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Author Topic: Is there an actuary in the house ?  (Read 3050 times)

Offline RD

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Is there an actuary in the house ?
« on: 31/03/2012 17:49:25 »
What are the odds of five coffin-dodgers independently failing to live up to their name within a period of two days in a nursing home which has had forty residents ? ...
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Tayside Police is making inquiries into the deaths of five elderly people at a nursing home in Broughty Ferry earlier this week.

"The force was advised on Tuesday, that five residents - a man aged 74 years old and four women aged 81, 88, 90 and 91 years old - had died during Sunday and Monday.

"While there are no apparent suspicious circumstances surrounding any of the deaths, Tayside Police is investigating the full set of circumstances
http://www.scotsman.com/news/elderly-residents-deaths-probed-1-2208878

It seems an astronomically unlikely coincidence if they are independent events rather than linked, (e.g. via infectious disease).
« Last Edit: 31/03/2012 18:09:52 by RD »


 

Offline Geezer

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Re: Is there an actuary in the house ?
« Reply #1 on: 31/03/2012 18:30:07 »
I suspect it's not all that unlikely. After the upper 80s, the croak factor must be pretty high.
 

Offline RD

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Re: Is there an actuary in the house ?
« Reply #2 on: 31/03/2012 19:13:14 »
I suspect it's not all that unlikely. After the upper 80s, the croak factor must be pretty high.

From the stats here the odds of an eighty year old snuffing-it in a particular 2 day period in the next year would be about 1 in 2800.
So what's the odds of five such deaths occurring in a two day period if they were independent unrelated events ?
« Last Edit: 31/03/2012 19:46:46 by RD »
 

Offline Geezer

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Re: Is there an actuary in the house ?
« Reply #3 on: 31/03/2012 19:34:24 »
Between 80 and 88 it shoots up by about 2.5. Pretty soon you get to the same point as birthdays.
 
I forget the number, but the odds of two people out of a group of 40 sharing the same birthday is really good. This is slightly different of course because it's not in a single year, but it's not all that different.
 
Wull ra Broughty Ferry Polis get ra Carnoustie Polis tae help them dae thir sums?
« Last Edit: 31/03/2012 19:36:01 by Geezer »
 

Offline CliffordK

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Re: Is there an actuary in the house ?
« Reply #4 on: 31/03/2012 20:01:14 »
It certainly is worth investigation.  However, people dying in a nursing home should not be treated as a surprise.

There are a number of different types of individuals in nursing homes.  Some long-term residents, perhaps with mental disorders.  Some residents in for acute short-term recovery care following an accident such as  recovery from a broken bone, but often still at great risk.  Some hospice care residents are admitted for their "final days", and often live less than a month.  Certainly, many of the 80 yr olds in the nursing home would not be considered "healthy".

So your stats for many of the 80 yr old patients in the nursing home snuffing it on a single day might be closer to 1:30. 

Here are the stats for the "Birthday Problem".  It would get much more complex for say 5 people in a group of 50 sharing the same birthday.  However, if one took 10,000 nursing homes of 50 individuals, it would not be surprising to have several nursing homes with large groups of people sharing the same birthday.  Of course birthdays and death dates are different, because one is not only interested in the day  of the year, but also which year it happens to occur in.

My guess is that several of these individuals (not necessarily all) died from a single cause, perhaps a bad case of the cold or flu, or even an unfortunate case of food poisoning.  Of course, it may not hurt to re-evaluate care procedures and infection control methodologies.

BTW:
How many 80 yr olds die within one month of hospital admission?  One week?

Does Scotland have Right-to-Die/Assisted-Suicide legislation?  Perhaps the individual deaths were actually connected.

Ahh.. found the "Right to Die" notes.
http://en.wikipedia.org/wiki/Assisted_suicide

Apparently there was a right to die bill that was defeated in Scotland a couple of years ago.  A new bill is in in the early stages of development.
http://www.scottish.parliament.uk/gettinginvolved/46127.aspx

Oregon and Washington have now passed Right to Die laws in the USA, and Montana apparently has no legal provisions against it.
« Last Edit: 31/03/2012 20:20:31 by CliffordK »
 

Offline Geezer

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Re: Is there an actuary in the house ?
« Reply #5 on: 31/03/2012 20:44:15 »
and Montana apparently has no legal provisions against it.

Montana has few legal provisions against anything   ;D
 

Offline RD

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Re: Is there an actuary in the house ?
« Reply #6 on: 31/03/2012 20:46:12 »
... closer to 1:30. 

an accumulator on five independent unrelated 1:30 events is 1: 24,300,000


Does Scotland have Right-to-Die/Assisted-Suicide legislation?

No, but a similar effect can be achieved by moving to Glasgow city centre :) ...

Quote
For here in this multi-deprived inner city area, the average life expectancy of a male is just 53.9 years
http://www.guardian.co.uk/society/2006/jan/21/health.politics
« Last Edit: 01/04/2012 11:33:45 by RD »
 

Offline CliffordK

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Re: Is there an actuary in the house ?
« Reply #7 on: 02/04/2012 02:22:56 »
... closer to 1:30. 
an accumulator on five independent unrelated 1:30 events is 1: 24,300,000

You've calculated 530=24,300,000, or the total number of ways that 5 people can die in a 30 day period with a chance of 1:30 to die each day.

However, you have over estimated the number significantly.  For those 5 individuals, there would be 30 different combinations that they could die on the same day (all on the first of the month, all on the second of the month, and etc...).

So, considering only 5 individuals, you've over-estimated by a factor of 30, and our actual number would be:
24,300,000/30 = 1:810,000.  Then consider 12 months, or 365 days a year.  So, let's divide that again by 12, and we get:  1:67,000 in any year.  If one considers the 16,100 US nursing homes, we end up with a 1:4 chance this happening in the USA in any year.

Let's consider nursing homes.

In the USA, there are about 16,100 nursing homes with about 1,492,200 residents, or about 93 residents per nursing home, or about 0.5% of our population.

So, rather than doing the statistics on only 5 patients, you need to consider all 93 patients per nursing home, and the thousands of nursing homes in any country.

I got lost on the statistics considering that as beds are emptied, they are refilled, length of stay, severity of the condition, hospice patients, and etc.

My guess is that these 5 patients has varying underlying conditions that made them unable to stay at home.  Emphysema, CHF, Liver or Kidney failure, Cancer, Broken Bones, Mental deterioration, strokes and vascular disease, etc.  They may have had DNR orders, which can also limit the medications and treatments that a patient will receive.

Then, on top of that some of them might have caught a common infectious disease (cold, flu, what-not), that sent them over the top.

So, one issue would be whether the nursing home had adequate infection control.

However, this is likely little more that a slight statistical anomaly.

Consider our stats above.  If a nursing home had 90 patients, each with an expected lifetime of less than 30 days, then one would expect about 3 to die a day, or 6 to die in almost every 2-day period.  That would be a bit high for a death rate, but not impossible for some hospice patient populations.  I believe my grandfather's stay in a nursing home was about 30 days from admission to death, and we got home-health care and hospice for my grandmother about 2 weeks before her death.
« Last Edit: 02/04/2012 02:24:52 by CliffordK »
 

Offline Geezer

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Re: Is there an actuary in the house ?
« Reply #8 on: 02/04/2012 03:25:28 »
I think it's a racing certainty.
 
2 out of 40 within 48 hours is probably quite common.
 
3 out of 40 within 48 hours is unsual, but not unexpected.
 
4 out of 40 within 48 hours may be a bit of a surprise, but it's likely to happen.
 
If if happens again the following week, it's a bit fishy.
 

Offline Ćthelwulf

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Re: Is there an actuary in the house ?
« Reply #9 on: 02/04/2012 06:41:05 »
I suspect it's not all that unlikely. After the upper 80s, the croak factor must be pretty high.

lol... charming Geezer.
 

Offline Geezer

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Re: Is there an actuary in the house ?
« Reply #10 on: 02/04/2012 08:40:40 »
I suspect it's not all that unlikely. After the upper 80s, the croak factor must be pretty high.

lol... charming Geezer.

Nasty, isn't it? But sooner or later we all realize that it's not going to go on for ever (in its present form, at least), so we better decide what we really want to do with what's left.
 
I'm still trying to figure out the second bit.
 

Offline RD

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Re: Is there an actuary in the house ?
« Reply #11 on: 02/04/2012 15:17:35 »
« Last Edit: 02/04/2012 15:20:39 by RD »
 

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Re: Is there an actuary in the house ?
« Reply #11 on: 02/04/2012 15:17:35 »

 

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