STUMP » Articles » Mortality with Meep: How Many Deaths Before it's No Longer a Coincidence?

Mortality with Meep: How Many Deaths Before it's No Longer a Coincidence?

by meep

19 June 2019, 06:24

Not about Goldfinger, nor a new version of Dylan.

I will start with the most recent story I saw:

New Jersey man, 55, is latest case of tourist’s death in Dominican Republic

The State Department confirmed to Fox News the latest American tourist to die in the Dominican Republic — reportedly a New Jersey man whose body was found on his hotel room floor.

Joseph Allen, 55, of Avenel, New Jersey, was found dead last Thursday morning, WABC reported.

….

Allen had complained about being hot at a pool and left to take a shower; he went to bed early and was found dead the next day, the report said.
….

The popular Caribbean vacation destination has been grappling with a rash of deaths of U.S. tourists in their hotel rooms at various resorts. Families of the tourists said they were generally in good health.

Of the seven other recent deaths that have become publicly known so far, Dominican investigators said five were caused by a heart attack. In the case of the other two — an engaged Maryland couple found dead on May 30 — a final report on the cause of death was pending.

In nearly all of them, officials said there were signs of pulmonary edema — a condition in which the lungs fill with fluid. The tourists ranged in age from 41 to 67.

The Dominican Ministry of Tourism has denounced what it has called an overreaction to what it characterized as coincidental.

Well, they would say that… but perhaps it’s true.

Let’s estimate!

FIGURING OUT THE PROBABILITIES

Obviously, a certain number of people are going to die while on vacation each year, and some may have trouble after drinking a bit much.

So, what would be the number of people dying before it’s justified to think it’s more than just coincidence?

This story says 9 deaths: Timeline of deaths – goes back approximately one year.

How many Americans visit the Dominican Republic each year?

According to Wikipedia, about 2 million Americans per year, but those people probably stay about a week each. I need to turn this number into people-years, aka, I divide that 2 million by 52 weeks (assuming 1 person stays about one week) in order to get the right number for “exposures”, that’s about equivalent to 38,500 people each staying one year to get exposure units.

So 9 people out of 38,500 people-years is an annualized q_x of 0.023%.

Let’s look at general mortality stats for Americans. At age 40, for men, mortality rates are 0.24% and for women, 0.14%.

Even at that relatively young age, the base mortality is ten times higher than the 9 deaths in DR.

Now, to be sure, the Social Security tables include people who have cancer and other illnesses, and people in very poor health are unlikely to be traveling to the DR for vacation.

BUT.

9 people out of the equivalent of almost 40,000 people is not really all that high of a mortality rate, even for ages 40-60.

It could really be coincidence.

Yes, there were some sudden deaths, and yes, DR doesn’t have great facilities for doing autopsies, etc.

There could be foul play, but 9 deaths do not necessarily show that. One could have foul play with only one death, sure, and there can be totally natural causes (like salmonella) for mass sicknesses.

Unfortunately, DR has a PR problem on its hands even if the math shows it’s a coincidence.

INTERLUDE: WIKIPEDIA QUALITY CONTROL

While perusing the Tourism to DR article, I noticed the following text – and I’m screenshotting it, because you have to see what this looks like to appreciate it:

That is sitting in the actual wiki article, not the Talk page.

That is frickin’ hilarious to me – the strikeout, the editorial comment, etc.

(Want me to edit? Pay me.)

HOW MANY WOULD IT TAKE?

Okay, statistically, how many “excess deaths” would it take before we can say it’s not a coincidence?

I’m going to use some very rough numbers, so the estimate will be more order-of-magnitude.

Given a range of ages are named, and the age range of visitors to the DR is probably not uniform, let’s just take a broad average of mortality rates.

We’ll start with the 38,500 people in “exposures”. The mortality rates for the age 40-60 group range from a low of 0.14% to a high of about 1%. For rough estimates, let’s go with 0.5%. (Yes, I know people both younger and older go visit the DR. This is a rough estimate.)

So we start with a base – how many American visitors would we expect to die over a one-year period? That’s 0.5% * 38500 = 193 people (I do not work with fractional people here). So we’re already starting with almost 200 people dead as expected.

How much more would it have to be, say, that we’re in a 1% situation? There are a few ways for us to figure this. Check out my article on approximating a problem like this.

I’m going to be lazy and just use a built-in function for Excel, and determine when we’re in a 99%+ situation: 225 people dead.

So, if 225 Americans died in the DR in one year, I might start to get suspicious.

That’s about 225-193 = 32 “excess” deaths to be an anomaly.

Of course, this is all dependent on my exposures and base estimate for mortality. It can be due to age mix I should expect more (or fewer) deaths.

If the exposure units really should be something less, like 20,000 (say, people average shorter than a week per visit), this is what it looks like:

How about what if the base mortality rate is half what I used above?

How about both lower exposure and lower mortality rate?

We’re still looking at dozens of people dead before the statistics alone indicate something untoward.

THE MATH DOESN’T MATTER WHEN IT COMES TO PEOPLE

Anyway, yes, the DR official spokesperson is correct: this may just be a coincidence for 9 deaths.

However, people are bad at determining probabilities, and small probabilities (as with death rates) are the most difficult for humans to treat with ‘intuitively’. People are especially off in estimation when death is involved.

Either way, the DR folks need to do some PR work because it can get away from them even if it really is coincidence.

I have a lot of sympathy for the DR folks, because my own gut reaction had been “Whoa, what’s going on in the DR?”

And then I thought, “I should be able to calculate if this is suspicious.”

And then: “Only 9 deaths? Well, if depends on how many people visit, and the age mix…”

It took me a lot of time to work through the probabilities to get a handle at what would be an unusual number of American deaths in the DR over one year.

You cannot expect other people to do that. It’s not necessarily obvious whether 9 deaths are a lot or not. Or whether to be suspicious of sudden deaths. My own father died of a heart attack suddenly, age 38, and that was very unusual, and yes, there was an autopsy. We investigate these things to see if anything is untoward, especially when it’s unexpected. It sounds like the DR doesn’t have the facilities to do proper investigations, which is partly what’s spurring the suspicions. It may turn out to be just coincidences with no easy way to show that.

People see patterns even when there’s none there, and patterns related to death are one of the strongest pattern-formers in our brains. So I can’t really blame even the media in this case – this is an extremely strong cognitive bias, and I had to sit down & do some figuring. FWIW, I have no idea what the total number of American deaths in DR was over the past year – these are 9 deaths we have heard about.

Recent media coverage:

So, I didn’t see it in the stories about the high schoolers that they were drinking, but the drinking age in DR is 18, so I’m going to just say they were drinking alcohol.

Now, lots of people get sick at these sort of resorts… because they drink too much.

It may turn out that the booze at specific resorts had stuff other than ethanol in it – methanol poisoning is still pretty common in places where regular booze is considered too expensive.

Anyway, even if nothing actually untoward is going on in the DR, they need to deal with the PR issue, partly by making sure the deaths are properly investigated even if the country itself doesn’t have the proper resources to do so. It sounds like American officials are getting involved, so I hope this gets cleared up soon.

STUMP » Articles » Mortality with Meep: How Many Deaths Before it's No Longer a Coincidence? » 19 June 2019, 06:24

Mortality with Meep: How Many Deaths Before it's No Longer a Coincidence?