Healthcare statistical mumbo jumbo

English: Diagram relating various pre-test pro...

Huh? (Photo credit: Wikipedia)

The media do have considerable trouble reporting health statistics partly because these statistics often report probabilities, estimates, and approximations. Phrases like “x times more likely” abound. Without knowing what the base likelihood is, we have no idea whether this is a lot or a little. So small numbers can sound impressive and people can be easily mislead into think that they might live forever. Like reporting that 42% of the population will die with or from cancer — the difference is important: men frequently die with prostate cancer, but not from it.

What do you think this paragraph means from The Guardian newspaper: (by the way, a search was unable to locate the relevant document the article was based on. Newspapers should these days cite the names of the documents, with links, to enable independent followup.)

“Twenty-year-olds are three times more likely to reach their 100th birthdays than their grandparents and twice as likely as their parents, official figures show. A baby born this year is almost eight times more likely to reach 100 than one born 80 years ago, according to the figures issued by the Department for Work and Pensions.  A girl born this year has a one-in-three chance of reaching their 100th birthday, while boys have a one-in-four chance.”

Many people look to the media for information on health, but it doesn’t help when within a single paragraph (!) we are confronted with this rush of statistics.

They sound important, like they ought to mean something. But what? Can these statistics be converted into something that might actually shed light on what the the numbers might mean or is the newspaper just repeating statistics in the usually confusing way papers do? (Another example of where papers confuse when they report statistics, is they’ll say something like the number of mortgages issues declined by 1% last month; of that 200 were remortgages. Huh?)

Today’s grandparents were probably born, say, 1930, when the life expectancy was about 60 years, while today it is about 75, and for a twenty year old today it is estimated at 100, 80 years from now. Life expectancy rose about 15 years between 1930 and today (about 80 years) and will rise a further 25 years by the year 2090. Hmmm, that suggests growth in improvement in life expectancy is accelerating as it will increase 40% or so more over the next 80 years than if it just continued at a steady, linear, pace.

Most people die by 100, and certainly for this discussion, we could say 99% of the population born in 1930 will be dead by 2030. So I had a tiny chance of living to 100 if I were born in 1930 and now a baby born today has an 8 times chance, which still seems like quite a small number. We also know it is twice as likely as that person’s parents, say born in 1950 of whom most will also be dead by 2050.

Let’s be generous: 1% of the population lives to 100 born in 1930, now 8% of the population will live to 100. Is that what they are saying? But it also says that boys have a 25% chance of having a 100th birthday, while girls have a 33% chance. Are they saying that of 100 boys, 25 ‘may live to 100’, and and is that broadly equivalent to an 8 times improvement over their grandparents? Hmmm.

So how many boys born today will live to 100? And how many girls? Answers need to take account of the probabilities, so we also need to know if the various statistics in the quote above are compatible with each other or are they inconsistent? Do you think an average person would understand the article? (By the way, we know that doctors often misunderstand what statistics like this mean when referring to the likelihood or not that people may or may not acquire a particular disease or condition, so if that is true, what are the chances for the rest of us: 1 in 50…..?)

Post your answers.

QED, I think.


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