Response Level

Response Level in EQ-5D and Other Health Status Instruments

A person completing the EQ-5D does not write down a number for mobility or pain. The respondent ticks one statement in each dimension, and the statement chosen, coded as a single digit, becomes part of a health profile that a value set later converts into a utility for QALYs. The number of statements offered and the words used for them decide how many health states an instrument can describe and how much change it can detect near full health. The EQ-5D-3L describes 243 health states and the EQ-5D-5L describes 3,125, and that difference comes entirely from adding two response levels to each of the same five dimensions. The meaning covered here is the answer category of a questionnaire item or dimension, not the attribute level of a discrete choice experiment, which shares the word.

Ordered categories and the codes attached to them

Response levels in a health status instrument are ordered by severity, with no problems first. The digits used to code them carry that order and nothing more, so the levels form an ordinal scale. A level coded 4 is worse than a level coded 2, but the code does not say that it is twice as bad, or that the gap between levels 1 and 2 equals the gap between levels 4 and 5.

The EuroQol user guides set out the two adult descriptive systems. In the EQ-5D-3L each of the five dimensions has three levels, described as no problems, some problems and extreme problems or unable to. In the EQ-5D-5L each dimension has five levels, described as no problems, slight problems, moderate problems, severe problems and unable to or extreme problems. In both versions the level chosen in each dimension gives one digit, and the five digits together form the health state code, with 11111 meaning no problems on any dimension.

A level code therefore cannot be read without its instrument. Level 3 is the worst level of the EQ-5D-3L but the middle level of the EQ-5D-5L, so the same digit describes very different health in the two versions.

How the number of levels sets the size of a descriptive system

A preference-based instrument defines its health states as every possible combination of one level from each dimension. The count grows multiplicatively, which is why a small change in the number of levels has a large effect on the work a valuation study faces.

$$S = \prod_{d=1}^{D} L_d$$

where $S$ is the number of distinct health states, $D$ is the number of dimensions and $L_d$ is the number of response levels in dimension $d$.

For the EQ-5D-3L, $S = 3^5 = 243$, and the EuroQol user guide gives the same total. For the EQ-5D-5L, $S = 5^5 = 3125$, again matching the user guide. Valuing thousands of states directly is impractical, so a value set is estimated from a sample of states with a model that assigns a utility decrement to each level of each dimension. As an illustration, a main-effects model for the EQ-5D-5L with one decrement for each of the four levels below no problems in each of five dimensions has 4 × 5 = 20 decrements, the same number as the 20-parameter hybrid model behind the England EQ-5D-5L value set.

How the EQ-5D-5L level labels were chosen

Level labels are where a respondent's experience meets the instrument, so their wording affects which level is chosen. Herdman and colleagues described the development of the EQ-5D-5L in 2011. Response scaling studies in the UK and Spain came first, and selecting labels at approximately the 25th, 50th and 75th centiles produced two alternative five-level versions.

Focus groups then slightly favoured the version worded slight, moderate and severe problems, with no problems and unable to do as the anchors in the functional dimensions, and similar wording was used for pain or discomfort and for anxiety or depression. Any even spacing of severity that results is a property of the wording, not of the numeric codes. Herdman and colleagues concluded in 2011 that further testing was needed to show whether the new version improved sensitivity and reduced ceiling effects.

Ceiling effects and the extra levels of the EQ-5D-5L

With only three levels, a person with mild problems has to choose between no problems and some problems, and some will choose no problems. A large share of respondents reporting 11111 is a ceiling effect, and it limits the ability of the instrument to show a benefit for people in fairly good health. Janssen and colleagues tested whether the extra levels helped.

Their 2013 study included 3,919 participants in six countries, drawn from eight patient groups with chronic conditions and a student cohort. The ceiling fell to 16.0 per cent with the EQ-5D-5L, against 20.2 per cent with the EQ-5D-3L, with relative reductions between 7.1 per cent in the Danish population and 49.0 per cent in the Dutch population. Absolute discriminatory power, measured by the Shannon index, was 1.87 for the five-level version and 1.24 for the three-level version, while relative discriminatory power measured by Shannon evenness improved only slightly, 0.81 against 0.78. The authors judged the EQ-5D-5L a valid extension of the three-level system that reduced the ceiling and improved discriminatory power.

The results show what extra levels can and cannot do. More levels spread respondents across more categories, which raises absolute information, but the five-level version still left about one respondent in six at the top of the scale in that study. A ceiling of this kind reflects the content of the dimensions as well as the number of levels, since a person whose problems lie outside the five dimensions can still report 11111.

Response levels inside a value set and a QALY

A value set turns each response level into a decrement from full health. The health state utility value for a profile is then 1 minus the sum of the decrements for the levels reported, under an additive model, and multiplying that value by time in the state gives QALYs. The decrements are estimated from preference data, so the distance between two levels in utility terms depends on the population that valued them and the method used, and can differ across dimensions.

This is where the ordinal nature of the levels is resolved. The codes 1 to 5 are not used as numbers in the utility calculation. Each level of each dimension receives its own estimated weight, which allows the step between slight and moderate pain to be worth more or less than the step between slight and moderate problems with self-care. Country value sets, such as the EQ-5D-3L value set used in the UK, assign different weights to the same levels because they reflect different populations' preferences.

Level sum score and summaries that treat codes as numbers

Some analyses skip the value set and add the level codes. Devlin, Parkin and Janssen describe this Level Sum Score as the sum of the level numbers across the five dimensions, which runs between 5 and 15 for the EQ-5D-3L and between 5 and 25 for the EQ-5D-5L. They note that it is sometimes misleadingly referred to as the misery score, and that it has been used as a crude measure of severity to gauge the validity of values obtained in valuation studies.

The same authors call the score a very crude summary and refer to the equally weighted Level Sum Score. Giving equal weight to every dimension and to every step between levels is itself a value judgement, and profiles as different as 22222, 33211 and 11233 all have a Level Sum Score of 10. Two profiles with the same score can therefore receive quite different utilities from a value set.

Illustrative worked example with two EQ-5D-5L profiles

All decrements in this example are illustrative and do not come from any published value set. Suppose a value set gives the following decrements, with no problems scored zero in every dimension. Self-care level 2 is 0.05, usual activities level 3 is 0.10, pain or discomfort level 2 is 0.07, mobility level 3 is 0.12 and anxiety or depression level 3 is 0.15.

Step 1 (first profile). Profile 12321 has levels 1, 2, 3, 2 and 1 for mobility, self-care, usual activities, pain or discomfort and anxiety or depression. Its Level Sum Score is 1 + 2 + 3 + 2 + 1 = 9. Its utility is 1-0.05-0.10-0.07 = 0.78.

Step 2 (second profile). Profile 31113 has moderate mobility problems and moderate anxiety or depression. Its Level Sum Score is 3 + 1 + 1 + 1 + 3 = 9, the same as the first profile. Its utility is 1-0.12-0.15 = 0.73.

Step 3 (QALYs). Over 2 years without discounting, the first profile yields 0.78 × 2 = 1.56 QALYs and the second 0.73 × 2 = 1.46 QALYs, a difference of 0.10 QALYs.

Equal Level Sum Scores hide a difference of 0.05 in utility and 0.10 QALYs over two years. Value sets, and not summed codes, therefore provide the weights used for QALYs.

Boundaries with nearby concepts

A response level belongs to the descriptive system of an instrument, while a health state is a full combination of levels across dimensions. The design choices behind the number and wording of levels are matters of response option design, and the levels themselves are what those choices produce. An attribute level in a discrete choice experiment is a value that an attribute takes in a choice task, set by the researcher, whereas a response level is chosen by the respondent to describe his or her own health.

The EQ-5D also includes the EQ VAS, a visual analogue scale for an overall rating of health. That format records a point on a continuous line, while the descriptive system asks for one ordered category per dimension. Non-preference-based instruments that measure health-related quality of life also use response levels, often summed into a total score, but their scores cannot weight life years until they are mapped onto a preference-based measure.

Common misreadings of response levels

Several mistakes come from treating level codes as if they were measurements. Most of them disappear once the codes are read as labels for ordered categories.

1. Mean level codes measure average severity. Averaging codes assumes equal spacing between levels and equal importance across dimensions, which neither instrument design nor valuation supports.
2. A level means the same thing in the three-level and five-level versions. Level 3 is extreme problems or unable to in the EQ-5D-3L and moderate problems in the EQ-5D-5L.
3. More levels remove ceiling effects. In Janssen and colleagues' comparison the five-level version reduced the ceiling but about 16 per cent of respondents still reported no problems on every dimension.
4. A higher Level Sum Score always means a lower utility. Profiles with the same score can differ in value, and a profile with a higher score can be valued above one with a lower score when the problems lie in dimensions that carry less weight.

Sources

• Brazier J, Ratcliffe J, Salomon JA, Tsuchiya A. Measuring and Valuing Health Benefits for Economic Evaluation. 2nd ed. Oxford: Oxford University Press; 2017.
• EuroQol Research Foundation. EQ-5D-3L User Guide. Rotterdam: EuroQol Research Foundation. https://euroqol.org/wp-content/uploads/2023/11/EQ-5D-3LUserguide-23-07.pdf
• EuroQol Research Foundation. EQ-5D-5L User Guide. Rotterdam: EuroQol Research Foundation. https://euroqol.org/wp-content/uploads/2023/11/EQ-5D-5LUserguide-23-07.pdf
• Herdman M, Gudex C, Lloyd A, et al. Development and preliminary testing of the new five-level version of EQ-5D (EQ-5D-5L). Quality of Life Research. 2011;20(10):1727-1736. https://doi.org/10.1007/s11136-011-9903-x
• Janssen MF, Pickard AS, Golicki D, et al. Measurement properties of the EQ-5D-5L compared to the EQ-5D-3L across eight patient groups: a multi-country study. Quality of Life Research. 2013;22(7):1717-1727. https://doi.org/10.1007/s11136-012-0322-4
• Devlin N, Parkin D, Janssen B. Analysis of EQ-5D profiles. In: Methods for Analysing and Reporting EQ-5D Data. Cham: Springer; 2020. Chapter 2. https://doi.org/10.1007/978-3-030-47622-9_2
• Devlin NJ, Shah KK, Feng Y, Mulhern B, van Hout B. Valuing health-related quality of life: an EQ-5D-5L value set for England. Health Economics. 2018;27(1):7-22. https://doi.org/10.1002/hec.3564