Let’s say there’s a 10% chance that any given person will catch pneumonia at some point in his life. Is that any different from saying 1 in 10 people will catch pneumonia at some point in their lives? Is there any case where the former is true (10% chance), but the latter isn’t (1 in 10)?
I’m inclined to think they’re the exact same data points, but math. It’s hard.
-Tom
Well, 1 in 10 will be too small a data set to extrapolate.
Right, but what about starting with the 10% data point? If that’s verifiable, can you translate that into saying 1 in 10?
-Tom
The numbers are right but they aren’t quite the same thing. 1 in 10 people get pneumonia over their lives, but you don’t necessarily have a 10% chance of catching it. You might work in the hospital, or you live in a submarine under the ocean. It would be wrong to say both the hospital worker and the submarine captain had the same odds.
I don’t think it is that simple as you could catch pneumonia multiple times in your life and some people may never get it which could skew the 1 in 10. You need to think of combinations and permutations. I have forgotten a lot of statistics since I studied it 20 years ago. If you give us an exact example of the context we can help you accordingly.
They are not different. Although many phrasings of ‘10% chance of catching pneumonia’ could be interpreted slightly differently in ways that would overlap with people who catch pneumonia more than once, and in that case it would be different. But the way you phrased it implies no overlap in my reading. But if there was a difference that’s where it would come from.
(Kind of like how having a 50% divorce race does not mean 1 in 2 people who get married have a divorce, since people with lots of divorces drive up the rate.)
Good, that’s what I thought. The phrasing is important – there’s a 10% chance you will catch pneumonia at some point in your life and therefore 1 in 10 people will catch pneumonia – so I’m less interested in whether you can change the phrasing to find a loophole and more interested in whether it’s accurate to present the data in either format.
-Tom
Not to bring the room down, but I’m looking at the likelihood of being diagnosed with cancer. On average, it’s around 40% in the US, varying by things like sex, race, geography, etc. Which is analogous to saying 2 in every 5 people will be diagnosed with cancer.
-Tom
That’s so sad to hear Tom, I hope your are one of the 60% going forward. Your example would be correct in this case.
Unfortunately, I missed that boat! The 60% are people who will never be diagnosed. The one I’m gunning for is the 80% of people who don’t die from cancer. :) And that’s not just gallows humor. That’s a staggering figure to me. 1 out of 5 people in the US will die from cancer. No doubt partly due to the fact that modern medicine keeps people alive much longer. Cancer rates in countries where people die younger are probably much lower.
-Tom
Is it possible that 100% of people have cancer, but only 40% are diagnosed due to symptoms due to growths? That is do all humans have benign cancer over the long term? If we lived to 500 what would the cancer rate be?
Way more interesting of a statistic is how many survive once diagnosed. You’d have to add to this stat the amount that have it and are not diagnosed and die never having been diagnosed.
My goddaughter, who seems to be doing fine now, only had a 4% chance to live given the survival rates of various types of cancer and how many organs it screwed up and how halves of kidneys she had left after surgery and so on. But I wonder how many people just get benign versions of her cancer. How would that effect the stats? Plus the remissions rate stats differ based on various post surgery/chemo/radiation courses and all kinds of variables. The metrics are super complicated!
Guap, glad to hear your goddaughter pulled through. That’s some serious math wizardry! Good for her. Next time I’m playing XCOM, I want her to press the keys for me every time I take a shot. :)
Here are the numbers from the American Cancer Society, which expresses them as both a percentage and “1 in X”.
I’ve never confirmed this – I’m not sure it’s even possible to confirm – but the chestnut I’ve always heard is that everyone will eventually get cancer. It’s just that most people die of something else first.
-Tom
It’s more the other way around. “Your” 10% chance of catching pneumonia is inferred from (maybe better is a corollary/restatement of) the fact that 1 in 10 people do get pneumonia. “You” in this case being a generic person in whatever group it is that the 1 in 10 statistic applies to.
Quite often 1 in 10 and 10% are used interchangeably. And if someone says you have a 1 in 10 chance of catching pneumonia then they most certainly mean you have a 10% chance. But if someone said, “1 in 10 people contracted pneumonia” then they could be referring to a situation involving ten people, which wouldn’t necessarily accurately represent your chances. If it’s on a homework problem then yes, they definitely mean 10%.
Edit: there could also be a case where a doctor says you have a 10% chance of catching pneumonia and not be implying that 1 in 10 people contract it because he may be basing the probability off of a factor unique to your situation.
Well. I do know that rates of pediatric cancer death have declined precipitously. It’s a long story but in the video I referenced in this blog entry, he says
You think you’re the only one losing kids today? 25 kids walked in here with cancer, only 5 are walking out. This ain’t no sitcom. It don’t wrap up all nice and tidy in 30 minutes. This is life, welcome to the real world.
The story he told (and it’s intense, give it a watch) takes place when Johnny Carson was still on the tonight show circa 1990-ish. I looked into this because only 5 kids surviving out of 25 with cancer seemed… dire. That’s a survival rate of, geez, 20%? I found pediatric cancer treatment survival rates have dramatically improved in the last 40 years, even in the last 20 years:
Because of major treatment advances in recent decades, more than 80% of children with cancer now survive 5 years or more. Overall, this is a huge increase since the mid-1970s, when the 5-year survival rate was about 58% … After accidents, cancer is the second leading cause of death in children ages 1 to 14. About 1,250 children younger than 15 years old are expected to die from cancer in 2016.
So fuck yeah science.