Homer Simpson (Photo credit: Wikipedia)
Let’s warm up with a quick arithmetic problem, which I want you to do in your head.
What is one thousand plus forty?
- Now add another thousand
- And thirty more
Plus twenty
- Plus another thousand
And finally, add an additional ten.
What’s the answer? According to Dean Buonomano, in his excellent book Brain Bugs, the majority of people give an answer of four thousand, instead of the correct answer of 3100.
“Most of us can find a face in the crowd faster than we can come up with the answer to eight times seven. The truth is—to put it bluntly—we suck at numerical calculations.”
I discuss this problem of innumeracy in my book Critical Decisions: “Throw enough numbers at people and many will experience negative emotions, emotions that often interfere with their ability to make good choices.”
I focus on these math problems because, for some very important medical decisions, the right choice depends on grasping some basic mathematics. And perhaps nowhere in medical care is there more math—more explicit discussion of numerical probabilities and five-year survival rates—than in the care of cancer patients. Consider this snippet of a hematologist trying to explain that there is a good chance a patient’s leukemia will respond to chemotherapy:
“So if you look at complete cytogenetic response rates in the chronic phase,” the hematologist explains, “it’s about 80%, and if you look at the accelerated phase, it’s about 15%. So, the drug doesn’t work in advanced disease very well. If you look at patients who get a complete cytogenetic response as their best response in the Iris trial, their risk of ever progressing in the next 4 years, so about 48 months roughly, is about 8% overall.”
I re-enact a bit more of this conversation in one of my book-related videos, which you can find here. But let it suffice to say for now that this visit goes on for quite a while, with a staggering number of numbers being thrown at this patient. But even in this short paragraph, the hematologist moves rapidly from response rate percentages to progression percentages—in the former, high numbers being good, in the latter, high numbers being bad. A very confusing switch around for patients to follow, in the context of what is no doubt an emotional clinical encounter.
Which raises a question: Why all this talk about math with patients? Shouldn’t all this number stuff be handled by physicians? Shouldn’t chemotherapy decisions be made by medical experts?
As it turns out, many such decisions depend strongly on patient preferences. Suppose that chemotherapy increases a patient’s odds of five-year survival from 30% to 35%, but that same chemotherapy also increases the chance that person will die in the next six months, from treatment complications. Should the patient take this chemotherapy? There is no simple medical answer to this question. The answer depends on this individual patient’s preferences for long-term versus short-term survival, with additional consideration for the burdens of chemotherapy. Making the right decision often means coming to grips with some math.
In future posts, I will show you some of the work I have done to make this math easier to understand. But meanwhile, let me leave you with another quote from Brain Bugs:
“We may have an inherent sense of the quantities one through three, but beyond that things get hazy—you may be able to tell at a glance whether Homer Simpson has two or three strands of hair, but you’ll probably have to count to find out whether he has four or five fingers.”
Only one adequate response I can give to that, as a physician who no doubt has overwhelmed too many of my patients with too much complicated math:
“D’OH!”
