November, 2020
Replication code for empirical example in the Appendix of “How do populations aggregate?” by Dennis M. Feehan and Elizabeth Wrigley-Field
NOTE: in order to run this code, you will have to download the life tables from the United States Mortality Database. This requires that you register (which is free).
The file you need is the bundled archive called lifetables.zip.
This analysis is based on the version of lifetables.zip
that was downloaded from the USMD website on March 21, 2019.
library(tidyverse)
Registered S3 methods overwritten by 'dbplyr':
method from
print.tbl_lazy
print.tbl_sql
── Attaching packages ─────────────────────────────────────────────────────────────────── tidyverse 1.3.0 ──
✓ ggplot2 3.3.2 ✓ purrr 0.3.4
✓ tibble 3.0.4 ✓ dplyr 1.0.2
✓ tidyr 1.1.2 ✓ stringr 1.4.0
✓ readr 1.4.0 ✓ forcats 0.5.0
── Conflicts ────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
x dplyr::filter() masks stats::filter()
x dplyr::lag() masks stats::lag()
library(HMDHFDplus)
library(patchwork)
library(here)
here() starts at /Users/dennis/Dropbox/aggregation/aggregation-code-release
Create directories for data and output
dir.create(here("raw-data"), showWarnings=FALSE)
dir.create(here("out"), showWarnings=FALSE)
# this should be whichever directory has the raw USMD data
usmd.data.dir <- here("raw-data")
# this is where we'll save outputs
out.dir <- here("out")
This chunk will ask you for your US Mortality Database username and password. Then it will download the lifetables for you.
usmd_uname <- readline("Your username:")
feehan@berkeley.edu
usmd_pwd <- readline("Your password:")
trixie
httr::GET(url = "https://usa.mortality.org/uploads/lifetables/lifetables.zip",
httr::authenticate(password=usmd_pwd, user=usmd_uname),
httr::write_disk(file.path(usmd.data.dir, 'lifetables.zip'),
overwrite = TRUE))
Response [https://usa.mortality.org/uploads/lifetables/lifetables.zip]
Date: 2020-12-16 18:35
Status: 200
Content-Type: application/zip
Size: 93.5 MB
<ON DISK> /Users/dennis/Dropbox/aggregation/aggregation-code-release/raw-data/lifetables.zip
Load the data
zipped_csv_names <- grep('\\.csv$', unzip(file.path(usmd.data.dir, 'lifetables.zip'), list=TRUE)$Name,
ignore.case=TRUE, value=TRUE)
state_codes <- c("AK", "AL", "AR", "AZ", "CA", "CO", "CT", "DC", "DE", "FL",
"GA", "HI", "IA", "ID", "IL", "IN", "KS", "KY", "LA", "MA", "MD",
"ME", "MI", "MN", "MO", "MS", "MT", "NC", "ND", "NE", "NH", "NJ",
"NM", "NV", "NY", "OH", "OK", "OR", "PA", "RI", "SC", "SD", "TN",
"TX", "UT", "VA", "VT", "WA", "WI", "WV", "WY")
# quick function to get the life table for a state
get_lt <- function(code, type='b', fmt="1x1", zipfn = file.path('raw-data', 'lifetables.zip')) {
fullpath <- glue::glue("lifetables/States/{code}/{code}_{type}ltper_{fmt}.csv")
this_lt <- read_csv(unz(zipfn, fullpath),
col_types='ccdcdddddddd') %>%
mutate(Age = HMDHFDplus::age2int(Age))
return(this_lt)
}
# read all the lifetables in
lts_both <- setNames(map(state_codes, ~get_lt(.x, 'b')), state_codes)
lts_male <- setNames(map(state_codes, ~get_lt(.x, 'm')), state_codes)
lts_female <- setNames(map(state_codes, ~get_lt(.x, 'f')), state_codes)
lts <- bind_rows(bind_rows(lts_both), bind_rows(lts_male), bind_rows(lts_female))
# save this to avoid having to re-load the data all the time
# (this is not necessary for replication, so commenting it out)
#write_csv(lts, file=file.path(out.dir, 'usmd_lts.csv'))
Number of records
lts %>% filter(Year == 2015) %>% nrow()
[1] 16983
```r
# quick function to get the life table for a state
get_lt <- function(code, type='b', fmt=\1x1\, zipfn = file.path('raw-data', 'lifetables.zip')) {
fullpath <- glue::glue(\lifetables/States/{code}/{code}_{type}ltper_{fmt}.csv\)
this_lt <- read_csv(unz(zipfn, fullpath),
col_types='ccdcdddddddd') %>%
mutate(Age = HMDHFDplus::age2int(Age))
return(this_lt)
}
# read all the lifetables in
lts_both <- setNames(map(state_codes, ~get_lt(.x, 'b')), state_codes)
lts_male <- setNames(map(state_codes, ~get_lt(.x, 'm')), state_codes)
lts_female <- setNames(map(state_codes, ~get_lt(.x, 'f')), state_codes)
lts <- bind_rows(bind_rows(lts_both), bind_rows(lts_male), bind_rows(lts_female))
# save this to avoid having to re-load the data all the time
# (this is not necessary for replication, so commenting it out)
#write_csv(lts, file=file.path(out.dir, 'usmd_lts.csv'))
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In these life tables, mx is not exactly equal to dx / Lx. We'll add a column that is.
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```r
lts <- lts %>% mutate(dx.over.Lx = dx/Lx)
Go through and calculate reldiff by age and sex when aggregation is incorrect
reldiffs <- lts %>%
filter(Year == 2015) %>%
split(list(.$Sex, .$Age)) %>%
map_df(function(asdat) {
## only look at states with at least 1 death
asdat <- asdat %>% filter(dx > 0)
direct.agg.mx <- sum(asdat$dx) / sum(asdat$Lx)
# harmonic mean of rates, weighted by deaths (correct)
hm.mx.d <- hmean(asdat$dx.over.Lx, asdat$dx)
# arithmetic mean of rates, weighted by nLx (correct)
am.mx.L <- weighted.mean(asdat$dx.over.Lx, asdat$Lx)
# arithmetic mean of rates, weighted by deaths (incorrect)
am.mx <- weighted.mean(asdat$dx.over.Lx, asdat$dx)
# arithmetic mean of rates, unweighted (incorrect)
uam.mx <- mean(asdat$dx.over.Lx)
# arithmetic mean of death rates, weighted by exposure, squared
am.m.d2 <- weighted.mean(asdat$dx.over.Lx, asdat$Lx)^2
# arithmetic mean of squared death rates, weighted by exposure
am.m2.d <- weighted.mean(asdat$dx.over.Lx^2, asdat$Lx)
# appropriately weighted cv2.mx
w.cv2.mx <- (am.m2.d/am.m.d2) - 1
# the weighted cv (not squared)
w.cv.mx <- sqrt(w.cv2.mx)
# diff in arithmetic mean weighted by deaths, relative to true aggregate value
reldiff <- (am.mx - direct.agg.mx) / direct.agg.mx
# diff in unweighted arithmetic mean, relative to true aggregate value
reldiff2 <- (uam.mx - direct.agg.mx) / direct.agg.mx
return(tibble(age=asdat$Age[1],
sex=asdat$Sex[1],
n=nrow(asdat),
direct=direct.agg.mx,
# correct harmonic mean
hm=hm.mx.d,
# arithmetic mean with wrong weights
am=am.mx,
# arithmetic mean with no weights
uam=uam.mx,
reldiff.am = reldiff,
reldiff.uam = reldiff2,
w.cv.mx = w.cv.mx,
w.cv2.mx = w.cv2.mx))
}) %>%
mutate(sex = dplyr::recode(sex,
'b'='Both sexes',
'm'='Males',
'f'='Females'))
fig.h <- 5
fig.w <- 8
am.reldiffs <- ggplot(reldiffs) +
geom_point(aes(x=age, y=reldiff.am, color=sex)) +
expand_limits(y=c(0,.6)) +
theme_minimal() +
ylab("Relative error") +
ggtitle("Relative error\nusing arithmetic mean\nweighted by deaths")
#ggsave(plot=am.reldiffs, filename='am-reldiffs.pdf', height=fig.h, width=fig.w)
am.reldiffs
uam.reldiffs <- ggplot(reldiffs) +
geom_point(aes(x=age, y=reldiff.uam, color=sex)) +
expand_limits(y=c(0,.6)) +
theme_minimal() +
ylab("Relative error") +
ggtitle("Relative error\nusing arithmetic mean\nunweighted")
#ggsave(plot=uam.reldiffs, filename='uam-reldiffs.pdf', height=fig.h, width=fig.w)
uam.reldiffs
fig.h <- 5
fig.w <- 8
relerr.plot <- (uam.reldiffs | am.reldiffs) + plot_annotation(tag_levels = 'A')
ggsave(plot=relerr.plot, filename=file.path(out.dir, 'relerrs.pdf'), height=fig.h, width=fig.w)
Plot the actual aggregate death rates
agg.pseudous <- ggplot(reldiffs) +
geom_point(aes(x=age, y=direct, color=sex)) +
theme_minimal() +
scale_y_log10() +
ylab("nMx") +
ggtitle("True aggregate\nage-specific death rate\n(logged)")
#ggsave(plot=agg.pseudous, filename='agg-pseudo-us.pdf', height=fig.h, width=fig.w)
agg.pseudous
Plot the variance in means
cv.pseudous <- ggplot(reldiffs) +
geom_point(aes(x=age, y=w.cv.mx, color=sex)) +
theme_minimal() +
ylab("CV") +
ggtitle("Coefficient of variation in\ndeath rates\nacross sub-populations")
cv.pseudous
```r
cv.pseudous <- ggplot(reldiffs) +
geom_point(aes(x=age, y=w.cv.mx, color=sex)) +
theme_minimal() +
ylab(\CV\) +
ggtitle(\Coefficient of variation in\ndeath rates\nacross sub-populations\)
cv.pseudous
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" />
<!-- rnb-plot-end -->
<!-- rnb-chunk-end -->
<!-- rnb-text-begin -->
Directly compare rel-sd and error in second strategy
<!-- rnb-text-end -->
<!-- rnb-chunk-begin -->
<!-- rnb-source-begin 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 -->
```r
cv2.relerr.plot <- ggplot(reldiffs) +
#geom_point(aes(x=w.cv2.mx, y=reldiff.am, color=log(direct))) +
geom_abline(intercept=0, slope=1, color='grey') +
geom_point(aes(x=w.cv2.mx, y=reldiff.am)) +
#xlim(0,.1) + ylim(0,.1) +
xlab("Squared coefficient of variation in death rates") +
ylab("Relative error\nusing arithmetic mean\nweighted by deaths") +
theme_minimal() +
coord_equal()
cv2.relerr.plot
fig.h <- 5
fig.w <- 5
ggsave(plot=cv2.relerr.plot,
filename=file.path(out.dir, 'cv2-relerr.pdf'), height=fig.h, width=fig.w)