1) The study explores whether the distribution of the EQ-5D-5L index in English patient populations shows clustering, as is often seen with the EQ-5D-3L index. 2) The analysis found some clustering in the distributions of the EQ-5D-5L index for different patient groups, but that the profile data alone did not account for the clusters. Different value sets used to calculate the index also generated different clusters. 3) The results indicate that careful exploratory analysis of EQ-5D-5L index data is needed to account for features like clustering, and ensure appropriate statistical techniques are employed.

1. The Distribution of the EQ-5D-5L Index
in Patient Populations
Yan Feng1, Nancy J. Devlin1, Andrew Bateman2,3, Bernarda Zamora1, David Parkin4
For more information, contact: yfeng@ohe.org
1. BACKGROUND
• EQ-5D data are often summarised by a single number index, calculated by
applying value sets to EQ-5D profiles (Szende, 2007).
• The distribution of the EQ-5D-3L index in patient populations often shows two
distinct groups (Parkin et al, 2016), arising from both the distribution of ill health
and how the EQ-5D-3L index is constructed.
• There are good grounds for hypothesising that the EQ-5D-5L index data might not
have the two-group distribution commonly observed for the EQ-5D-3L.
 Studies comparing the three- and five-level versions of EQ-5D report a wider
spread of profiles for the EQ-5D-5L (e.g. Feng et al, 2015).
 The distribution of values in the EQ-5D-5L value set for England (Devlin et al,
2016) does not have the two group shape of the EQ-5D-3L value set.
• To date, there are few empirical studies of how the EQ-5D-5L index is distributed.
Acknowledgements
1. This project was funded by a grant from the EuroQol Research Foundation, and
supported by the National Institute for Health Research (NIHR) Collaboration for
Leadership in Applied Health Research and Care East of England at Cambridgeshire and
Peterborough NHS Foundation Trust.
2. Views expressed are those of the authors, not necessarily the EuroQol Research
Foundation, the NHS, the NIHR or the Department of Health.
References
1. Szende, A., Oppe, M., Devlin, N., 2007. EQ-5D value sets: inventory, comparative review
and user guide. Dordrecht: Springer.
2. Devlin, N., Shah, K., Feng, Y., Mulhern, B., van Hout, B., 2016. Valuing health related
quality of life: an EQ-5D-5L value set for England. OHE Research Paper. London: Office
of Health Economics.
3. Feng, Y., Devlin, N., Herdman, M., 2015. Assessing the health of the general population
in England: how do the three- and five-level versions of EQ-5D compare? Health and
Quality of Life Outcomes (forthcoming).
4. Parkin, D., Devlin, N., Feng, Y., 2016. What determines the shape of an EQ-Index
distribution? Medical Decision Making (forthcoming).
5. van Hout, B., Janssen, M.F., Feng, Y.S., Kohlmann, T., Busschbach, J., Golicki, D., Lloyd,
A., Scalone, L., Kind, P., Pickard, A.S., 2012. Interim scoring for the EQ-5D-5L: Mapping
the EQ-5D-5L to EQ-5D-3L value sets. Value in Health, 15, pp.708-715.
2. AIMS
• To explore if the EQ-5D-5L index distribution in English patient populations
demonstrates clustering.
• To test the extent to which clustering of EQ-5D-5L profile data drives any observed
clustering of the EQ-5D-5L index; and the extent to which clusters are a product of
the value sets used to estimate the EQ-5D-5L index.
• To highlight the implications of our results for statistical analysis of EQ-5D-5L index
data.
3. METHODS
Data
• Data were obtained from Cambridgeshire Community Services NHS electronic
patient records data warehouse. The data set includes patients’ EQ-5D-5L profiles
before treatment.
• There were 30,284 patient observations across three patient groups:
musculoskeletal (MSK) physiotherapy services; specialist nursing services; and
community rehabilitation services.
• 1,730 of the 3,125 possible EQ-5D-5L profiles were reported by patients.
• All patients included were aged over 12 years.
EQ-5D-5L profiles analysis
• Exploring whether clusters can be distinguished using only information on the
numbers of levels within dimensions, dividing profiles into 2 groups in 3 ways:
 Profiles with level 5 in any dimension vs. no level 5 in any dimension
 Profiles with level 4 or 5 in any dimension vs. no level 4 or 5 in any dimension
 Profiles with level 3,4 or 5 in any dimension vs. no level 3, 4 or 5 in any dimension
• Examining the largest differences between values over all 3,125 profiles ordered by
size of the index.
EQ-5D-5L index analysis
• The EQ-5D-5L index was calculated using the ‘mapped’ value set (MVS) for the UK
(van Hout et al, 2012) and the value set for England (EVS) (Devlin et al, 2016).
• The kmeans cluster method and the Calinski–Harabasz pseudo-F index stopping
rule were used to search for the clusters in the index data.
• The initial k values were defined by 50 random draws from the range of the EQ-5D-
5L index distribution in our sample (MVS: 0.594 to 0.906; EVS: -0.281 to 0.951;
both excluding index=1) and one which assumed equal-sized k partitions.
4. RESULTS
• Table 1 shows that the distribution of profiles differ considerably across the different
dimensions and the treatment groups.
5. CONCLUSIONS
• Distributions of the EQ-5D-5L index in patient data shows some clustering.
• Profile data alone do not account for these clusters, and different value sets
generate different clusters.
• In analysing EQ-5D-5L index data, it is essential to undertake careful
exploratory data analysis to ensure that statistical techniques used take
account of features of the distribution of the data such as clustering.
1Office of Health Economics; 2Cambridgeshire Community Services NHS Trust;
3University of Cambridge; 4King’s College London
• Figures 1 and 2 show the distributions of the MVS and EVS data, with kernel
density estimates. Although they are similar, the EVS distribution does not have
such pronounced gaps between values.
• Figure 3 below shows the number of profiles that contain at least one Level 5,
Levels 4 or 5 and Levels 3, 4 or 5, and the range of index values that these
take. The number of profiles in the overlap between the ranges suggests that
the existence of worse levels does not in itself generate clusters.
• Although there are some large (>0.1) ‘gaps’ between index values when
ordered by size, this only identifies individual profiles with extreme (large or
small) differences in values, but does not identify divisions between clusters.
• Cluster analysis identifies clusters for both the EVS and MVS, and for all patient
groups:
 For all patients taken together, the EVS- and MVS-based indexes generate three
and two robust clusters respectively.
 Both the EVS- and MVS-based indexes generate two robust clusters from the
MSK patients and four robust clusters from the specialist nursing patients.
 For the community rehabilitation patients, the EVS- and MVS-based indexes
generate two and four clusters respectively.
• Results using the kmedians analysis are consistent with those from the kmeans
analysis and did not demonstrate greater robustness.