I was reading an article in the Atlantic when I was stopped cold by this sentence:
“This trend [i.e., personality change among older people] is probably observed in older populations in part because older adults are more likely to experience brain changes such as cognitive impairment and dementia.”
The Alzheimer’s Association suggests that “6.7 million Americans age 65 and older are living with Alzheimer’s in 2023. Seventy-three percent are age 75 or older.”
The report also notes that just 10.7% of people over 65 have Alzheimer’s. That’s a lot, but it also means nearly 90% of people over 65 do *not* have Alzheimer’s.
Now you read meet someone over 65. You are asked to bet that this person suffers from Alzheimer’s. You’re more likely to win the bet if you bet “no.” Older people may be “more likely” to have Alzheimers, but not by a whole lot.
What’s going on here is a common statistical fallacy. News writers and advocacy organizations tend to reframe statistics as scary numbers.
It’s especially common when a small number of people experience an outcome out of a large pool of “possibles.”
For example, a high percentage of hard drug users begin their drug use with marijuana.
But what happens if we go on to conclude that marijuana is a gateway drug? Now we’re justified in applying draconian measures to punish marijuana users. But in reality, we have a large pool of “possibles” – the marijuana users – and a small number of hard drug users.
Let’s illustrate with imaginary round numbers. The actual facts are much more murky and controversial.
Suppose 10,000 people in a city smoke marijuana. One percent – 100 – go on to hard drug use.
Let’s say only 150 people in the city use hard drugs: the 100 from the marijuana smokers and 50 who started directly with hard drugs.
We could say 67% of hard drug users started with marijuana, which would be scary. But would we then decide it’s cost-effective and reasonable to ban marijuana among the 99% who never make the leap?
We would do better to look at percentage of marijuana users who move on to hard drug. This is more complicated since researchers distinguish lifetime from casual users and stratify by socioeconomic factors.
Or here’s an even more bizarre example with real numbers:
100% of all animals who get feline leukemia (FELV) are cats. So when we see a cat, do we see a furry creature who’s a leukemia case waiting to happen?
In fact, according to this Cornell University veterinary website, only 2-3% of all cats will be FELV-positive. It seems like a lot because there are, well, millions and millions of cats.
A Spanish article gets it right:
“… there is a tendency to assume that the majority of elderly people live as dependent, with disabilities or even believe that those two terms (dependence and disability) are interchangeable. …Just because the majority of people with disabilities are elderly people doesn’t mean that the majority of seniors suffer from any kind of disability, nor that every disabled person is an elderly person, nor that those previous terms are interchangeable.”
Let’s look at a couple of medical examples based on published numbers.
A research study reports that “approximately 54% of strokes and 47% of coronary heart diseases, worldwide, are attributable to high blood pressure.” Scary! But it also means that about 46% of strokes and 53% of coronary heart diseases are *not* attributable to high blood pressure. Presumably, those patients have normal blood pressure or other factors making their blood pressure irrelevant.
But what happens if we ask, “What’s my likelihood of a stroke or heart disease if I have blood pressure?”
That would seem to be a useful number if you want to seek treatment. And I’ve had a lot of trouble tracking it down.
The well-regarded SPRINT study compared a “composite” of cardiovascular outcomes (myocardial infarction, other acute coronary syndromes, stroke, heart failure, or death from cardiovascular causes) in the standard vs. intensive treatment groups.
The standard group lowered their blood pressure to 140/90 while the intensive group went down to 120/80. The difference? 1.65% in the “intensive” group vs. 2.19% per year in the “standard” group. SPRINT participants were over 50 with a history of at least one cardiovascular disease risk factor.
Once again, only a tiny percentage of the population with high blood pressure seems likely to suffer the consequences.
The CDC reports that 81% of COVID-19 deaths in 2020 occurred among those aged 65 and over. That seems like a big number translating to 282,836 deaths.
Yet millions of people are over 65. The COVID-19 “age-adjusted death rate” for the age 65 and over population was “533.5 per 100,000 standard population.”
So according to the CDC, it looks like 81% of Covid deaths were among those age 65…but only .5% of those over 65 died of Covid. Once again, if you know nothing about a person except their age, you’d come out ahead if you bet they wouldn’t die of Covid.
Note that I am not a doctor or any kind of medical professional. I don’t even know first aid.
I’m looking at the story the numbers tell. I am not giving medical advice.
But it seems reasonable to ask: How far should medical reports go in presenting the risk of a serious disease?
Do we encourage thousands – maybe millions – of people to accept treatment for a condition when there’s a very small risk they will get the condition? Should we at least give them an informed choice?
Perry Wilson, who is not just a doctor but a respected researcher at Yale Medical School, wrote a book, How Medicine Works and What To Do When It Doesn’t.
In that book, he acknowledges the tiny percentage of improvement associated with intensive treatment in the Sprint study. However, he suggests that a case can be made for accepting intensive treatment even with this small risk difference. Lowering blood pressure calls taking pills that aren’t super-expensive and, he suggests, are associated with few side effects.
Yet, to his credit. Dr. Wilson acknowledges that some people will not agree. Some will frame the choice differently.
Others might point out that most people aren’t interested in statistics. They want a strong recommendation from a busy doctor who’s got maybe 20 minutes to spend with them. That’s not nearly enough time to review the data.
Unfortunately, without an accurate understanding of the statistics, we won’t have a choice to frame. We’ll simply be scared of the big numbers the journalists – and some medical professionals – are throwing at us.
So let’s say you’re 65. You knew that only .5% of people over 65 are likely to die from Covid. Would you make choices that are different compared to those you’d make from knowing that 81% of people who died from Covid were over 65?
I know what I’d do. You make your own choices. I’d argue that your choices should be informed, not driven by big-number hysteria.
If you look in