Reporting EQ-5D Severity and Distributional Summaries

Overview

In addition to descriptive system tables, EQ-5D data can be summarised using measures that describe the severity and distribution of observed health states.

This vignette introduces the severity and distributional reporting methods available in eq5d, including the Level Sum Score (LSS), Level Frequency Score (LFS), Shannon’s entropy and evenness, and measures derived from health state cumulative frequency distributions.

Example data

suppressPackageStartupMessages(library(eq5d))

## Example EQ-5D-3L data included with the package
dat <- read.csv(
  system.file("extdata", "eq5d3l_example.csv", package = "eq5d")
)

## For an ungrouped population-level example
dat1 <- subset(dat, Group == "Group1")

## Example EQ-5D-3L profile (single observation)
scores <- unlist(dat1[1, c("MO", "SC", "UA", "PD", "AD")])

Severity measures

Severity measures provide concise summaries of EQ-5D health states and can be reported alongside descriptive system tables.

The eq5d package provides two severity measures:

the Level Sum Score (LSS)
the Level Frequency Score (LFS)

# Example severity summaries
lss(scores, version = "3L")
lfs(scores, version = "3L")

LSS is calculated by summing the reported levels across dimensions, with higher values indicating greater severity.

LFS provides a compact description of the EQ-5D profile based on the frequency of observed response levels within the health state.

These measures can be reported alongside descriptive system tables to provide additional information about health state severity.

Shannon’s entropy and evenness

The distribution of observed EQ-5D health states can also be summarised using Shannon’s entropy and Shannon’s evenness. These measures are calculated at the population level and therefore require a dataset of observed EQ-5D profiles.

# Shannon's entropy and evenness for a population
shannon(dat1, version = "3L")
#>   dimension    H H.max    J
#> 1        MO 0.99  1.58 0.62
#> 2        SC 1.00  1.58 0.63
#> 3        UA 1.10  1.58 0.69
#> 4        PD 0.95  1.58 0.60
#> 5        AD 0.99  1.58 0.62

Shannon’s entropy was first applied to EQ-5D data by Janssen et al. (2007) as a way of describing the information contained within observed health state distributions. Shannon’s entropy (H’) reflects the diversity of observed responses while Shannon’s evenness (J’) measures how evenly responses are distributed relative to the maximum possible entropy.

These measures are often used to assess how much variation is present in the observed responses and can help identify concentration of responses arising from effects such as limited variation or ceiling effects.

Health state distribution summaries

In addition to severity measures and entropy statistics, eq5d provides summaries of how health states are distributed within a population. These summaries are based on health state cumulative frequency data generated using eq5dcf().

# Health state cumulative frequency object
cf <- eq5dcf(dat1, version = "3L")

The Health State Density Index (HSDI) summarises the concentration of observed health states within a population. It can be useful when comparing the distribution of health states across different groups or datasets.

idx <- hsdi(dat1, version = "3L")
idx
#> [1] 0.49

The Health State Density Curve (HSDC) provides a graphical representation of the cumulative distribution of health states.

plot_hsdc(cf, hsdi = idx)

When interpreted alongside HSDI, the HSDC can help compare the distribution of health states across populations and identify differences in concentration across the health state spectrum.

Comparing groups

When severity or distributional summaries are required for multiple groups, the data can be split before analysis. The helper functions below provide a convenient way to generate grouped HSDI and HSDC summaries.

# Grouped HSDI
hsdi_by_group <- make_hsdi_by_group(
  dat,
  group = "Group",
  version = "3L"
)

hsdi_by_group
#> Group1 Group2 
#>   0.49   0.46

# Grouped HSDC data
hsdc_by_group <- make_hsdc_by_group(
  dat,
  group = "Group",
  version = "3L"
)

plot_hsdc(hsdc_by_group, hsdi = hsdi_by_group, group = "Group")

Grouped summaries can be useful when comparing the distribution of health states across study groups, populations or time points. These summaries are intended to complement descriptive system tables and other EQ-5D reporting outputs.

Summary

This vignette introduced severity and distributional reporting methods available in eq5d, including LSS, LFS, Shannon’s entropy and evenness, and health state distribution summaries based on cumulative frequency distributions. These measures can complement descriptive system tables by providing additional information about the severity, diversity and distribution of observed health states.