Reporting EQ-5D Change Analysis

Introduction

A central use of EQ-5D data is the assessment and reporting of change in health over time, for example before and after treatment or intervention. Because EQ-5D describes health across multiple dimensions using ordinal response levels, appropriate reporting of change requires methods that preserve this multidimensional structure.

This vignette describes the change analysis methods available in eq5d and how they can be used to report changes in EQ-5D over time. It builds on earlier vignettes covering descriptive system reporting and other EQ-5D summaries.

Understanding EQ-5D change

Change in EQ-5D profiles may involve improvement in some dimensions, deterioration in others, or no change at all. Even when overall utility index scores improve on average, individual patterns of change may be heterogeneous or mixed.

For this reason the change analysis functions in eq5d focus on:

profile-based descriptions of change
individual-level classification prior to population-level summaries
reporting change using more than a single summary measure

Preparing longitudinal EQ-5D data

Longitudinal EQ-5D data are most commonly stored in long format, with one row per observation and repeated observations for each individual. A clear definition of pre- and post-intervention health states is required before change analysis can be performed.

The change-analysis functions in eq5d support a formula interface that makes this pairing explicit, specifying both the EQ-5D dimensions and the variable that defines time ordering.

suppressPackageStartupMessages(library(eq5d))

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

## Construct a simple long-format example
## (for illustration only)
dat_long <- dat
dat_long$id <- rep(seq_len(nrow(dat_long) / 2), each = 2)
dat_long$visit <- dat_long$Group

Paretian Classification of Health Change (PCHC)

The Paretian Classification of Health Change (PCHC) classifies individual changes in EQ-5D profiles between two time points into mutually exclusive categories, including improvement, deterioration, mixed change, and no change.

PCHC preserves the multidimensional structure of EQ-5D and summarises individual change between two observations.

The example below uses the formula interface introduced above.

pchc(
  MO + SC + UA + PD + AD ~ visit | id,
  data = dat_long,
  version = "3L"
)
#>                     Number Percent
#> No change               14      14
#> Improve                 59      59
#> Worsen                  14      14
#> Mixed change            13      13
#> Total with problems    100     100
#> No problems              0       0

If the time variable contains exactly two observed levels, pre- and post-intervention states are inferred automatically. When the ordering is ambiguous, the pre.level and post.level arguments should be supplied explicitly.

The package supports both long-format longitudinal data and explicitly paired pre- and post-intervention datasets. For simplicity, the examples below use paired datasets; the same summaries can be obtained from long-format data using the formula interface shown above.

## Prepare paired pre/post datasets
pre  <- dat[dat$Group == "Group1", ]
post <- dat[dat$Group == "Group2", ]

pchc_res <- pchc(pre, post, version = "3L", summary = TRUE)
pchc_res
#>                     Number Percent
#> No change               14      14
#> Improve                 59      59
#> Worsen                  14      14
#> Mixed change            13      13
#> Total with problems    100     100
#> No problems              0       0

The resulting table summarises the overall pattern of change within the study population and can be reported alongside descriptive system summaries at baseline and follow-up.

Probability of Superiority

Probability of Superiority (PS) provides a population-level summary of change by comparing pre- and post-intervention responses on each EQ-5D dimension and quantifying the balance between improvement and deterioration.

Unlike PCHC, PS is returned as a separate estimate for each EQ-5D dimension and can be presented using reporting tables where required.

ps_res <- ps(pre, post, version = "3L")
ps_res
#> $MO
#> [1] 0.6
#> 
#> $SC
#> [1] 0.62
#> 
#> $UA
#> [1] 0.69
#> 
#> $PD
#> [1] 0.66
#> 
#> $AD
#> [1] 0.55

table_ps(ps_res)
#>   Dimension   PS
#> 1        MO 0.60
#> 2        SC 0.62
#> 3        UA 0.69
#> 4        PD 0.66
#> 5        AD 0.55

PS should be interpreted as a comparative probability rather than as an individual-level effect measure. Unlike PCHC, it does not classify individual change trajectories and should therefore be viewed as complementary to, rather than a replacement for, profile-based classifications.

Relationship between PCHC and PS

PCHC and PS provide different perspectives on change:

PCHC describes the pattern of change experienced by individuals.
PS summarises the balance of improvement and deterioration within the population.

Reporting both summaries together provides a richer account of longitudinal EQ-5D change than either approach alone.

Health Profile Grid

Visualisation can support the interpretation of change summaries. The Health Profile Grid (HPG) provides a two-dimensional representation of ranked EQ-5D profiles before and after intervention. In eq5d, HPG data are generated using hpg() and visualised with plot_hpg().

hpg_obj <- hpg(
  pre,
  post,
  country = "UK",
  version = "3L",
  type = "TTO"
)

plot_hpg(hpg_obj, version = "3L")

Visualisations are most informative when interpreted alongside multidimensional change summaries.