Discussion: Detroit Marathon victims

It is very strange, I don't think it was just a coincidence:
http://www.freep.com/article/20091019/SPORTS23/910...

Much more of life is coincidence than pattern seeking humans want to admit.

If you don't think it was a coincidence, then what common factor do you think links the three deaths?

Wow, that's a toughie... what subtle factor must it be? Maybe they all tied their laces too tight? If the same three had tied their laces too tight but died walking up some stairs on the way to the mall it wouldn't be a coincidence - or would it?

Tooms, perhaps unintentionally, raises a pretty interesting point. What do we consider actual causes for events? Proximate causes? Or questionable causes?

If we wanted to step back a bit--did they die simply because they ran in the marathon? We might be inclined to more readily believe that was a cause (because it is so general and plausible), but it need not be. Their time, so to speak, might just have been up.

Elevation Chart
from Course Maps page

From here:

"Langdon collapsed on Michigan Avenue between the 11- and 12-mile markers at 9:02 a.m. Fifteen minutes later, Brown collapsed near the same spot."

"The youngest victim, Fenlon, collapsed at 9:18 a.m. just after finishing the half-marathon in 1:53:37."

Map of area (Acme Mapper)

These deaths are suspicious! Though J-man is right to point out that we often wrongly find patterns and "meaning" in events that are just coincidence (a built-in cognitive illusion), I'm holding out a non-trivial amount of probability that they were poisoned at the 10 or 11 mile water stop. (I know some people who would stop at nothing to prove that running is bad for your health.)

Whatever. It was totally aliens.

wow those guys are young. It is hell of a coincidence if it is one. I mean, what are the odds of that happening eh? weird... I say we have to call CSI ;-)

Alien cows. Mooo.

Why it suspicious? First - they all died within 2 miles.
Second - it was barely HALF marathon (for them). Lowlander or Billygoat are much tougher.
If to compare to New York City marathon where most of victims died on second half of course or even after the finish line - the Detroit's cases looks odd too.
The weather was relatively cool and the course profile in those miles - flat.
Third - the chances of coincidence. There were no dead runners on Detroit marathon for 32 years. But even if we take a more realistic number - 1 dead for 30,000 marathon starters - the chance to die for 3 runners (on race with 18,000 runners) - about 15%. A chance to die on any given 2 miles section on for 1 runner (on race with 18,000 runners) - a bit more than 1%. For 3 runners - about 0.007%. Other word - 1 out of 15,000 marathon event with 20,000 runners. Were there 15,000 marathon events (with 20,000 runners) in the world history???

I am not going to assess the probabilities (yet). feet can probably do it faster. They may be small, but many times probabilities like this are not as small as they seem.

I will ask, however, what causal explanation would you propose?

Why, when presented with a phenomenon, seek out the least likely explanations for it first? (I'm actually interested in that phenomenon myself, but I digress.)

It seems like too much House M.D.

All three were running the half. They were all on a pace to break 2 hours. The 26-yr old finished in 1:53:37. The 36-yr old was on pace for 1:47:xx, and the 65-yr old (with the least data) would have been under 1:57:00 at his 6mi pace.

Since someone else mentioned crazy theories, I'll throw in mine.

My 100% guess (WAG) is Carbon Monoxide Poisoning from the 200+ meter section along and above the interstate (in low wind conditions) just before the 12 mile point. They're all three near the end of their race, pushing hard, and they pass through exhaust fumes that suddenly reduce their ability to process oxygen. (Apparently, a standard pulse oximeter will show adequate blood oxygen---a CO-oximeter is needed to show CO poisoning.)

It would be nice to know the traffic situation on that road and whether other runners noticed fumes, or got symptoms like "headache, nausea, malaise, and fatigue" after passing that point. If you had splits data you could show if other runners slowed after this section.

That wiki link (above) shows concentrations of CO and how fast they can affect you. Take that table and the knowledge that these three (and everyone else too) are sucking in as much air as they can, and it seems plausible.

As theories go, it's pretty thin.

Nice guess Matt...but that expressway has been there every year. And I've run in lots of CO without effect; I love these ambulances parked along the race course that run their diesel engines in runners' faces...

But another coincidence, for this year only....H1N1 or Swine flu. The US just last week moved officially into "epidemic" status, with 40% of specimens analyzed now found to be positive for H1N1, and a sharp increase of those dying of the disease.

Symptoms of H1N1 include tiredness, difficulty breathing, and pressure in the chest. Could extreme exertion trigger a dangerous acceleration of the severity of this disease in just two hours? Would inexperienced marathon runners continue to push themselves beyond their body's ability to recover even tho they were experiencing tiredness, shortness of breath and pressure in their chest, just as they expected?

One of the dead was 65; only 7% of those found with H1N1 have been 65 or older....But 14% of those dying from the disease were in this age group. The CDC states that older folks with the disease, while few in number, are automatically "High Risk."

2 chitownclark: Were they registered for 1/2 Marathon? I thought they aimed a marathon distance. If so, then just desregard my last post.
2 j-man: I don't want to through any theory: there are doctors to make autopsies and police (FBI) to investigate in case it needed.
If they aimed a 1/2 Marathon (?)-they just were pushing hard at finish.

The results page shows all three of them in the half marathon. You have to search by name.

Would autopsies show evidence of cedarcreek's proposed cause of death?

Yes.

A news story with some relevant statistics about number of runners, deaths, etc http://www.google.com/hostednews/ap/article/ALeqM5...

Interesting, is there any runers' deaths statistics by gender? I just realized, ALL cases what I heard about involved men.

But, if it were carbon monoxide related, I would think the likelihood of carbon monoxide poisoning, strictly speaking, is absurdly low. After all, you are in an open space and moving through the air at ~10mph. The concentration is just not that high.

Mind you, I am not a doctor. I am just curious what an autopsy is going to show if the cause of death were actually somehow related to carbon monoxide associated with the expressway.

I'll still hazard that it was the usual faulty human wiring or piping failing under load.

A not quite hypothetical question:

If you were a 65-year-old who has run many marathons, and you were running a half marathon---If your first six miles were 53:27, what is a reasonable split for the second six miles? What would be a decent negative split?

2 cedarcreek: Strat is ussually faster, then there is a slower mid-toward the end part. I think the second 6 miles should be around 54.00-54.30

A recent (2002) sudden death at the Boston Marathon was of a woman, Cynthia Lucero, of hyponatremia. See http://www.restonrunners.org/special/hyponatremia/... for the story.

a related NPR story seems to suggest that too many people are attempting long running events with a body not fully prepared for it

http://www.npr.org/templates/story/story.php?story...

...too many people are attempting long running events with a body not fully prepared...

Yes, but that, carbon monoxide, and other factors mentioned are not unique to this year. The question is: why would 3 runners die within 15 minutes of each other THIS YEAR ONLY? As SV pointed out, the chances of this happening are 1:15 000 marathons, or 0.007%.

The only cause so far identified, unique to this year alone, is the H1N1 epidemic.

As SV pointed out, the chances of this happening are 1:15 000 marathons, or 0.007%.

Careful. Are you sure this probability calculation was done correctly?

2 jjcote: As I mentioned above (2009-10-20 16:28:41) the calculation was based on a FALSE notion that those 3 runners died on an ordinary segment (from 11.5 to 13 miles) while running Marathon (actually, they didn't - they ran HALFmarathon). Besides, there were two other inaccuracies: 1. The rate of fatalities /per starter on marathon is not 1:30,000 (as I thought), but even smaller - 1:125,000.
2. I calculated the probability to occur such an event on a certain given section of 2 miles, while I had to calculate the probability of happening this on a whole marathon distance.
P.1 reduses the chances by 4, p.2 increases them by 13. So if my original notion was correct, the chances to happening this whould be 1:4600 marathons. [assumption: y=c (where: y - chance to die on certain mile; c -constant); for this particular case (11.5-13 miles) we'll have almost a same result if y=ax (y - chance to die on certain mile; x - the certain mile, a- coefficient]

But the section from 11.5 to 13 miles on HALFmarathon is NOT an ordinary one. This is a very special final one-when runners are tired and try to push hard.

There are many ways of calculating probabilities in these cases, and pitfalls in interpreting the numbers. One interesting issue is the following. One can calculate the probability that three particular runners (specified in advance) would die 15 minutes apart in the Detroit half-marathon (astronomically low, but not relevant to whether we should assess it as a coincidence). One can calculate the probability that some three runners in the race would die within 15 minutes of each other (still very, very low, but not so astronomical; but also not the right probability to consider). Or one can calculate the probability that three runners in some half-marathon, sometime (within our sphere of news reporting?) would die within 15 minutes of each other (maybe not all that low (given the number of half-marathons that have been run within our sphere of news reporting), but arguably the relevant probability to consider in comparing the coincidence hypothesis with, say, my homicide by poisoned water hypothesis).

like: what is the chance of someone dying at exactly 9:02, and during a marathon? Probably some heavy conspiracy that Obama was behind, so he can invade Pakistan!

Perhaps something was indeed rotten in the state of Denmark, the poisoned water theme is plausible: some saboteur/weirdo having fun - perversity abounds.

PBricker, it's worse than that, you should consider the probability that three people in some sport die in some unexpectedly small period of time... like the orienteers way back when...

It's all due to the sad state of American healthcare, which makes money on treating catastrophic illnesses and ignores prevention so that treatment would be the most expensive one possible. When people with legitimate health suspicions are told to take anti-anxiety pills, bets are not too many marathon or half-marathon runners will have had a full cardio check-up with stress test, which is needed to discover some common conditions that can result in sudden death during the exercise.

I think sometime chance and luck are to blame rather than a pattern.

Last month me and my wife went to a fashon runway show (please don't ask why I have agreed to be subjected at that!!!) there were 300+ people in attendence. At the entrance everyone was encouraged to fill a raffel ticket for 3 prises 250, 500 and 1000 dollars. I assume more than 2/3 filled out one. The tickets were in a big urn and each of the three winning tickets was picked by a different model after mixing and shaking the urn at the end of the show.
I won the 250$ certificate and my wife won the 1000 $ certificate.

So by pure luck we won 2 out of 3 prices from at least 200 - 250 people. What's the chance for that:
1/250 x 3 (I have 3 chances to win a ticket) x
1/250 x 3 ( and my wife has 3 chances to win one of the prices)

~1/9000 chance if 3/4 have filled raffle tickets.

So coincidences do happen (and my wife now walks around with an armani shirt and pants :) )

But didn't she do that already? ;)

Nikolay...

First, congratulations on your family's good fortune. But, the chances of something like that happening are greater than you estimate. You estimated the chance that you and your wife would win two prizes. But, if we assume that the 200 people represent 100 couples, then there are 100 times as many ways that SOME couple could have achieved that feat - or a chance of slightly over 1% (using your assumptions). Still a long shot, but not as much as you suggest.

This points out a difference is estimating risk/evaluating coincidence that many people make. The chance of a coincidental occurrence happening "here, now, to me (or a loved one)" may be very small. But the chance of it happening "at all, to someone else" is much greater.

I don't know anything special about the Detroit deaths, but there is a difference in saying that it is "odd that something like this occurred" and saying that it is "odd that it occurred to those three people in that race".

The key lesson is, as you note, that coincidences do happen - AND that they happen much more often if you remove the personal connection element.

(To me, most of the mathematical analysis in this discussion has focused on the correct scenario, but some of the verbal analysis seems to have strayed towards the personal.)

@Clem:
thanks god she doesn't !!!

My sympathies go to the families of the three Detroit victims. However with regard to many of the above posts one would think that in a country that has people take off their shoes before they board an airplane officials would be looking at all possibilities beyond coincidence for those three deaths.
H1N1 okay, CO ok but lets imagine that the next great terrorist plot against the USA will be deaths caused by poisoning of hundreds or thousands of runners in a great marathon like the NYC or Boston. They would want to try out thier method first by slipping a few samples in to the drinks at a feed station at some marathon. If they slipped this concoction that acted to make it look like the victim had suffered a heart attack in to half a dozen water cups they would find that one runner dropped the cup, two would splash the fluid on their head and three would drink it resulting in their deaths.
I hope it is just that I am watching too much 'House', CSI's and NCIS but for the sake of runners in future marathons I hope that complete toxicology screens have been done on those three unfortunate runners in Detroit so that poisoning can be ruled out.

OMG...let's not start another Tylenol scare....

...that resulted in everything from yogurt to airline meals being "Sealed for your protection - reject if seal broken." How much fun will those water stops be then...trying to break a difficult seal while running 7-minute miles?

Or, even worse, no water stations at all...from golf courses to 5k's to A-meets.

The Tylenol killer was never found. But nevertheless, it IS true that James Lewis, the only real suspect and the man that spent 15-years in jail for an extortion attempt related to the Tylenol killings, has been released, and is now living as a free man in Massachusetts.

I think one possibility to consider is use of EPO. This is a topic that surfaced in the orienteering community about 15-20 years ago with a number of deaths on the Swedish O-team which were officially attributed to Taiwan flu, but there was a lot of speculation that it might have been excessively thick blood from EPO overdose. I would assume in a case like this that autopsies would get done on all three runners, and if there were indications of either poisoning or drug use it will show up.

Several have speculated as to probabilities, but it's not hard to run the actual numbers. One could quibble about any of these, but we're just looking for some idea of whether this is anamolous so, approximations will do.

Age-adjusted death rate for participants: 4x10E-3
Death rate for a 15-minute period: 1.1x10E-7
Chance of 3 in a given 15-minute period: 1.5x10E-21
Ways to pick three from a field of 5000: 7x10E11
Chances of seeing this in a specific marathon (20 15-minute periods): 2.2x10E-8
Similar sized marathons in last 20 years: 10000
Probabilty of seeing this in last 20 years: 0.0002

That's what those of us who have published epidemiological studies call REALLY FRIGGIN SIGNIFICANT. Somethin's up.

I'm still not buying it. But I'm only a part-time actuarial assistant, so I checked with a full-time actuary. He ran some quick numbers, and the way he calculated it, based on the probability of death in a marathon being 0.8 per 100000 participants, using a Poisson distribution, you might expect to see three deaths in one race of 18000 participants about once every 2500 events.

There are a lot of ways to crunch numbers, and a lot of ways to do it wrong. Different assumptions are the first step toward different results. Each reader can decide which calculation he believes, and can use that information to decide whether to look for an underlying cause for these deaths. Personally, I'm not persuaded that there's a likely connection.

It is interesting that everyone calculated probabilities of similar orders of magnitude. From .00007 to .0002 to .0004. (Sure ~6X different, but that isn't so much.)

But, I am still a skeptic.

No. The number I listed is 0.00045 for each event. ebuckley's number is 0.0002 for it occurring in the last twenty years.

Oh yes. That is quite different. Sorry.

2 ebuckley: This happened on HALFmarathon--on final 1.5 miles and after the finish line. One shouldn't treat that section as an ordinary one out of 8 others. I think, that is the most extreme part of halfmarathon course. On other hand, the death rate on halfmarathon is much-much lower than on marathon. For instance, I can't recall any fatalities on NYC halfmarathon series (Mnhtn, Brnx, Brkln, Queens, StIsland and City) for last 3 years (about 40,000 participants each year).
So, the whole thing still looks for me very-very odd.

2 gordhun: That thought already crossed my mind--even before Houses. I hope the autopsies' results will be released before ING NYC Marathon.

In comments on the original news stories a couple people alluded to reports that in addition to the deaths "hundreds" of people also became ill. I haven't found any confirmation. Anyone know if it is true?

That would be more more of a red flag, if in fact there were hundreds of people more ill than usual after a long race. Once you have a couple of deaths on your hands, though, you might notice the typical effects of running a long way more than you would otherwise.

Definitely. I would be less of a skeptic in that case.

Actually, I have no problem reconciling JJ's numbers and mine. The original skeptisism (as I read it, anyway) was that the marathon had nothing to do with the deaths. In such a case, you'd have to take the age-adjusted death rate across all activities. JJ's actuary did what all insurance types do when assessing risk of an event and adjusted for the inherent increase in risk due to participating in a marathon. Also note that he used a MUCH larger field. My calculations used marathons of 5000 or so because that's a much more common number of people to see in a marathon. Obviously, if you triple the field size, you triple the likelihood of any given number of deaths. And, yes, given the size a Poisson model does have advantages over Bernoulli, but we're just doing SWAG's here, so that seems uneeded complexity. Also note that the bit about this occuring in the first half is relevant if using JJ's numbers, but not if using mine (since the activity itself is not considered).

Lies, Damn Lies, and Statistics, but I think it is pretty clear that this is an anomalous event.

Isn't the Poisson a limiting case of the binomial, which is itself a special case of a Bernoulli?

I do like using the Poisson when we are discussing random events in a time context.

Strange how everyone is focused on the absolute probability that it happen by coincidence. It doesn't matter how unlikely the event was. It happened. What matters is comparative: given that this event occurred, is the coincidence hypothesis more likely than the conspiratorial (and causal) hypotheses combined? It's because I think the conditional probability of the coincidence hypothesis, given that the event occurred, is more than one-half that I think it was probably a coincidence. Because I don't think it is close to 1, I have a non-negligible degree of belief that one of the conspiratorial (or causal) hypotheses is true.

OMG! A Bayesian has entered the room! Let the Frequentist assaults begin!

If the hypothesis is that running in the event itself was the risk factor that led to the deaths, I'll definitely buy that. If three people died of heart attacks while sitting in the audience of a particular basketball game, I'd consider that to be a more unusual event.

Aren't we all Bayesians?

Keynes was, if you put stock in his witticisms. That is one of his more appealing characteristics.

Who needs a university education when you can learn everything on Attackpoint? :-)

I wonder why our sport have a reputation as a nerd-magnet? Never mind, I'm an orienteer so I'm enjoying the debate.

Eric wrote: "Obviously, if you triple the field size, you triple the likelihood of any given number of deaths"

Self-evidently, one should always beware of statements that begin with the words 'obviously' or 'clearly'.

Consider a non-commutative field of two runners...

I interpreted Eric's statement as 'for large fields and small probabilities of deaths iid over runners conditional on the race' for which it is indeed approximately true. (That is, I posted a snarky comment about the probability of 10000 deaths in a 5000-runner race, then had the unusual - for me - good taste to delete it.)

Actually, I'd drop the iid part. As long as the two poplations are similarly stratified, there's no problem with each runner having a different probability. I'm not even sure independence is a big issue for the field-size statement to stand. Of course, it would change the alpha-risk of the multiple death anylysis significantly if there was a correlation among runners. (Does knowing that others are falling ill/dead make you more or less likely to become ill/dead yourself? Not sure on that one.)

Hold on, I agree for the probability of a single death... but for multiple events, I don't think the probability scales linearly with the field size. I could be very wrong here, but it seems like ye are forgetting the (n choose 3) term... so for treble the field size, one gets 9 times the likelihood. Approximately. Assuming probability << 1/fieldsize.

No, you're right, it's not linear. Oops. But you are still not quite right: for three deaths, (n choose 3) actually scales as field size cubed, so, three times the field, 27 times the likelihood of three deaths. But this does assume (1-p)^(field size) is close to 1, which, as you say, requires p very small.

yep, of course... post-post-prandial-seminar-induced tiredness :)

In determining probabilities, I think it is proper to temperature-adjust, which no one has done. A very disproportionate number of marathon deaths have occurred at high temperatures, and are not relevant here.

I am a proud Bayesian. Frequentism, as an analysis of probability, is bankrupt. Though, of course, frequencies are sometimes the best evidence we have for our probability judgments.

Hee, hee, well my degree is from Cornell where the only good Bayesians are dead Bayesians. I had one prof who couldn't even bring himself to writing the prior on the board. He put little tildas and primes all over the place to indicate that this was just a "model" and not really what was going on.

I'm an engineer, not a zealot, so I use whichever seems to work best in a given situation. My current side project is very much Bayesian.

All of a sudden, this conversation has taken a detour to resemble something from Star Trek:

>I'm an engineer, not a zealot
reminds me of
"I'm a surgeon, not a psychiatrist." and
"I'm a doctor, not a moon shuttle conductor/bricklayer/whatever."

But I left off the obligatory "Dammit, Jim!"

Not having read about this from a philosophical angle, I wonder if Hajek's critique is considered definitive? Some of his arguments come across more as cavils and hectoring than knockout punches. But, maybe the strategy of 30 (or 15) criticisms is one of assassination by paper cuts?

The arguments may not all be of equal weight, but they aren't exactly paper cuts etiher: the falsity of Frequentism is vastly overdetermined, both mathematically and philosophicallly. I would say that included among the 30 arguments Hajek gives, one finds versions of most the arguments that today would be taken to be definitive. Some were given long ago by well-known opponents to Frequentism such as the much-beloved Keynes, who spent a decade of his life developing a "logical theory" of probability (now almost universally rejected).

The "big picture" problem with Frequentism is this. Frequentism grew out of the positivist/operationist philosophy of science which was dominant in the first half of the 20th century. On this view, a sort of rabid empiricism, concepts, including the theoretical concepts of science, are meaningful only if they can be given operationist definitions, definitions in terms of observable measurement procedures. Positivism/operationism of that sort has been thoroughly discredited; it confuses the meaning of scientific statements with what would count as evidence for the statement. Frequentism is an instance of this operationist approach, and suffers the same fate.

Having read the paper in its entirety, I agree I was too quick to dismiss its cumulative force. I thought it finished strong, so to speak.

I was so impressed that Clem read a philosophy paper to the end, that I figured I should read Eric's side project on developing a communication device for ALS sufferers. Very interesting! I doubt it could do much for Hawking's communication with, say, Penrose (amusing, though, to see what message it suggested for the string 'black hole'); but I suppose even Hawking has to pee.

Yes, reading Eric's thing is my next project. But, first I need to get some stuff done!

The point of all this statistical number-crunching is to determine if the 'events' are likely or not likely to be coincidence. I'll leave that to the mathematicians.

If the answer is 'not likely' let's discuss conspiracy theories again.

A mass poisoning reminiscent of the Tylenol scare was done just recently at Harvard.

http://news.bostonherald.com/news/regional/view/20...

I work in the auto industry and did some work on azides back in the early 80's and have some knowledge of the chemical and its hazards. http://www.informaworld.com/smpp/content~content=a...

Interestingly, the biological effects include lowered blood pressure and heart rate, among other not so pleasant effects. Also "Symptoms are often compared with those of cyanide."
http://en.wikipedia.org/wiki/Sodium_azide

How would forcing lowered heart rate and blood pressure play out on someone under extreme physical exertion? Maybe not a good combination.

Sodium azide was the inflator in airbags into the 90's but has been phased out. I would guess, though, that it could still be easily obtained from junkers, or if you're so inclined, from stealing airbags. One airbag contains perhaps 50 grams more or less.

Azides can be detected from autopsy lab tests, although I don't remember if there is a limited window of detection as result of a slow decomposition reaction in the blood plasma.

I aint a lab tech, so I don't know if azide would be detected in routine screening after an autopsy. Must it be suspected, then tests specific to azide run? Or does it come along for the ride with all the others, like cocaine. If it must be suspected first, then it could be missed. BTW, that was a nice piece of chemical detective work by the Harvard investigators .

Extraplating from the oral LD50 for rats, the human oral LD50 is about 2 grams for a 150lb man. Sodium azide is highly soluble in water and 2 grams is about the size of 1/4 sugar cube. That's not much and could easily be slipped into a drink, and may not be noticed.

Anyway, just speculating. It's been done only a couple months ago.

From November 10th:

Runner, 65, died of natural causes in Free Press marathon

If you're going to read one of these, read the Dayton Daily News article. It mentions "cardiac dysrhythmia" (wiki) for the two younger men, where the DFP just says "heart attacks".

{update: DFP now says, "Both men suffered cardiac dysrhythmia and died of heart attacks..." link}

Detroit Free Press: 3 Detroit marathon deaths all traced to natural causes, Nov 30, 2009

Dayton Daily News (AP): Heart abnormalities blamed in 2 runners' deaths, Nov 30, 2009