The Math of Medical Decisions

I’ve spent the summer immersed in medical decisions around several loved ones, so this blog has been brewing for a while. At each appointment, I am struck by HOW MUCH MATH patients need to know in order to understand the choices framed by their doctors. There are always odds, statistics, costs, benefits, side effects, down sides, and probabilities to weigh. Nothing in medicine is ever 100%.

Scratch that. We actually went through an ordeal this summer where the number 100% came up twice, and the decision was still not simple. We had a bat flying around our house, out of our sight for a time, while our two kids were asleep in their room with the door open. Here is the background information we learned (from sites like CDC and WHO):

About 1 person dies in the U.S. each year from rabies. This number is much higher in countries where dogs are not vaccinated.

Of the deaths in the U.S., most are caused by bats.

Most bats do not have rabies: recent estimates are around 1%. (Bats are also endangered.)

If someone is asleep, there is no way to know if they’ve been bitten or scratched by a bat. The marks are microscopic.

So here’s where the 100% comes in:

If a person is bitten by a rabid bat and not treated before symptoms develop, he or she faces certain death. There is nothing that can be done. 100% fatality rate.

The post-exposure rabies vaccine is 100% effective when administered correctly.

So what’s your choice? If it were you, would you vaccinate the children or not? What are the odds that the one bat in the house was one of the 1% that’s rabid, and actually made it into the kids’ room, and bit them? Is that the number we should calculate?

Does it make a difference that the vaccine is a 4-part series of painful shots given over a few weeks?

Does it make a difference in your calculation that the first visit to the Emergency Department for the first round of shots billed insurance for….wait for it…more than $11,000?

When is it worth it? When is it feasible? What’s the right decision?

Last week, I was in the mammography waiting room, chatting with a woman who, like me, is 41 with a mother who had or has breast cancer. We’re both on the same high-risk protocol, although her insurance isn’t as good as mine, so she only gets MRIs every other year instead of annually, as recommended. While we waited in our blue robes, she told me about her mother’s journey through breast cancer. She said, “My mom waived chemo because of vanity. They told her her 10-year survival rate would go from 81% to 92% with chemo. In that appointment, my mom said, ‘Those are both over 50, right? Those are good, right? Then I’m not doing it.'”

Each medical decision needs to be made by a specific person, according to their values, in their context. I am in no way judging her decision. What concerned me was that I wasn’t sure her mother understood the math involved. What does she think “over 50%” means? Does she understand what an 11% difference in her survival rate means?

Later that day, I was told I have breast cancer. I know from my experience with my mother that there will be mathematically based choices to make at every stage of this journey. For example, my tumors will likely be Oncotype tested, which will yield a score my medical oncologist will use to decide whether I need chemotherapy or not. The Oncotype test supposedly gives a score from 0 – 100, but look how it’s used (from breastcancer.org):Screen Shot 2014-10-02 at 10.34.00 PM

If a patient hears lower is better, and she has a score of 32 out of 100, that sounds pretty low, doesn’t it? Except, no.

So, here’s where I’m going with all of this. Are we equipping our students to reason through these decisions? To make sense of risks vs. benefits, odds, data, or scales from 1 – 10, 1 – 100, 1 – 5000, all used in different ways? When we wring our hands about “real world” applications of math, we talk about making change and saving for retirement. But, at some point, every one of our students will be a patient.

As I face the medical road ahead of me, I am well aware of the privileges I have going in to treatment:

  • I have the open doors that come from my socioeconomic status: access to great care and the means to pay for it.
  • I have a job I can keep through this treatment, and don’t have to choose between care and financial ruin.
  • I have a home where I feel safe and am supported by my family.
  • We have a larger community and support network that will help us.
  • I am not likely to be discriminated against during my treatment, or face language barriers.

But I have a second set of assets too:

  • I have the literacy skills to make sense of a new glossary of medical terms, read technical articles, and communicate my needs with my support network.
  • I have the science background to understand protocols based on clinical trials and data collection. I have enough biology to build a general understanding of what’s happening in my body, enough chemistry to have a sense of what these medications do, and enough physics to understand some of the testing I’ve been through. (Speaking of, thank you to the physicists and engineers behind MRI, which may have saved my life.)
  • I have the mathematical background to understand the results I’m given and reason quantitatively through the decisions I’ll need to make.

That second set of assets comes from my education. Which begs the question, what should we do, as teachers, to equip our students with these skills? Assets that can never be taken away from them? Let me be perfectly clear: I am not suggesting we replace half of the tedious, textbook cell phone cost and rate word problems with scary cancer cost and rate word problems. For the love of Pete, that’s NOT what I’m saying. What I’m saying—asking really—is what are we doing to develop the kind of numeracy and quantitative reasoning our students can use in novel, complex, vital, contextualized decisions?

Could we start by remembering that’s one of our goals?

I’ll be getting a big round of pathology results back next Thursday. I have a lot to be scared of, but at least I am confident I will understand the results. I know my family and I will be able to talk through the options with my doctors, listen carefully to their counsel, and make the best decisions we can for me, at my age, with my history, in my context.

I want our students to have the same comfort and confidence when it’s their turn to make medical decisions.

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0 thoughts on “The Math of Medical Decisions

  1. Tracy,
    I am so sorry you are facing this. I have a mother who fortunately is a breast cancer survivor, but I will someday be sitting in that doctor’s office awaiting results as well. Right before her diagnosis I was listening to a Joel Osteen audiobook and I don’t remember the exact story. Basically he said that researchers have shown that the palm tree is the strongest tree as it withstands such tremendous trials. But the coolest thing they found is that once a palm tree goes through a hurricane its root system actually gets stronger. So a palm tree goes through such hardships, BENDING but never breaking and afterwards is stronger because of the trial it went through. I encouraged my mom to think of herself as that palm tree…she may bend and waiver but she won’t break. She is now known as Palm Tree Patty. I encourage you to visualize yourself in that same way. You are in my prayers as I pray that your results come back the best they can and that you find strength to fight what is coming.

    1. Thank you so much, Christina. I love that image. I will hold it with me.

      Please tell me you’re getting checked? My mother’s diagnosis may have saved my life.

  2. When I taught our somewhat lengthy unit on statistics, I often focused on medical examples for the reasons you articulate above; if the statistics my students learn is bound to a particular discipline, medicine is one that they are all going to have to face at some point in their life.

    I’m also sorry that you have to make sense of this particular statistical information at this moment in your life.

    1. Thanks so much, David.

      One of my favorite professors in college was a physics professor who used to co-teach a class called “The Ethics of Medical Decision Making” with an ethics professor and a sociologist. I wish I had taken it. They did lots of stats, and focused on the tough choices. If you have limited resources, do you save this one child with x, or vaccinate y number of kids. No easy answers. Anyway, all that’s to say that I think medicine is a great context for learning statistics. Thanks again.

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