Sunday, December 15, 2013

Death: Fun with numbers


This is about one's chance of dying, a topic I would think is of interest to just about anyone.  The chances of death are measured in clever ways by the authors of The Norm Chronicles: Stories and numbers about danger, Michael Blastland and David Spiegelhalter, Brits.

Blastland and Spiegelhalter calculated the “micromort,” a one in a million chance of dying, for a wide variety of activities. Everything carries a little risk, they point out. The chance of getting hit by an asteroid is one in a million over a lifetime. That's one micromort. So might as well calculate the risks of things you can control, so you know what it costs before you take a flight in a small aircraft, base jump, or light up a cigarette. What’s it going to cost you. The risk of something horribly dramatic taking your life in a given day is about one in a million – that's one micromort.

Being a baby is risky business, it turns out. Over a lifetime we risk about one micromort a day but the first year it's 4,300, and that's in the U.K. This is as risky as riding a motorcycle around the world. It's worse in the first few weeks, worse for underweight babies, for boys, and for children of young mothers. And Britain is a relatively safe place; worldwide, infants risk an average 40,000 micromorts (ten times the U.K.’s value). In Sierra Leone DR Congo infant mortality three times higher still. At the same time, worldwide risk of birthing, for mothers, is about 2,100 micromorts, each time. For perspective, it's just 200 in the U.S. but 11,000 in Chad.

After the age of 1 things improve quickly and by 7 we enter our safest year, risking just 100 U.K. micromorts for the entire year. That’s equivalent to less than eight and a half days of risk for a British infant; less than a day’s risk for a baby in central Africa.

Life choices are interesting: a minute of take-off or landing on an airplane is worth an hour of flight, but the chance of an individual dying on a commercial airline flight is just 1 in 9 million. So each airline flight is about a tenth of a micromort, that is, unless it’s a small aircraft in which case risk is a full micromort every six minutes – and that's about as dangerous as walking or bicycling. Now if you choose to jump out of the plane, with a parachute, it will cost about 10 micromorts -- a bit less for novices, who don't take extra risks, Rock climb for 3; hang glide for 8 and a base jump will cost you 430 micromorts. Scuba diving costs 8. Walk or cycle 30 miles for 1 micromort, ride a motorcycle that distance for 4. Drive a car 333 miles or take a train 7,500 miles for one micromort, isn’t this fun? Run a marathon? Seven micromorts. Two hundred for catching measles in Britain, about the same if you want a CAT scan. Careful, having your heart valve replaced will cost 52,000 micromorts.

In the U.S., workers risk 4 micromorts a year just for being murdered at work. Worldwide the risk of a fatal work related accident is 160 per year. Coal mining costs 650 and commercial fishing is the worst in Britain, at 1,020 micromorts annually. These comparable figures make legislation quite interesting. What is the cost of a micromort? What are acceptable levels of risk? Gets practical, fast.

Remember the dangers of infancy? Old age is worse for a lot of things, and dramatically so when it comes to avoidable accidental deaths. The graph shows very few such deaths until 19 when it jumps to about 200 micromorts per year for males (vehicle accidents, mainly), then fairly steady on until 70 when it spikes sharply and doesn't stop: 500 by the late 70s, 1,000 a year by 85 and then 2,500 thereafter.

It reminds me of the joke about three senior citizens: “My vision is so bad I can’t see who I’m talking to, one says. “My neck has gotten so stiff I can’t turn my head,” another replies. “I get dizzy,” the third one said “It’s just terrible being old. But … at least we can still drive.”

Besides micromorts, the authors also calculated microlives, a millionth, more or less, of an adult life -- 30 minute packets. Spend them any way you choose. All things considered, one cigarette reduces life expectancy by an average of 15 minutes -- half a microlife. Get it? That’s not only eight bucks a pack, it’s also five hours of your life, thank you.

Alcohol, as we know, is good in small doses. The first drink of the evening will actually buy you an extra 33 minutes of life but then you pay 21 minutes for each drink thereafter. Every inch of waistline costs 30 minutes every day you carry it. Two hours of watching TV costs one microlife too. On the other hand you can gain microlives for good behavior: two and a half hours a week of light exercise means a 19 % reduction in risk of death, which would come to about an hour of the day. So a daily jog of 22 minutes will extend your life by an hour each time – that’s a pretty good deal, right? Run for an hour run a day and you get an hour and a half back. Hey, regular exercise doesn't cost anything, it's extra credit.

You get two extra hours a day just for being female, but anyone can get two hours for eating five servings of fruit or vegetables.

The book put quite a few things in a new perspective for me. I’d heard of it through The Economist so I shouldn’t have been too surprised that much of the data was for Britain. The authors tried to make it more interesting than numbers numbers numbers by adding a lot of dialogue between three fictitious characters: risk-taking Kelvin, regular-guy Norm and timid Prudence. Those parts -- about a third of the book -- were predictable and a little annoying. But it was really quite interesting to look at death this way.

I so happened to have on my desk a copy of the Center For Disease Control’s National Vital Statistics Reports, it’s an esoteric subscription I have that is also quite interesting if you take the time. This report, Vol 61:9 May 2013, was called “U.S. Life Tables Eliminating Certain Causes of Death 1999-2001.” What it does, for the most part, is extract from death data one cause of death, to see what happens.

There are some summary data, to be sure. In the U.S. generally 31% die of major heart disease, 22% of cancer, and 7% of stroke. Women live longer than men. But we already know that well enough from newspapers.

Honestly it’s the sort of thing Blastland and Spiegelhalter could base another book on but these data are for the U.S. Read the tables directly to put yourself to sleep: Ok, if we cure diabetes 3.3% of black women will die between the ages of 50-55. Compare to another table to learn it would be 3.4% otherwise.

With a little calculation, though, I came up with some pretty interesting things myself. If we discovered a cure for Alzheimer's, for example, white females would expect an additional 72 days of life expectancy at birth, black ones 44 days, white males would gain 33 days and blacks 18. That’s because women overall live 5 years 4 months longer than men and Caucasians live 5 years 8 months longer than African Americans. Older women get Alzheimer's because women get older. On the other hand if you could eliminate all homicide, white women would live an extra 26 days, black women 80 days, white men an extra 62 days on average and black men 360 days, that's almost a full year longer for life expectancy for every black male, without murder. Three hundred and forty three of these days involve firearms.

On the other hand suicide costs white men an average 157 days of their lives, black men just 80 days, and women of either race just 42. Why? I don't know and the NVSR doesn't come with commentary. All these data can be broken down by age, too, so while the prospect of motor vehicle accidents cost a newborn 204 days in life expectancy, it costs me at my age only 29 because my reckless years are over.

I recently watched a horrifying youtube compilation of parkour accidents. Every one in it was male. So if you take away unintentional injury it's not surprising that boys will live an extra 401 days on average. Girls would gain just 197 days.

That's the kind of thing you can get from the CDC if you read the tables carefully and do a little work with excel. See ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/Publications/NVSR/61_09/ for all the tables I looked at, or go back a folder from there for other publications.  Or just go to http://www.cdc.gov/nchs/ and poke around. 

Be careful though. According to Norm every two hours in front of the screen will cost you a microlife. Get up and walk around every now and then and earn it back.

14 comments:

  1. A micromort for an asteroid hit? Really?

    -signed, Astronomer in Madison...

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  2. yes.
    http://www.bbc.com/future/story/20120222-waiting-for-a-rock-to-fall/1. :)

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  3. Don't probabilities rely on an underlying model, like a Gaussian distribution? What is the distribution for an event that has never happened? What is the 1-sigma probability? 2-sigma?

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  4. I also sense a conflation of asteroids and meteorites. The size distribution is a power law (looks linear on a log plot). The vastly more common impacts are also vastly less powerful. Wouldn't you need to know the exponent of the power law in addition to historical frequency to even guess at an underlying distribution? Huh? Huh? ;-)

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  5. Can't you get the exponent from the historical frequency of the largest events, and the current frequency of the small ones? That's what I would do. :)

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  6. That would be a good way, I think! But the guy in the article doesn't even mention it. Here's another way to question probabilities not based on an underlying model. Is there a difference between mean rates (91 deaths per year) and probabilities? Say you have one breakfast per day. Your rate of breakfasting is about 10^-5 breakfasts per second (on average). But is my chance of finding you eating one (the probability) the same as the mean rate? No! If it's dinnertime, the probability is zero, even though the mean rate is still 10^-5/s.

    In the article's case, conflating a mean rate (averaged over millenia) to a probability of something that has never actually happened is sketchy.

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  7. This is fun to think about! On further thought, it seems that in computing a rate, you can only choose a denominator that has some rough correlation with the event you're describing. So with breakfasts, I can talk about a rate of one per day, or per month, or per year, but not per hour or per minute or per second. Breakfast doesn't occur on those smaller time scales. So with large asteroids, you can talk about X deaths per hundred million years, but not per year. Your time granularities have to match. What do you think?

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  8. I believe there is periodicity to meteor strikes through the year, as we go through a debris belt, but is there periodicity to the major astroid strikes? If not, then the time frame of that wouldn't matter would it? Chance of it happening could be in seconds or millenium?

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  9. But if the large ones don't hit every second, it doesn't make sense to use "seconds" in the denominator. Or years. Or centuries. The more infrequent they are, the less appropriate is the "per lifetime" denominator. The only denominator that makes sense for life-altering asteroids is "per hundred million years".

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  10. And in the case of a denominator of "per hundred million years", the only numerator that makes sense for human occupation of earth is "zero".

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  11. I don't agree. The time frame of most interest to people, when it comes to meteor deaths, cancer, accidents, heart attack etc. is lifetime. So the natural denominator is average life expectancy for really unlikely events. Or, if you have the tables, "the remainder of your own lifetime" would be of use.

    For other things, like riding a motorcycle, the best denominator would be 1,000 miles, or 5 hours, or something easy to relate to. For a bungee jump, each time.

    For some of these the result may be very small, but not 0. Then you just add them all up to see what your risk is in, say, a day. Divide by 86,400 for the risk in a second -- that's just as legitimate but probably just hard to relate to again.

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  12. I agree that a lifetime is an interval of interest, but the universe isn't obligated to make sense on that timescale for all things! If you want to talk about asteroids and human lifetimes, that's great, but then the right answer for a probability is zero.

    If your probability of eating breakfast is 1/86400 per second, then that means if I view you at random seconds, I'd *never* catch you eating. If I ask, did he eat breakfast in that second that has just passed, the answer would surely be no. But if your rate is one breakfast per day, and I observe you for a day, and then ask, did he eat breakfast that day, the answer would be yes.

    One final question, and then I'll stop. Do you think that "11.5 femto-breakfasts per nanosecond" is meaningful? It's mathematically equivalent to one per day, but which has meaning?

    In my example, expressing asteroid numbers in human lifetimes is like having to talk about femto-breakfasts to squeeze them down into our lifetime.

    You don't eat breakfasts on nano-second timescales, nor do asteroid hit earth on human timescales. It's the same thing.

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  13. But this was fun!

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  14. But let's say it takes 30 minutes to eat breakfast, that's a lot of femtoseconds. 24 hours in a day divided by 0.5 equals 48. 1/48 is about .02 so if you called me up randomly there's a 2% chance I'm eating breakfast. Say a 3% chance for lunch, 4% for a nice dinner, altogether 9% chance I'm at a meal, 9.1 because you have to count my snack time That's not trivial. The asteroid is just also factoring in an occasional Indian lunch buffet. Although it happens a couple times a year, because it's in the context of me eating, it makes sense to add it with the denominator set at one-day.

    We'll call this unit a micropork.

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