an unrelated lung cancer. A fan, I was greatly saddened at the news of his passing, a feeling that wells up again as I write this. Because I wish I could tell him how much that essay has helped me, and not for the first time. There is solace to be found in a good book.
Thank god I turned my mind to Gould’s writing this morning. I could have wasted my time praying.
