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Numeracy: Live Long and Prosper

Literacy in math could save your life

It’s not a word you hear every day.  Numeracy.  Even if you’re unfamiliar with the word, if you’re reading this, chances are good that you have it.  You work with analytics; you work with numbers. I have a theory that because of your day job with data, you’re better equipped to navigate everyday life.  You have a skill you may not even know you have: the ability to understand numbers.  Not everyone maths.

What is numeracy?

Numeracy is the ability to understand mathematical concepts and apply them in everyday life.  It includes data literacy, the ability to understand graphs and charts.  It includes understanding and applying probabilities and risk evaluation to your daily decisions.  It’s using numerical data to make informed decisions.  

You can know the basics of arithmetic, or even more complex calculus or trig, but numeracy is understanding the concepts.  For example, you may know how to add and subtract, but not be able to balance your checkbook.  You may know that one number is larger than another, but have a hard time understanding what the better deal is: 3 bananas for $0.69 or a dozen for $3.

Health numeracy is the concept applied to medicine.  Numeracy in health underscores the ability to assess risk and understand probabilities.   It’s not just the ability to understand numbers, but the ability to apply concepts that use numbers and the associated quantitative reasoning.  

Why is numeracy important?

One area in which even well-educated people have trouble with numeracy is risk perception.  Both doctors and patients have difficulty making logical decisions based on known data points.  And, if doctors don’t understand it, how can they effectively convey it to their patients to make informed decisions?

The importance of numeracy is more important than ever in managing your own health.  Over the past decade or so, medicine has moved from a paternalistic approach (“do this, it’s the right thing to do”), to more of a shared patient-centered approach.  There is more of a burden on the patient to understand the information he or she is presented in order to make an informed choice. The patient is actually empowered.  With that comes responsibility.  

Innumeracy, for example, cannot analyze the risks vs. benefits of screening procedures.  A certain level of numeracy is required for even medication compliance.  You have to count the pills and put them in the weekly pill box.  How do you calculate half of your 7.5 mg pill dosage?  Low numeracy in the patient or the provider, limits the understanding of risk.  Ultimately, it can affect positive outcomes.  

A practical example

In every visit to the doctor you have to use your numeracy to process what you’re hearing and make informed decisions.  

  • Your cholesterol level is affected by multiple factors:  Genetic (~60%), Diet (~10%), Exercise (~15%) and lifestyle choices the remaining.  Health-healthy diets may lower your LDL cholesterol by 5 to 15%.  If you exercise more, can you keep your beer?  (Source: American Heart Association and National Institutes of Health)
  • Cancer is the second leading cause of death in the US, 600,000.  About 8% of those are due to colon cancer.  Colonoscopies will detect more than 75% of bowel cancers.  The complication rate is between 1 and 3 out of 1,000 procedures.  About 3 or 4 cancers will be detected for every 1,000 procedures performed.  It looks like the complication rate is about the same as the detection rate.  Do the benefits outweigh the risks?
  • Cardiac arrhythmias are bad.  The heart doesn’t pump enough blood.  As many as 10% of patients with Ventricular Fibrillation die from it.  In one study of 1498 patients, 755 participants received a new drug, and 743 were given a placebo. Of the 89 patients who died during the study, 26 had received the placebo.  Should this drug go to market?

Here’s another.  A question very much like this is included on an assessment to evaluate clinical numeracy.  

Imagine you have a friend who has her annual mammogram.  The mammogram indicates the presence of a mass.  Given the following information, how would you help her put the results in context?

Mammogram Results of 100 Women
Tested PositiveTested NegativeTotal
Actually has a tumor9110
Does not have a tumor98190
Totals1882100
Summary
True Positive (tested positive and has tumor)9/100Sensitivity of test
True Negative (tested negative and does not have tumor)81/100Specificity of test
False Positive (tested positive, but does not have tumor)9/100
False Negative (tested negative, but does have tumor)1/100
Total True Positives (True Positives + False Negatives)10/100Prevalence of cancer
Total Positive Results (True  Positives + False Negatives)18/100
Total Negative Results (True  Negatives + False Positives)82/100
True Positives + True Negatives90/100Accuracy of test

I’ll do my best to explain this.  It’s important to understand.  It’s easier than counting cards at the Blackjack table, but, like at the casino, you need to concentrate.  We’ll walk through the solution step-by-step.

Step 1: Calculate the probability of testing positive 

From the Summary table above we see that the total probability for testing positive is 18% (18/100).  

Step 2: Calculate the probability of having a tumor

Given a positive result of the mammogram, the probability of actually having a tumor is:

(True Positive Rate) (Total True Positives Rate) / (Total Positive Results Rate)

This is equivalent to:

(Sensitivity of the test)(Prevalence of Cancer) / (Positive Test Rate)

Substituting the values:

(0.90)(0.10) / (0.18) =0.50 = 50%

The probability that your friend actually has a tumor, given that she tested positive, is 50%.  It’s serious, but still the flip of a coin until more tests are done.  

The point here is not to give you medical advice but to show you how many calculations there are in everyday conversations with your doctor.  You should be able to use this same process, substituting any disease and any test.  

Know math, be healthy, live longer

Health-related numeracy skills have been shown to correlate positively in predicting medical outcomes, such as diabetes management.  The ability to use and understand mathematical concepts improves the quality of the decisions we make, and better health choices lead to better life outcomes.  Use your numeracy skills to manage your own health and make better informed shared decisions with your medical professional.  

Source: Much of the information in this article is based on the work of V. F. Reyna, W. L. Nelson, P. K. Han, & N. F. Dieckmann (2009)  and published in the academic paper, How numeracy influences risk comprehension and medical decision making.

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