We are a flawed species. You can point to cancers, the recurrent laryngeal nerve, or our ridiculous childbirth, but our inability to comprehend probability is creeping into modern life. From the lottery to video games to the stock market, our blindness to the realities of probability lead us to make decisions that would make followers of Homo economicus blush.

The Miracle of Cards

Depending on your beliefs, you may acknowledge that some miraculous events have occurred in human history. Even the less spiritually inclined of us would recognise that some quite implausible situations have come to pass. However a smaller group of people would consider shuffling a pack of cards to be miraculous, yet with every shuffle the odds are that you are the first person in history to see that particular combination, and it’s likely to remain so.

Given a standard deck of cards, the number of possible decks is easily calculable as 52!.

52! = 8065817517094390000000000000000000000000000000000000000000000000000

This number just so happens to be greater than the number of atoms in the universe. Essentially the odds of you receiving that particular deck are smaller than selecting a particular atom anywhere in existence.

Our Friend Monty

You’re presented with three doors behind one is a car, behind the others are bananas. After you choose your door the kindly game show host reveals a banana behind one of the other doors, and gives you a chance to change your choice. What should you do?

If you’re familiar with the Monty Hall problem, you’re probably confident in knowing that switching doors gives you a 66.6…% chance of victory. There’s a good explanation of why this is the case here. Let it suffice to say for now that the answer to relatively simple questions such as this is unintuitive to the majority.

In Relation to Medicine

So why am I writing about this? Everyday doctors rain down doom upon poor unsuspecting patients. There’s a 16.7% risk of developing stroke, there’s a 22.6% chance of cancer diagnosis, there’s a 23% probability of dying from heart disease.

Statistics and probability are essential tools in the era of evidence-based medicine. We use them routinely to prove new treatments, verify existing practises, and prevent bad outcomes, but time and time again studies have shown that patients’ understanding of their treatment and prognosis often deviates from reality.

This can lead to confusion about the outcomes of treatment leading to harm from unmet expectations, and furthermore patients favouring one kind of treatment over another based on mistaken assumptions. This paper led from previous work showing patients overestimating their chance of survival, to show how expectations can shift the decision regarding life extending versus palliative care.

Issues surrounding communication in healthcare, particularly about end-of-life care, are at the forefront of the media’s and the public’s concerns. This extends to uncertainty towards the definitions various terms take on, and even more worryingly patients and doctors have separate connotations and meanings.

Mazur and Hickam found that although there was a common pattern in the probabilities patients associate with certain words, there were large ranges with words such as probable, possible, and likely. This adds to the debate about whether discussions should lean towards the qualitative or numerical.

Even more confoundingly the orientation statistics are displayed in can also influence understanding. The statements 3 out of 100 die and 97 out of 100 live will convey different implications to patients. While framing an outcome in a negative carries the chance of distress, statements framed only in the positive may not give patients an accurate portrayal of severity.

Ultimately this boils down to an issue of informed consent, and how patients can make decisions without needing to have a medical degree. Towards this end there are a few simple considerations that can make the doctor-patient relationship more inline:

  • Supplement verbal explanations with numerical data
  • Use absolute risk where possible
  • Give both a negative and a positive frame
  • Use a consistent denominator for odds
  • Visual aids can be a useful way to present risk

At the end of the day the message is a familiar one, care needs to be taken when broaching difficult topics. It’s become one of the universal mantras of patient-centred medicine, such that it occupies an entire domain of the GMC’s Good Medical Practice. Fortunately there are a growing number of resources for doctors and patients alike, and in an age of growing information availability hopefully this problem can become a diminishing one.