Slope index of inequality
Julian Flowers
26 August 2015
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Calculating slope of index inequality (SII) in R
- SII is a widely used measure of health inequality which summarises the distribution of a health outcome measure (e.g. life expectancy) against a socioeconomic measure such as life expectancy
- When used life expectancy it can be interpreted as the absolute differnce in years within a larger group of the least and most deprived subgroups
- In this example we have extracted male and female life expactancy values (2008-11), IMD scores, and 2013 total populations from National General Practice Profiles
- We then calculate on the basis of general practice, the SII for each CCG for male and female life expectancy in a few lines of code
- the method can be used to calculate SIIs for any area based on sub areas and for any health measure given the population, health value, deprivation score a
Read data
Takes a data frame with area name/ code, population, deprivation score, health measure(s)
sii <- read.csv("~/Downloads/sii.csv")
head(sii)## Pr.code CCG Pop IMD Lem Lef
## 1 A81001 NHS Hartlepool And Stockton-On-Tees CCG 4084 26.09 76.24 81.98
## 2 A81002 NHS Hartlepool And Stockton-On-Tees CCG 20111 28.44 77.12 81.81
## 3 A81003 NHS Hartlepool And Stockton-On-Tees CCG 3542 42.12 75.94 80.95
## 4 A81004 NHS South Tees CCG 8513 31.01 76.72 81.36
## 5 A81005 NHS South Tees CCG 7953 13.92 82.03 82.95
## 6 A81006 NHS Hartlepool And Stockton-On-Tees CCG 12221 29.81 76.76 81.40dim(sii)## [1] 7891 6Install and load packages; look at data summary; remove NAs
- We use dplyr to easily calculate necessary variables for each group of CCGs, and the broom package to perform regression and produce output in a tidy format
- Look at data summary
library(dplyr)##
## Attaching package: 'dplyr'
##
## The following object is masked from 'package:stats':
##
## filter
##
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(broom)
library(Hmisc)## Loading required package: grid
## Loading required package: lattice
## Loading required package: survival
## Loading required package: Formula
## Loading required package: ggplot2
##
## Attaching package: 'Hmisc'
##
## The following objects are masked from 'package:dplyr':
##
## combine, src, summarize
##
## The following objects are masked from 'package:base':
##
## format.pval, round.POSIXt, trunc.POSIXt, unitslibrary(ggplot2)
sii <- tbl_df(sii)
summary(sii)## Pr.code CCG
## A81001 : 1 NHS Northern, Eastern And Western Devon CCG: 123
## A81002 : 1 NHS Birmingham Crosscity CCG : 115
## A81003 : 1 NHS Cambridgeshire and Peterborough CCG : 106
## A81004 : 1 NHS Sandwell And West Birmingham CCG : 105
## A81005 : 1 NHS Dorset CCG : 99
## A81006 : 1 NHS Liverpool CCG : 94
## (Other):7885 (Other) :7249
## Pop IMD Lem Lef
## Min. : 0 Min. : 2.86 Min. :70.01 Min. :76.61
## 1st Qu.: 3700 1st Qu.:13.56 1st Qu.:77.16 1st Qu.:81.66
## Median : 6211 Median :21.41 Median :78.79 Median :83.04
## Mean : 7053 Mean :23.51 Mean :78.69 Mean :83.00
## 3rd Qu.: 9552 3rd Qu.:31.74 3rd Qu.:80.32 3rd Qu.:84.34
## Max. :52386 Max. :68.47 Max. :90.07 Max. :91.88
## NA's :15 NA's :260 NA's :261sii <- na.omit(sii)
summary(sii)## Pr.code CCG
## A81001 : 1 NHS Northern, Eastern And Western Devon CCG: 120
## A81002 : 1 NHS Birmingham Crosscity CCG : 112
## A81003 : 1 NHS Cambridgeshire and Peterborough CCG : 104
## A81004 : 1 NHS Sandwell And West Birmingham CCG : 100
## A81005 : 1 NHS Dorset CCG : 94
## A81006 : 1 NHS Liverpool CCG : 87
## (Other):7610 (Other) :6999
## Pop IMD Lem Lef
## Min. : 0 Min. : 2.86 Min. :70.01 Min. :76.61
## 1st Qu.: 3703 1st Qu.:13.48 1st Qu.:77.16 1st Qu.:81.66
## Median : 6210 Median :21.23 Median :78.79 Median :83.04
## Mean : 7058 Mean :23.38 Mean :78.69 Mean :83.00
## 3rd Qu.: 9564 3rd Qu.:31.43 3rd Qu.:80.31 3rd Qu.:84.34
## Max. :52386 Max. :68.47 Max. :90.07 Max. :91.88
## Calculate mean IMD and life expectancy values per CCG (for use later)
aggsii <- summarise(group_by(sii, CCG), mean(IMD), mean(Lem), mean(Lef))
head(aggsii)## Source: local data frame [6 x 4]
##
## CCG mean(IMD) mean(Lem) mean(Lef)
## 1 NHS Airedale, Wharfdale And Craven CCG 24.13765 77.61882 82.06824
## 2 NHS Ashford CCG 33.34071 78.61429 83.50286
## 3 NHS Aylesbury Vale CCG 15.43619 80.21000 84.08524
## 4 NHS Barking And Dagenham CCG 21.22400 78.85450 82.74200
## 5 NHS Barnet CCG 13.09299 80.00672 83.89388
## 6 NHS Barnsley CCG 29.44405 77.43676 81.88351Call cumsum function (written by Hugh Mallinson)
source('~/Downloads/findXvals.R')
cumrank## function (xvals)
## {
## prop <- xvals/sum(xvals)
## cumprop <- numeric(length(xvals))
## output <- numeric(length(xvals))
## cumprop[1] <- prop[1]
## output[1] <- prop[1]/2
## for (i in 2:length(xvals)) {
## cumprop[i] <- sum(prop[1:i])
## output[i] <- prop[i]/2 + cumprop[i - 1]
## }
## FindXVals <- output
## }Calculate relative rank
sii1 <- sii %>% arrange(CCG, IMD) %>% group_by(CCG) %>% mutate(relrank = cumrank(Pop))
head(sii1); tail(sii1)## Source: local data frame [6 x 7]
## Groups: CCG
##
## Pr.code CCG Pop IMD Lem Lef
## 1 B83006 NHS Airedale, Wharfdale And Craven CCG 10758 7.00 80.45 83.39
## 2 B83021 NHS Airedale, Wharfdale And Craven CCG 12748 9.84 77.68 78.64
## 3 B82028 NHS Airedale, Wharfdale And Craven CCG 13912 10.31 80.36 85.18
## 4 B83002 NHS Airedale, Wharfdale And Craven CCG 4526 10.70 80.17 85.45
## 5 B82099 NHS Airedale, Wharfdale And Craven CCG 4109 11.39 81.02 85.27
## 6 B82007 NHS Airedale, Wharfdale And Craven CCG 9309 12.04 75.77 80.71
## Variables not shown: relrank (dbl)## Source: local data frame [6 x 7]
## Groups: CCG
##
## Pr.code CCG Pop IMD Lem Lef relrank
## 1 M81073 NHS Wyre Forest CCG 8503 13.82 79.63 85.55 0.6573086
## 2 M81068 NHS Wyre Forest CCG 13106 17.28 78.98 84.99 0.7535265
## 3 M81608 NHS Wyre Forest CCG 2921 18.94 80.71 85.69 0.8248896
## 4 M81090 NHS Wyre Forest CCG 3217 23.17 81.11 85.49 0.8522201
## 5 M81027 NHS Wyre Forest CCG 6922 44.47 76.46 82.30 0.8973658
## 6 M81015 NHS Wyre Forest CCG 8064 50.11 74.99 81.25 0.9640936Set up variables for regression analysis (for SII for male life expectancy)
sii1 <- sii %>% arrange(CCG, IMD) %>% group_by(CCG) %>% mutate(relrank = cumrank(Pop),
tot = sum(Pop), prop = Pop/tot, Y = sqrt(prop)*Lem, a = sqrt(prop), b = relrank * a)
head(sii1[,5:12])## Source: local data frame [6 x 8]
##
## Lem Lef relrank tot prop Y a b
## 1 80.45 83.39 0.0344245 156255 0.06884900 21.10935 0.2623909 0.009032676
## 2 77.68 78.64 0.1096413 156255 0.08158459 22.18775 0.2856302 0.031316860
## 3 80.36 85.18 0.1949506 156255 0.08903395 23.97826 0.2983856 0.058170435
## 4 80.17 85.45 0.2539503 156255 0.02896547 13.64433 0.1701925 0.043220422
## 5 81.02 85.27 0.2815814 156255 0.02629676 13.13843 0.1621628 0.045662013
## 6 75.77 80.71 0.3245176 156255 0.05957569 18.49404 0.2440813 0.079208690Calculate SIIs
siiM <- sii1 %>% group_by(CCG) %>% do(tidy(lm(Y ~ 0 + a + b, data=.))) ##set intercept at 0
siiM <- filter(siiM, term == "b") %>% mutate (lci = estimate - 1.96*std.error,
uci = estimate + 1.96*std.error) %>%
select(CCG, estimate, lci, uci) ##extract SII values from regression and calculate 95% CIs
head(siiM)## Source: local data frame [6 x 4]
## Groups: CCG
##
## CCG estimate lci uci
## 1 NHS Airedale, Wharfdale And Craven CCG -6.388822 -9.381419 -3.396226
## 2 NHS Ashford CCG -4.618791 -6.727257 -2.510325
## 3 NHS Aylesbury Vale CCG -7.403199 -10.178371 -4.628027
## 4 NHS Barking And Dagenham CCG -6.277636 -7.384998 -5.170273
## 5 NHS Barnet CCG -4.050214 -5.146874 -2.953554
## 6 NHS Barnsley CCG -6.445051 -7.874487 -5.015614Same for female LE
sii2 <- sii %>% arrange(CCG, IMD) %>% group_by(CCG) %>% mutate(relrank = cumrank(Pop),
tot = sum(Pop), prop = Pop/tot, Y = sqrt(prop)*Lef, a = sqrt(prop), b = relrank * a)
siiF <- sii2 %>% group_by(CCG) %>% do(tidy(lm(Y ~ 0 + a + b, data=.))) ##set intercept at 0
siiF <- filter(siiF, term == "b") %>% mutate (lci = estimate - 1.96*std.error,
uci = estimate + 1.96*std.error) %>%
select(CCG, estimate, lci, uci) ##extract SII values from regression and calculate 95% CIs
head(siiF)## Source: local data frame [6 x 4]
## Groups: CCG
##
## CCG estimate lci uci
## 1 NHS Airedale, Wharfdale And Craven CCG -3.9265523 -7.753242 -0.09986274
## 2 NHS Ashford CCG -0.2193803 -1.826304 1.38754370
## 3 NHS Aylesbury Vale CCG -3.7221070 -5.674428 -1.76978574
## 4 NHS Barking And Dagenham CCG -5.2663517 -6.472143 -4.06056026
## 5 NHS Barnet CCG -3.2725833 -4.340735 -2.20443173
## 6 NHS Barnsley CCG -4.4419603 -5.805199 -3.07872185Extract SIIs and plot
tidy(model)## term estimate std.error statistic p.value
## 1 (Intercept) -1.704137 0.1652248 -10.31405 2.156211e-20
## 2 x 0.886490 0.0427591 20.73220 2.064050e-52Compare distributions
## x y
## 1 -3.9265523 -6.388822
## 2 -0.2193803 -4.618791
## 3 -3.7221070 -7.403199
## 4 -5.2663517 -6.277636
## 5 -3.2725833 -4.050214
## 6 -4.4419603 -6.445051
Show values
## Source: local data frame [6 x 11]
##
## CCG estimate lci uci
## 1 NHS Airedale, Wharfdale And Craven CCG -6.388822 -9.381419 -3.396226
## 2 NHS Ashford CCG -4.618791 -6.727257 -2.510325
## 3 NHS Aylesbury Vale CCG -7.403199 -10.178371 -4.628027
## 4 NHS Barking And Dagenham CCG -6.277636 -7.384998 -5.170273
## 5 NHS Barnet CCG -4.050214 -5.146874 -2.953554
## 6 NHS Barnsley CCG -6.445051 -7.874487 -5.015614
## Variables not shown: CCG.1 (fctr), estimate.1 (dbl), lci.1 (dbl), uci.1
## (dbl), mean(IMD) (dbl), mean(Lem) (dbl), mean(Lef) (dbl)## [1] 209 11## Classes 'tbl_df', 'tbl' and 'data.frame': 209 obs. of 11 variables:
## $ CCG : Factor w/ 209 levels "NHS Airedale, Wharfdale And Craven CCG",..: 1 2 3 4 5 6 7 8 9 10 ...
## $ estimate : num -6.39 -4.62 -7.4 -6.28 -4.05 ...
## $ lci : num -9.38 -6.73 -10.18 -7.38 -5.15 ...
## $ uci : num -3.4 -2.51 -4.63 -5.17 -2.95 ...
## $ CCG.1 : Factor w/ 209 levels "NHS Airedale, Wharfdale And Craven CCG",..: 1 2 3 4 5 6 7 8 9 10 ...
## $ estimate.1: num -3.927 -0.219 -3.722 -5.266 -3.273 ...
## $ lci.1 : num -7.75 -1.83 -5.67 -6.47 -4.34 ...
## $ uci.1 : num -0.0999 1.3875 -1.7698 -4.0606 -2.2044 ...
## $ mean(IMD) : num 24.1 33.3 15.4 21.2 13.1 ...
## $ mean(Lem) : num 77.6 78.6 80.2 78.9 80 ...
## $ mean(Lef) : num 82.1 83.5 84.1 82.7 83.9 ...