4 ms·

But even the small counties have populations in the several hundreds or thousands, right? Outliers that die at 33 or 103 affect the average little when you have

by flexie 9y ago

But even the small counties have populations in the several hundreds or thousands, right? Outliers that die at 33 or 103 affect the average little when you have a population of 2,000.

deleted 9y ago
[deleted]
generj 9y ago
You'd think that, but the US has about 724 deaths per 100,000. In a county with fewer than 10,000 people that leaves only about 72 deaths per year. Loving County in Texas has 112 residents. "35 counties have a population under 1,000; 307 counties have a population under 5,000; 709 counties have a population under 10,000" [0]. I haven't read the paper, so I don't know their exact methodology but if they just took a snapshot in 1980 and then in 2014 a county of 10,000 would only be looking at about 145 deaths total. That's small enough that it's pretty possible for outliers to have a big impact. In a county of 1,000 there are only 7 deaths a year, so if you only look at two years that's a total of 14 deaths. It doesn't take a lot to jostle the numbers when you don't have many observations. In any case, this isn't the main contributor here, as pointed out elsewhere. But it is a good thing to be aware of whenever county level statistics are provided. [0]https://en.wikipedia.org/wiki/County_(United_States)#Population https://en.wikipedia.org/wiki/County_(United_States)#Populat...
- itissid 9y ago
  It seems they are being smart about using counties: "All analyses were carried out at the county level. Counties were combined as needed to create stable units of analysis over the period 1980 to 2014, reducing the number of areas analyzed from 3142 to 3110 (eTable 1 in the Supplement). For simplicity, these units are referred to as “counties” throughout." They also use https://en.wikipedia.org/wiki/Small_area_estimation https://en.wikipedia.org/wiki/Small_area_estimation which seems like a way to deal with the counties with small sizes. And from what I can tell they are using hierarchical models that should have some regularizing effect from larger populations.
tmalsburg2 9y ago
(See edit below.) Intuitively what you say makes sense. However, I just ran a simulation in R based on census data (actual county sizes from [1]) and the result is that you do get by-county age differences of up to ~17 years just by chance. These bigger differences do not occur often but the assumptions I made in the simulation are fairly conservative and the true random variation could easily be bigger. So 20 years does not seem absurd. [1] https://factfinder.census.gov/faces/tableservices/jsf/pages/productview.xhtml?pid=PEP_2015_PEPANNRES&src=pt https://factfinder.census.gov/faces/tableservices/jsf/pages/... In the spirit of open science, the code for the simulation: library(tidyverse) read_csv("co-est2016-alldata.csv") %>% filter(SUMLEV=="050") %>% select(county=CTYNAME, pop=POPESTIMATE2016) %>% group_by(county) %>% mutate(age = mean(rbinom(pop, 100, 0.7))) -> d range(d$age) ggplot(d, aes(age)) + geom_histogram() Running the simulation repeatedly yields maximal differences between counties between 16 and 19 years. EDIT: False alarm. I incorrectly assumed that census data sets uses unique identifiers for counties and that introduced a bug in the simulation. After correcting it, the simulation shows that random variation indeed explains only very small differences in life expectancy of about one year. Corrected simulation code below: read_csv("co-est2016-alldata.csv") %>% filter(SUMLEV=="050") %>% mutate(county_id = 1:n()) %>% select(county_id, county=CTYNAME, pop=POPESTIMATE2016) %>% group_by(county_id) %>% mutate(age = mean(rbinom(pop[1], 100, 0.7))) %>% ungroup -> d range(d$age) Life expectancy as a function of county population: http://imgur.com/a/0LgGZ http://imgur.com/a/0LgGZ
- MR4D 9y ago
  Thanks for sharing! It would be interesting to know the standard deviation for counties less than say, 10,000 people, as well as the for counties larger than 10,000 people.
  - deleted 9y ago
    [deleted]
  - tmalsburg2 9y ago
    See the plot that I linked in the post above.

by flexie 9y ago

But even the small counties have populations in the several hundreds or thousands, right? Outliers that die at 33 or 103 affect the average little when you have a population of 2,000.

deleted 9y ago

[deleted]

generj 9y ago

You'd think that, but the US has about 724 deaths per 100,000. In a county with fewer than 10,000 people that leaves only about 72 deaths per year. Loving County in Texas has 112 residents. "35 counties have a population under 1,000; 307 counties have a population under 5,000; 709 counties have a population under 10,000" [0]. I haven't read the paper, so I don't know their exact methodology but if they just took a snapshot in 1980 and then in 2014 a county of 10,000 would only be looking at about 145 deaths total. That's small enough that it's pretty possible for outliers to have a big impact. In a county of 1,000 there are only 7 deaths a year, so if you only look at two years that's a total of 14 deaths. It doesn't take a lot to jostle the numbers when you don't have many observations. In any case, this isn't the main contributor here, as pointed out elsewhere. But it is a good thing to be aware of whenever county level statistics are provided. [0]https://en.wikipedia.org/wiki/County_(United_States)#Population https://en.wikipedia.org/wiki/County_(United_States)#Populat...

itissid 9y ago
It seems they are being smart about using counties: "All analyses were carried out at the county level. Counties were combined as needed to create stable units of analysis over the period 1980 to 2014, reducing the number of areas analyzed from 3142 to 3110 (eTable 1 in the Supplement). For simplicity, these units are referred to as “counties” throughout." They also use https://en.wikipedia.org/wiki/Small_area_estimation https://en.wikipedia.org/wiki/Small_area_estimation which seems like a way to deal with the counties with small sizes. And from what I can tell they are using hierarchical models that should have some regularizing effect from larger populations.

tmalsburg2 9y ago

(See edit below.) Intuitively what you say makes sense. However, I just ran a simulation in R based on census data (actual county sizes from [1]) and the result is that you do get by-county age differences of up to ~17 years just by chance. These bigger differences do not occur often but the assumptions I made in the simulation are fairly conservative and the true random variation could easily be bigger. So 20 years does not seem absurd. [1] https://factfinder.census.gov/faces/tableservices/jsf/pages/productview.xhtml?pid=PEP_2015_PEPANNRES&src=pt https://factfinder.census.gov/faces/tableservices/jsf/pages/... In the spirit of open science, the code for the simulation: library(tidyverse) read_csv("co-est2016-alldata.csv") %>% filter(SUMLEV=="050") %>% select(county=CTYNAME, pop=POPESTIMATE2016) %>% group_by(county) %>% mutate(age = mean(rbinom(pop, 100, 0.7))) -> d range(d$age) ggplot(d, aes(age)) + geom_histogram() Running the simulation repeatedly yields maximal differences between counties between 16 and 19 years. EDIT: False alarm. I incorrectly assumed that census data sets uses unique identifiers for counties and that introduced a bug in the simulation. After correcting it, the simulation shows that random variation indeed explains only very small differences in life expectancy of about one year. Corrected simulation code below: read_csv("co-est2016-alldata.csv") %>% filter(SUMLEV=="050") %>% mutate(county_id = 1:n()) %>% select(county_id, county=CTYNAME, pop=POPESTIMATE2016) %>% group_by(county_id) %>% mutate(age = mean(rbinom(pop[1], 100, 0.7))) %>% ungroup -> d range(d$age) Life expectancy as a function of county population: http://imgur.com/a/0LgGZ http://imgur.com/a/0LgGZ

MR4D 9y ago
Thanks for sharing! It would be interesting to know the standard deviation for counties less than say, 10,000 people, as well as the for counties larger than 10,000 people.
- deleted 9y ago
  [deleted]
- tmalsburg2 9y ago
  See the plot that I linked in the post above.