New Methods for Analysing the Distribution of 5Q 5D Observations
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This document summarizes new methods for analyzing the distribution of EQ-5D health state observations. The objectives are to describe the distribution of health profiles within EQ-5D data, demonstrate differences between the 3L and 5L versions, and compare new methods to existing ones like the Shannon Index. Several new measures are introduced, including the Health State Density Curve and Index, which help show how a few profiles account for most observations. Results show the 5L has less clustered data than the 3L. The proportion of rare profiles increases with greater health gains after interventions. Overall, the new methods provide ways to systematically analyze and report the distribution of EQ-5D profile data.
New Methods for Analysing the Distribution of 5Q 5D Observations
- 1. New methods for analysing the distribution of EQ-5D observations Zamora B, Parkin D, Feng Y, Bateman A, Herdman M, Devlin N Advances in Patient Reported Outcomes Research Conference Oxford 8th June 2017
- 3. 08/06/17 3 Rationale • EQ-5D profile data often summarised by utilities • But important to understand the characteristics of the underlying profile data • These are often clustered, with relatively few profiles accounting for the vast majority of observations. • Different instruments have different levels of clustering eg 5L vs 3L • Different patient groups may have different levels of clustering (with implications for managing care)
- 4. 08/06/17 4 Objectives • To develop methods for describing the distribution of profiles within PRO data • To demonstrate the use of the methods on EQ-5D data from the NHS • To demonstrate differences between the clustering of data between the 3L and 5L • To demonstrate the properties of the new methods, compared with existing methods (eg Shannon’s Index)
- 5. Methods
- 6. 08/06/17 6 New Method Based on existing method Meaning HSDC Health State Density Curve Lorenz curve A cumulative frequency curve that compares the distribution of patients with the distribution of profiles HSDI Health State Density Index 1-Gini coefficient It measures inequality of the distribution of a categorical variable. Value 1 for total equality Shannon Index (H’) Information theory, also ecological diversity and evenness It measures absolute discriminatory power. Maximum absolute discriminatory power equals log(number profiles) for uniform distribution Shannon Evenness index (J’) It measures relative discriminatory power in the unit interval. Value 1 for total equality/ evenness/maximum relative discriminatory power Power Law It assumes exponential growth of the form captured in the HSDC The slope of linear regression of the cumulative proportion of observations on the logarithm of cumulative proportion of profiles captures the degree of concentration
- 7. 08/06/17 7 Comparison of HSDI and J • We find the following stylised facts: 1. HSDI is more sensitive than J to rare profiles 2. J does not decrease below 1 when the estimated small proportion of rare profiles is due to random variations. HSDI is oversensitive to random variations. 3. HDSI decreases in parallel to the estimated proportion of rare . 4. The J index is more sensitive to rare observations for the 3L than for the 5L distribution. • We find the following anomaly: Non-linear relationship with the proportion of rare profiles: When the distribution is separated in different groups: one highly concentrated and another one uniformly distributed
- 8. 08/06/17 8 Properties of the Power Law • We find the following stylised facts: 1. The goodness of fit of the power law is better for the EQ-5D-5L than for the EQ-5D-3L distributions 2. The goodness of fit of the power law improves when removing the ceiling (observations in the most frequent profile)
- 9. Results in Population and Patient Datasets
- 10. 08/06/17 10 Population and Patient Datasets N % female Mean age (years) Age range Cambridgeshire NHS: All Patients 30,284 59.6 59.1 13-104 Cambridgeshire NHS: MSK 19,999 59.8 52.5 13-96 Cambridgeshire NHS: Specialist Nursing 3,366 52.1 67.0 17-104 Cambridgeshire NHS: Rehabilitation 6,919 62.5 74.4 18-103 Health Survey for England 2014 7,085 56.1 49.7 16 and over NHS PROMs Hernia 2009-10 19,416 1.3 62.8 20 and over NHS PROMs Hernia 2010-11 21,265 1.2 62.7 20 and over NHS PROMs Hernia 2011-12 7,927 0.1 64.8 20 and over NHS PROMs Hips 2009-10 29,506 59.9 68.8 20 and over NHS PROMs Hips 2010-11 37,923 60.6 68.6 20 and over NHS PROMs Hips 2011-12 5,194 67.4 69.8 20 and over NHS PROMs Knee 2009-10 32,078 56.7 69.7 20 and over NHS PROMs Knee 2010-11 39,098 57.5 69.7 20 and over NHS PROMs Knee 2011-12 4,913 61.3 70.1 20 and over NHS PROMs Varicose Veins 2009-10 7,923 72.0 52.6 20 and over NHS PROMs Varicose Veins 2010-11 8,141 71.4 53.0 20 and over NHS PROMs Varicose Veins 2011-12 2,258 76.5 54.4 20 and over
- 11. 08/06/17 11 Results (1) HSDI=0.21 0 20406080 100 0 20 40 60 80 100 Cumulative percentage of observations Cambridgeshire: All Patients HSDI MSK=0.19 HSDI Nursing=0.34 HSDI Rehab=0.39 0 20406080 100 0 20 40 60 80 100 Cumulative percentage of observations total evenness MSK Nursing Rehabilitation Cambridgeshire: By Condition 𝐻𝑆𝐷𝐼 = 𝑖=1 𝑆 𝑥𝑖 − 𝑥𝑖−1)(𝑦𝑖 + 𝑦𝑖−1 HSDI=1-(area between diagonal and HSDC)/area under the diagonal) Inequality
- 12. 08/06/17 12 Results (2) Number of pro- files S Shannon index H' HSDI Shannon Even- ness J' Bias H' EQ-5D-5L profiles Cambridgeshire NHS: All Patients 1,730 5.89 0.21 0.79 0.05 Cambridgeshire NHS: MSK 1,141 5.41 0.19 0.77 0.08 Cambridgeshire NHS: Specialist Nursing 732 5.38 0.34 0.82 0.46 Cambridgeshire NHS: Rehabilitation 1,240 6.39 0.39 0.90 0.23 EQ-5D-3L profiles Health Survey for England 2014 94 1.92 0.09 0.42 0.02 NHS PROMs Hernia – Before 143 2.30 0.06 0.46 0.00 NHS PROMs Hernia – After 140 1.89 0.05 0.38 0.00 NHS PROMs Hips – Before 147 3.00 0.11 0.60 0.00 NHS PROMs Hips – After 158 2.71 0.09 0.54 0.00 NHS PROMs Knee – Before 147 2.87 0.10 0.57 0.00 NHS PROMs Knee – After 153 2.85 0.09 0.57 0.00 NHS PROMs Varicose Veins - Before 104 2.32 0.09 0.50 0.01 NHS PROMs Varicose Veins - After 98 1.89 0.07 0.41 0.01
- 13. 08/06/17 13 Results (3) .2.4.6.8 1 index 0 .2 .4 .6 .8 proportion rare profiles MSK .2.4.6.8 1 0 .2 .4 .6 .8 proportion rare profiles Specialist Nursing .2.4.6.8 1 0 .1 .2 .3 .4 .5 proportion rare profiles Rehabilitation J in blue, HSDI in green Regressions of J and HSDI indexes on proportion of rare profiles
- 15. Conclusions
- 16. 08/06/17 16 Conclusions • The measures reported here can be used to report and summarise the distribution of EQ-5D profile data • We find a stable linear decreasing relationship between the indexes and the proportion of rare profiles • The EQ-5D-5L has less clustering than the EQ-5D-3L. Notably, we find this occurs within the most frequent profiles rather than by generating more rare profiles • The relative importance of rare profiles increases with the level of health gained after the four interventions in PROMs data. This is associated with larger inequality (ie more tightly clustered) EQ-5D-3L profile data in PROMs after than before surgery
- 17. 08/06/17 17 This research has been funded by EuroQol group. Opinions expressed here are those of the authors and do not necessarily represent those of the EuroQol Research Foundation. We are grateful to Nils Gutacker and participants at the Winter HESG 2017 meeting for useful comments. This research will be published as OHE Research Paper in summer 2017. For further information, contact bzamora@ohe.org Office of Health Economics (OHE) Southside, 7th Floor 105 Victoria Street London SW1E 6QT United Kingdom +44 20 7747 8850 www.ohe.org