Calculating EQ-5D indices and summarising profiles with eq5d
EQ-5D
EQ-5D is a popular health related quality of life instrument used in the clinical and economic evaluation of health care. Developed by the EuroQol group, the instrument consists of two components: health state description and evaluation.
For the description component a subject self-rates their health in terms of five dimensions; mobility, self-care, usual activities, pain/discomfort, and anxiety/depression using either a three-level (EQ-5D-3L and EQ-5D-Y) or a five-level (EQ-5D-5L) scale.
The evaluation component requires a patient to record their overall health status using a visual analogue scale (EQ-VAS).
Following assessment the scores from the descriptive component can be reported as a five digit number ranging from 11111 (full health) to 33333/55555 (worst health). A number of methods exist for analysing these five digit profiles. However, frequently they are converted to a single utility index using country specific value sets, which can be used in the clinical and economic evaluation of health care as well as in population health surveys.
The eq5d package provides methods for the cross-sectional and longitudinal analysis of EQ-5D profiles and also the calculation of utility index scores from a subject’s dimension scores. Additionally, a Shiny app is included to enable the calculation, visualisation and automated statistical analysis of multiple EQ-5D index values via a web browser using EQ-5D dimension scores stored in CSV or Excel files.
Value sets for EQ-5D-3L are available for many countries and have been produced using the time trade-off (TTO) valuation technique or the visual analogue scale (VAS) valuation technique. Some countries have TTO and VAS value sets for EQ-5D-3L. Additionally, EQ-5D-3L “reverse crosswalk” value sets published on the EuroQol website that enable EQ-5D-3L data to be mapped to EQ-5D-5L value sets are included.
For EQ-5D-5L, a standardised valuation study protocol (EQ-VT) was developed by the EuroQol group based on the composite time trade-off (cTTO) valuation technique supplemented by a discrete choice experiment (DCE). The EuroQol group recommends users to use a standard value set where available.
The EQ-5D-5L “crosswalk” value sets published by van Hout et al as well as that for Russia are also included. The crosswalk value sets enable index values to be calculated for EQ-5D-5L data where no value set is available by mapping between the EQ-5D-5L and EQ-5D-3L descriptive systems.
The recently published age and sex conditional based mapping data by the NICE Decision Support Unit are also now part of the package. These enable age-sex based EQ-5D-3L to EQ-5D-5L and EQ-5D-5L to EQ-5D-3L mappings from dimensions and exact or approximate utility index scores.
Additional information on EQ-5D can be found on the EuroQol website as well as in Szende et al (2007) and Szende et al (2014). Advice on choosing a value set can also be found on the EuroQol website.
Installation
You can install the released version of eq5d from CRAN with:
And the development version from GitHub with:
Quick Start
library(eq5d)
#single calculation
#named vector MO, SC, UA, PD and AD represent mobility, self-care, usual activites, pain/discomfort and anxiety/depression, respectfully.
scores <- c(MO=1,SC=2,UA=3,PD=2,AD=1)
#EQ-5D-3L using the UK TTO value set
eq5d(scores=scores, country="UK", version="3L", type="TTO")
#> [1] 0.329
#Using five digit format
eq5d(scores=12321, country="UK", version="3L", type="TTO")
#> [1] 0.329
#EQ-5D-Y using the Slovenian cTTO value set
eq5d(scores=13321, country="Slovenia", version="Y3L", type="cTTO")
#> [1] 0.295
#EQ-5D-5L crosswalk
eq5d(scores=55555, country="Spain", version="5L", type="CW")
#> [1] -0.654
#EQ-5D-3L reverse crosswalk
eq5d(scores=33333, country="Germany", version="3L", type="RCW")
#> [1] -0.329
#EQ-5D-5L to EQ-5D-3L NICE DSU mapping
#Using dimensions
eq5d(c(MO=1,SC=2,UA=3,PD=4,AD=5), version="5L", type="DSU", country="UK", age=23, sex="male")
#> [1] 0.083
#Using exact utility score
eq5d(0.922, country="UK", version="5L", type="DSU", age=18, sex="male")
#> [1] 0.893
#Using approximate utility score
eq5d(0.435, country="UK", version="5L", type="DSU", age=30, sex="female", bwidth=0.0001)
#> [1] 0.302
#multiple calculations using the Canadian VT value set
#data.frame with individual dimensions
scores.df <- data.frame(
MO=c(1,2,3,4,5), SC=c(1,5,4,3,2), UA=c(1,5,2,3,1), PD=c(1,3,4,3,4), AD=c(1,2,1,2,1)
)
eq5d(scores.df, country="Canada", version="5L", type="VT")
#> [1] 0.949 0.362 0.390 0.524 0.431
#data.frame using five digit format
scores.df2 <- data.frame(state=c(11111, 25532, 34241, 43332, 52141))
eq5d(scores.df2, country="Canada", version="5L", type="VT", five.digit="state")
#> [1] 0.949 0.362 0.390 0.524 0.431
#or using a vector
eq5d(scores.df2$state, country="Canada", version="5L", type="VT")
#> [1] 0.949 0.362 0.390 0.524 0.431Value sets
The available value sets can be viewed using the valuesets function. The results can be filtered by EQ-5D version, value set type or by country.
# Return TTO value sets with PubMed IDs and DOIs (top 6 returned for brevity).
head(valuesets(type="TTO", references=c("PubMed","DOI")))
#> Version Type Country PubMed DOI
#> 1 EQ-5D-3L TTO Argentina 19900257 10.1111/j.1524-4733.2008.00468.x
#> 2 EQ-5D-3L TTO Australia 21914515 10.1016/j.jval.2011.04.009
#> 3 EQ-5D-3L TTO Bermuda 38982011 10.1007/s10198-024-01701-2
#> 4 EQ-5D-3L TTO Brazil 29702778 10.1016/j.vhri.2013.01.009
#> 5 EQ-5D-3L TTO Canada 22328929 10.1371/journal.pone.0031115
#> 6 EQ-5D-3L TTO Chile 22152184 10.1016/j.jval.2011.09.002.
# Return VAS value sets with ISBN and external URL (top 6 returned for brevity).
head(valuesets(type="VAS", references=c("ISBN","ExternalURL")))
#> Version Type Country ISBN
#> 1 EQ-5D-3L VAS Belgium 1-4020-5511-0
#> 2 EQ-5D-3L VAS Denmark 1-4020-5511-0
#> 3 EQ-5D-3L VAS Europe 1-4020-5511-0
#> 4 EQ-5D-3L VAS Finland 1-4020-5511-0
#> 5 EQ-5D-3L VAS Germany 1-4020-5511-0
#> 6 EQ-5D-3L VAS Iran <NA>
#> ExternalURL
#> 1 https://eq-5dpublications.euroqol.org/download?id=0_54011&fileId=54420
#> 2 https://eq-5dpublications.euroqol.org/download?id=0_54011&fileId=54420
#> 3 https://eq-5dpublications.euroqol.org/download?id=0_54011&fileId=54420
#> 4 https://eq-5dpublications.euroqol.org/download?id=0_54011&fileId=54420
#> 5 https://eq-5dpublications.euroqol.org/download?id=0_54011&fileId=54420
#> 6 <NA>
# Return EQ-5D-5L value sets (top 6 returned for brevity).
head(valuesets(version="5L"))
#> Version Type Country PubMed DOI ISBN ExternalURL
#> 1 EQ-5D-5L CW Bermuda 38982011 10.1007/s10198-024-01701-2 <NA> <NA>
#> 2 EQ-5D-5L CW Denmark 22867780 10.1016/j.jval.2012.02.008 <NA> <NA>
#> 3 EQ-5D-5L CW France 22867780 10.1016/j.jval.2012.02.008 <NA> <NA>
#> 4 EQ-5D-5L CW Germany 22867780 10.1016/j.jval.2012.02.008 <NA> <NA>
#> 5 EQ-5D-5L CW Japan 22867780 10.1016/j.jval.2012.02.008 <NA> <NA>
#> 6 EQ-5D-5L CW Jordan 39225720 10.1007/s10198-024-01712-z <NA> <NA>
# Return all French value sets.
valuesets(country="France")
#> Version Type Country PubMed DOI ISBN ExternalURL
#> 1 EQ-5D-3L TTO France 21935715 10.1007/s10198-011-0351-x <NA> <NA>
#> 2 EQ-5D-5L CW France 22867780 10.1016/j.jval.2012.02.008 <NA> <NA>
#> 3 EQ-5D-5L VT France 31912325 10.1007/s40273-019-00876-4 <NA> <NA>
# Return all EQ-5D-5L to EQ-5D-3L DSU value sets without references.
valuesets(type="DSU", version="5L", references=NULL)
#> Version Type Country
#> 1 EQ-5D-5L DSU China
#> 2 EQ-5D-5L DSU Germany
#> 3 EQ-5D-5L DSU Japan
#> 4 EQ-5D-5L DSU Netherlands
#> 5 EQ-5D-5L DSU SouthKorea
#> 6 EQ-5D-5L DSU Spain
#> 7 EQ-5D-5L DSU UKAnalysis of EQ-5D Profiles
A number of methods have been published that enable the analysis of EQ-5D profiles, most recently in the open access book Methods for Analysing and Reporting EQ-5D Data by Devlin, Janssen and Parkin. The eq5d package includes R implentations of some of the methods from this book and from other sources that may be of use in analysing EQ-5D data.
Cumulative frequency analysis
The eq5dcf function calculates the frequency, percentage, cumulative frequency and cumulative percentage for each five digit profile in an EQ-5D dataset. Either a vector of five digit profiles or a data.frame of individual dimensions can be passed to this function in order to summarise data in this way.
library(readxl)
#load example data
data <- read_excel(system.file("extdata", "eq5d3l_example.xlsx", package="eq5d"))
#run eq5dcf function on a data.frame
res <- eq5dcf(data, "3L")
# Return data.frame of cumulative frequency stats (top 6 returned for brevity).
head(res)
#> State Frequency Percentage CumulativeFreq CumulativePerc
#> 1 11121 36 18.0 36 18.0
#> 2 11111 24 12.0 60 30.0
#> 3 22222 21 10.5 81 40.5
#> 4 22221 18 9.0 99 49.5
#> 5 11221 12 6.0 111 55.5
#> 6 21221 11 5.5 122 61.0Summarising the Severity of EQ-5D Profiles
The eq5d package includes methods for summarising the severity of EQ-5D health state. The Level Sum Score (LSS) treats each dimension’s level as a number rather than a category. Each number is added up to produce a score between 5 and 15 for EQ-5D-3L and 5 and 25 for EQ-5D-5L.
lss(c(MO=1,SC=2,UA=3,PD=2,AD=1), version="3L")
#> [1] 9
lss(55555, version="5L")
#> [1] 25
lss(c(11111, 12345, 55555), version="5L")
#> [1] 5 15 25The Level Frequency Score (LFS) is an alternative method of summarising profile data developed by Oppe and de Charro. Here the frequency of the levels for each health state are characterised. As described in Devlin, Janssen and Parkin’s book, the full health profile 11111 for EQ-5D-5L has 5, 1 s, no level 2, 3, 4 and 5s, so the LFS is 50000; the health profile 55555 is 00005; profiles such as 31524 and 53412 would be 11111.
Paretian Classification of Health Change
The Paretian Classification of Health Change (PCHC) was developed by Devlin et al in 2010 and is used to compare changes in individuals over time. PCHC classifies the change in an individual’s health state as better (improvement in at least one dimension), worse (a deterioration in at least one dimension), mixed (improvements and deteriorations in dimensions) or there being no change in the health state. Those classified in the No change group with the 11111 health state can be separated into their own “No problems” group. PCHC can be calculated using the pchc function.
library(readxl)
#load example data
data <- read_excel(system.file("extdata", "eq5d3l_example.xlsx", package="eq5d"))
#use first 50 entries of each group as pre/post
pre <- data[data$Group=="Group1",][1:50,]
post <- data[data$Group=="Group2",][1:50,]
#run pchc function on data.frames
#Show no change, improve, worse, mixed without totals
res1 <- pchc(pre, post, version="3L", no.problems=FALSE, totals=FALSE)
res1
#> Number Percent
#> No change 5 10
#> Improve 32 64
#> Worsen 10 20
#> Mixed change 3 6
#Show totals, but not those with no problems
res2 <- pchc(pre, post, version="3L", no.problems=FALSE, totals=TRUE)
res2
#> Number Percent
#> No change 5 10
#> Improve 32 64
#> Worsen 10 20
#> Mixed change 3 6
#> Total 50 100
#Show totals and no problems for each dimension
res3 <- pchc(pre, post, version="3L", no.problems=TRUE, totals=TRUE, by.dimension=TRUE)
res3
#> $MO
#> Number Percent
#> No change 16 57.1
#> Improve 11 39.3
#> Worsen 1 3.6
#> Total with problems 28 56.0
#> No problems 22 44.0
#>
#> $SC
#> Number Percent
#> No change 10 37.0
#> Improve 14 51.9
#> Worsen 3 11.1
#> Total with problems 27 54.0
#> No problems 23 46.0
#>
#> $UA
#> Number Percent
#> No change 10 25
#> Improve 26 65
#> Worsen 4 10
#> Total with problems 40 80
#> No problems 10 20
#>
#> $PD
#> Number Percent
#> No change 27 57.4
#> Improve 19 40.4
#> Worsen 1 2.1
#> Total with problems 47 94.0
#> No problems 3 6.0
#>
#> $AD
#> Number Percent
#> No change 7 30.4
#> Improve 9 39.1
#> Worsen 7 30.4
#> Total with problems 23 46.0
#> No problems 27 54.0
#Don't summarise. Return all classifications
res4 <- pchc(pre, post, version="3L", no.problems=TRUE, totals=FALSE, summary=FALSE)
head(res4)
#> [1] "Improve" "Improve" "Improve" "Improve" "Improve"
#> [6] "Mixed change"Probability of Superiority
The Probability of Superiority (PS) is a non-parametric measure of effect size introduced by Buchholz et al in 2015 and enables the assessment of paired samples of EQ-5D profile data in the context of assessing changes in health in terms of improvement or deterioration. For each EQ-5D dimension the number of subjects that have improved over time is divided by the total number of matched pairs. Ties (those with no changes) were accounted for through the addition of half the number of ties to the numerator. The score is less than 0.5 if more patients deteriorate than improve, 0.5 if the same number of patients improve and deteriorate or do not change and greater than 0.5 if more patients improve than deteriorate.
library(readxl)
#load example data
data <- read_excel(system.file("extdata", "eq5d3l_example.xlsx", package="eq5d"))
#use first 50 entries of each group as pre/post
pre <- data[data$Group=="Group1",][1:50,]
post <- data[data$Group=="Group2",][1:50,]
res <- ps(pre, post, version="3L")
res
#> $MO
#> [1] 0.6
#>
#> $SC
#> [1] 0.61
#>
#> $UA
#> [1] 0.72
#>
#> $PD
#> [1] 0.68
#>
#> $AD
#> [1] 0.52Health Profile Grid
The Health Profile Grid (HPG) was also introduced by Devlin et al in 2010. The HPG provides a visual way to observe changes in individuals between two time points. The HPG requires profiles for each time point to be ordered from best to worst. The hpg function uses a specified value set for this with profiles being assigned a ranking between 1 and 243 for EQ-5D-3L and 1 and 3125 for EQ-5D-5L based on severity (1 being the best and 243/3125 the worst). The rankings for the two time points for each individual are plotted with the location of each point showing whether there has been an improvement or deterioration. The further a point is above the 45° line, the great the improvement in an individuals health. Conversely, the further below the line a point is the more health has deteriorated. Those individuals on the line show “no change”.
library(readxl)
#load example data
data <- read_excel(system.file("extdata", "eq5d3l_example.xlsx", package="eq5d"))
#use first 50 entries of each group as pre/post
pre <- data[data$Group=="Group1",][1:50,]
post <- data[data$Group=="Group2",][1:50,]
#run hpg function on data.frames
#Show pre/post rankings and PCHC classification
res <- hpg(pre, post, country="UK", version="3L", type="TTO")
head(res)
#> Pre Post PCHC
#> 1 11 8 Improve
#> 2 161 8 Improve
#> 3 23 1 Improve
#> 4 20 1 Improve
#> 5 23 9 Improve
#> 6 33 97 Mixed change
#Plot data using ggplot2
library(ggplot2)
ggplot(res, aes(Post, Pre, color=PCHC)) +
geom_point(aes(shape=PCHC)) +
coord_cartesian(xlim=c(1,243), ylim=c(1,243)) +
scale_x_continuous(breaks=c(1,243)) +
scale_y_continuous(breaks=c(1,243)) +
annotate("segment", x=1, y=1, xend=243, yend=243, colour="black") +
theme(panel.border=element_blank(), panel.grid.minor=element_blank()) +
xlab("Post-treatment") +
ylab("Pre-treatment")
Shannon’s Indices
Shannon’s indices were first used to assess how evenly EQ-5D dimension scores or health states in a dataset are distributed by Janssen et al in 2007. Shannon’s H’ (diversity) index represents the absolute amount of informativity captured with Shannon’s J’ (evenness) index capturing the evenness of the distribution of data. Shannon’s J’ is calculated by dividing H’ by H’ max to give a value between 0 and 1. Lower values indicate more diversity and higher values indicate less.
library(readxl)
#load example data
data <- read_excel(system.file("extdata", "eq5d3l_example.xlsx", package="eq5d"))
#Shannon's H', H' max and J' for the whole dataset
shannon(data, version="3L", by.dimension=FALSE)
#> $H
#> [1] 4.17
#>
#> $H.max
#> [1] 7.92
#>
#> $J
#> [1] 0.53
#Shannon's H', H' max and J' for each dimension
res <- shannon(data, version="3L", by.dimension=TRUE)
#Convert to data.frame for ease of viewing
do.call(rbind, res)
#> H H.max J
#> MO 1 1.58 0.63
#> SC 0.97 1.58 0.61
#> UA 1.22 1.58 0.77
#> PD 1.13 1.58 0.71
#> AD 1.09 1.58 0.69Health State Density Curve and Health State Density Index
The Health State Density Curve (HSDC) was introduced by Zamora et al in 2018 and provides a graphical way to depict the distribution of EQ-5D profiles. The cumulative frequency of health profiles ranked from most to least frequent is plotted against the cumulative proportion of the distinct health profiles (red line) and can be compared a uniform distribution representing total equality (black line). The Health State Density Index (HSDI) is based on the area formed by the diagonal line representing total equality and the line of the HSDC. The HSDI has a value between 0 and 1 where a value of 0 represents total inequality and 1 total equality.
#load example data
data <- read_excel(system.file("extdata", "eq5d3l_example.xlsx", package="eq5d"))
#Calculate HSDI
hsdi <- hsdi(data, version="3L")
#Plot HSDC
cf <- eq5dcf(data, version="3L", proportions=T)
cf$CumulativeState <- 1:nrow(cf)/nrow(cf)
#Plot data using ggplot2
library(ggplot2)
ggplot(cf, aes(CumulativeProp, CumulativeState)) +
geom_line(color="#FF9999") +
annotate("segment", x=0, y=0, xend=1, yend=1, colour="black") +
annotate("text", x=0.5, y=0.9, label=paste0("HSDI=", hsdi)) +
theme(panel.border=element_blank(), panel.grid.minor=element_blank()) +
coord_cartesian(xlim=c(0,1), ylim=c(0,1)) +
xlab("Cumulative proportion of observations") +
ylab("Cumulative proportion of profiles")
EQ-5D-DS
The eq5dds function is an R approximation of the Stata command written by Ramos-Goñi & Ramallo-Fariña. The function analyses and summarises the descriptive components of an EQ-5D dataset. The “by” argument enables a grouping variable to be specified when analysing the data subgroup.
set.seed(12345)
dat <- data.frame(
matrix(
sample(1:3, 5*12, replace=TRUE), 12, 5,
dimnames=list(1:12, c("MO","SC","UA","PD","AD"))
),
Sex=rep(c("Male", "Female"))
)
eq5dds(dat, version="3L")
#> MO SC UA PD AD
#> 1 8.3 33.3 33.3 41.7 16.7
#> 2 58.3 50.0 25.0 16.7 33.3
#> 3 33.3 16.7 41.7 41.7 50.0
eq5dds(dat, version="3L", counts=TRUE)
#> MO SC UA PD AD
#> 1 1 4 4 5 2
#> 2 7 6 3 2 4
#> 3 4 2 5 5 6
eq5dds(dat, version="3L", by="Sex")
#> data[, by]: Female
#> MO SC UA PD AD
#> 1 0.0 33.3 33.3 33.3 0.0
#> 2 66.7 50.0 33.3 16.7 16.7
#> 3 33.3 16.7 33.3 50.0 83.3
#> ------------------------------------------------------------
#> data[, by]: Male
#> MO SC UA PD AD
#> 1 16.7 33.3 33.3 50.0 33.3
#> 2 50.0 50.0 16.7 16.7 50.0
#> 3 33.3 16.7 50.0 33.3 16.7Helper functions
Helper functions are included, which may be useful in the processing of EQ-5D data. get_health_states returns a vector of all possible five digit health states for a specified EQ-5D version. get_dimensions_from_health_states splits a vector of five digit health states into a data.frame of their individual components and get_health_states_from_dimensions combines indiviual dimensions in a data.frame into five digit health states.
# Get all EQ-5D-3L five digit health states (top 6 returned for brevity).
head(get_all_health_states("3L"))
#> [1] "11111" "11112" "11113" "11121" "11122" "11123"
# Split five digit health states into their individual components.
get_dimensions_from_health_states(c("12345", "54321"), version="5L")
#> MO SC UA PD AD
#> 1 1 2 3 4 5
#> 2 5 4 3 2 1Example data
Example data is included with the package and can be accessed using the system.file function.
# View example files.
dir(path=system.file("extdata", package="eq5d"))
#> [1] "eq5d3l_example.csv" "eq5d3l_example.xlsx"
#> [3] "eq5d3l_five_digit_example.csv" "eq5d3l_five_digit_example.xlsx"
#> [5] "eq5d5l_example.csv" "eq5d5l_example.xlsx"
# Read example EQ-5D-3L data.
library(readxl)
data <- read_excel(system.file("extdata", "eq5d3l_example.xlsx", package="eq5d"))
# Calculate index scores
scores <- eq5d(data, country="UK", version="3L", type="TTO")
# Top 6 scores
head(scores)
#> [1] 0.760 0.796 -0.003 0.796 0.656 1.000Shiny web interface
The calculation (and visualisation) of multiple EQ-5D indices can also be performed by upload of a CSV or Excel file using the packaged Shiny app. This requires the shiny, DT, FSA, ggplot2, ggiraph, ggiraphExtra, mime, PMCMRplus, readxl, shinycssloaders and shinyWidgets packages. Ideally the CSV/Excel headers should be the same as the names of the vector passed to the eq5d function i.e. MO, SC, UA, PD and AD or the column name “State” if using the five digit format. However, a modal dialog will prompt the user to select the appropriate columns if the defaults can not be found.
The app is launched using the shiny_eq5d function.
Alternatively, it can be accessed without installing R/Shiny/eq5d by visiting shinyapps.io.
License
This project is licensed under the MIT License - see the LICENSE.md file for details.