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Topic: 10 will get you 20?
Replies: 9   Last Post: Jan 25, 2014 5:37 PM

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David Bernier

Posts: 3,892
Registered: 12/13/04
Re: 10 will get you 20?
Posted: Jan 25, 2014 5:37 PM
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On 01/25/2014 10:58 AM, JohnF wrote:
> John <Man@the.keyboard> wrote:
>> JohnF wrote:
>>> Bart Goddard <> wrote:
>>>> JohnF wrote in news:lc00k7$k56$

>>>>> A tv news documentary touting the accomplishments of
>>>>> some medical volunteer group in Afghanistan (sorry,
>>>>> don't recall and failing to google exactly who)
>>>>> stated that, "During the past 10 years life expectancy
>>>>> has increased from 42 years to 62 years."
>>>>> Just curious, and not particularly important,
>>>>> but with what confidence can they make that
>>>>> statement? In particular, imply that any such
>>>>> measured change was caused by their efforts?
>>>>> Firstly, I'm thinking it's kind of hard to
>>>>> imagine observing that. Suppose they have the
>>>>> normal (approximation to Poisson) distributions
>>>>> for age at death for 2004,...,2013. So if the
>>>>> mean u_2004 = 42, then what's happening in the
>>>>> intervening years such that u_2014 = 62?
>>>>> That is, how does the mean age at death increase
>>>>> by 20 years in just 10 years (assuming indigenous
>>>>> population only, e.g., no huge immigrant influx
>>>>> of old people, etc)?

>>>> Probably they have a statistic that says something
>>>> like "If an infant makes it to age 1, then his
>>>> life expectancy is 70 years." Then if they cut
>>>> the infant mortalitiy rate in half (via better
>>>> clinics and fewer bombings) they bring the average
>>>> life expectancy up dramatically.

>>> Yes, that's exactly what happened, as per link in
>>> preceding followup.
>>> What this means, math-wise, is that number-of-people
>>> versus age-at-death distribution has (at least) two peaks,
>>> with an "extra" peak showing lots of people dying
>>> before age 5. So the distribution isn't normal/poisson,
>>> like I'd implicitly assumed. And that explains my question.
>>> Then the math exercise question that I was kind of
>>> asking, in the context suggested by the documentary, is
>>> as follows. Suppose the distribution were normal.
>>> Is there now any way you can introduce some public
>>> health improvements, and after 10 years claim a life
>>> expectancy improvement of 20 years?

>> That's easy:
>> 1: make everyone born after 2004 immortal apart from one weakness or
>> "Achilles's Heel".
>> 2: after 10 years, institute a policy of killing those who reach 62
>> years of age using that one weakness.

> Hmmm... have you seen the movie
> That would work eventually, but I'm not sure the LE would
> be 62 in 2014. That is, the >>measured<< LE wouldn't be 62 in 2014,
> though in 2014 you could reliably predict it would eventually
> become 62.


I wouldn't be suprized that they use mortality rates, say d_n is the
estimated probability that someone who reaches the age n won't
live to be
n+1, for n = 0, 1, 2, ... 130. Those could be estimated from
mortality trends for 2013, say. So, it wouln't follow
a cohort over 70+ years (a group of people) ...

If P_0 is a "fictitious" cohort of 100,000 live births,
all the same date and year, 1 year later there will be:

P_1 = P_0 - P_0 d_0 people alive
then 2 years later,
P_2 = P_1 - P_1 d_1 people alive

P_{n+1} = P_n - P_n d_n people alive after
exactly n+1 years.

The d_0 P_0 who die before age 1.0 are deemed to have lived 0.5 years
on average.

The d_n P_n who die after age n exactly but before age n+1 exactly
are deemed to have lived n+ 1/2 years on average.

So LE ~= [ sum_{n = 0 ... 130} d_n P_n * (n+ 1/2) ]/P_0 , with
P_0 = 100,000 (live births ).

David Bernier


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