Introduction 1 2 1 3 4 5 7 8 9 4 10 11 12 14 15 16 17 12 13 18 20 Our aim is to investigate the discriminatory power of the EQ-5D, HUI2 and HUI3 in a general population sample, as expressed by Shannon’s indices. Informativity was assessed separately by dimension and by MAUI as a whole. Methods Data http://www.ahrq.gov/rice/ 21 22 23 Instruments 6 1 Table 1 Level descriptions for common dimensions between EQ-5D, HUI2 and HUI3 EQ-5D HUI2 HUI3 Mobility Mobility Ambulation No problems in walking about Able to walk, bend, lift, jump, and run normally for age Able to walk around the neighbourhood without difficulty, and without walking equipment Some problems in walking about Walks, bends, lifts, jumps, or runs with some limitations but does not require help Able to walk around the neighbourhood with difficulty; but does not require walking equipment or the help of another person Confined to bed Requires mechanical equipment (such as canes, crutches, braces, or wheelchair) to walk or get around independently Able to walk around the neighbourhood with walking equipment, but without the help of another person Requires the help of another person to walk or get around and requires mechanical equipment as well Able to walk only short distances with walking equipment, and requires a wheelchair to get around the neighbourhood Unable to control or use arms and legs Unable to walk alone, even with walking equipment. Able to walk short distances with the help of another person, and requires a wheelchair to get around the neighbourhood Cannot walk at all Self-care Self-care  No problems with self-care Eats, bathes, dresses, and uses the toilet normally for age  Some problems washing or dressing self Eats, bathes, dresses, or uses the toilet independently with difficulty  Unable to wash or dress self Requires mechanical equipment to eat, bathe, dress, or use the toilet independently  Requires the help of another person to eat, bathe, dress, or use the toilet  Pain/Discomfort Pain Pain No pain or discomfort Free of pain and discomfort Free of pain and discomfort Moderate pain or discomfort Occasional pain. Discomfort relieved by non-prescription drugs or self-control activity without disruption of normal activities Mild to moderate pain that prevents no activities Extreme pain or discomfort Frequent pain. Discomfort relieved by oral medicines with occasional disruption of normal activities Moderate pain that prevents a few activities Frequent pain; frequent disruption of normalactivities. Discomfort requires prescription narcotics for relief Moderate to severe pain that prevents some activities Severe pain. Pain not relieved by drugs and constantly disrupts normal activities Severe pain that prevents most activities Anxiety/Depression Emotion Emotion Not anxious or depressed Generally happy and free from worry Happy and interested in life Moderately anxious or depressed Occasionally fretful, angry, irritable, anxious, depressed, or suffering "night terrors" Somewhat happy Extremely anxious or depressed Often fretful, angry, irritable, anxious, depressed, or suffering "night terrors" Somewhat unhappy Almost always fretful, angry, irritable, anxious, depressed Very unhappy Extremely fretful, angry, irritable, anxious, or depressed usually requiring hospitalization or psychiatric institutional care So unhappy that life is not worthwhile   Cognition Cognition  Learns and remembers school work normally for age Able to remember most things, think clearly and solve day to day problems  Learns and remembers school work more slowly than classmates as judged by parents and/or teachers Able to remember most things, but have a little difficulty when trying to think and solve day to day problems  Learns and remembers very slowly and usually requires special educational assistance Somewhat forgetful, but able to think clearly and solve day to day problems  Unable to learn and remember Somewhat forgetful, and have a little difficulty when trying to think or solve day to day problems   Very forgetful, and have great difficulty when trying to think or solve day to day problems   Unable to remember anything at all, and unable to think or solve day to day problems Shannon’s indices: background and properties 17 24 25 26 30 In information theory, the information of a signal is distinguished from the meaning or the semantic content of a signal. Rather, the information is quantified and is identified with uncertainty. Informativity is dependent on the number of classes (e.g. bits or response options) and the distribution of the observations (the ‘signal’) among classes. For classifications, this implies that if one would want to develop a useful (informative) distinction between, say, European countries, distinguishing between Scandinavian and non-Scandinavian countries would be far less informative than distinguishing between Northern, Western, Eastern and Southern European countries. Note that the latter classification not only contains more categories but the countries are also more evenly distributed among categories. \documentclass[12pt]{minimal}
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$$\end{document} J 32 17 33 J J H H max H H max H J 26 34 35 Shannon indices applied to MAUIs p p C L p i i th H max 2 L n n n H 2 2 2 1.30 H max 2 J 0.82 1 H J L 1 1 1 H J H J 1 H J H Fig. 1 H J  C P max p i i H′ max 2 P max N H max J H J Results The mean age of the respondents was 42.9 years (range: 18.0–99.3 years), with 42.2% of the respondents being male. White (non-Hispanic) respondents were 1,435 (38.9%), non-Hispanic blacks were 1,018 (27.6%) and Hispanic were 1,100 (29.8%). 2 Table 2 N   Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 EQ-5D Mobility 82.17 17.53 0.30 – – – Self care 95.58 4.01 0.41 – – – Usual activities 84.88 13.57 1.54 – – – Pain/Discomfort 61.28 34.71 4.01 – – – Anxiety/Depression 73.86 23.57 2.57 – – – HUI2 Sensation 44.54 43.54 10.76 1.16 – – Mobility 87.24 8.48 3.60 0.68 0.00 – Emotion 69.20 27.85 1.82 0.65 0.49 – Cognition 68.36 29.94 1.63 0.08 – – Self-care 96.64 2.95 0.19 0.22 – – Pain 48.17 40.94 7.10 2.98 0.81 – HUI3 Vision 48.50 47.87 1.00 2.47 0.03 0.14 Hearing 94.58 0.92 1.52 1.65 0.30 1.03 Speech 92.68 4.82 2.03 0.43 0.03 – Ambulation 87.24 8.48 2.55 1.06 0.51 0.16 Dexterity 92.44 5.82 0.79 0.70 0.14 0.11 Emotion 72.50 22.32 3.74 1.16 0.27 – Cognition 68.36 4.15 17.85 7.37 2.19 0.08 Pain 49.34 33.73 11.46 4.01 1.46 – 2 H J H Fig. 2 H \documentclass[12pt]{minimal}
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\begin{document}$${^{\dag}}$$\end{document} H J  J 3 Table 3 H J   EQ-5D HUI2 HUI3 P max 243 8000 972,000 Observed health states 91 322 694 H max 7.92 12.97 19.89 Estimation H J H J H J N 6.24 0.79 8.57 0.66 10.96 0.55 N 6.37 0.80 9.12 0.70 12.29 0.62 N 6.41 0.81 9.48 0.73 13.36 0.67 Discussion We compared the discriminatory power of the EQ-5D, HUI2 and HUI3 in the general population, using Shannon’s indices of absolute and relative informativity, for each dimension separately and by MAUI as a whole. As might be expected in a general population sample, most respondents reported no problems on all dimensions and there were fewer responses with increasing level severity. An exception is HUI3 Cognition, where respondents reported more problems on levels 3 and 4 than on level 2. This is probably due to the fact that this dimension is not unidimensional, and levels 2 and 3 are conceptualized parallel rather than ordinal. That is, HUI3 Cognition level 2 focuses on problems in thinking and problem solving, level 3 addresses problems in remembering, whereas level 4 combines the problems mentioned in levels 2 and 3. 2 H 2 J 2 Overall, performance in terms of informativity of EQ-5D, HUI2 and HUI3 of the common dimensions varies over dimensions. The Pain/Discomfort dimension of EQ-5D, but perhaps also other dimensions, might benefit from an extension to 4 or 5 levels. HUI2 and HUI3 might benefit from more sensitive grading terms in their level descriptions, especially the ‘threshold’ level 2, in Ambulation (HUI3) and Self-Care (HUI2). When assessing informativity by instrument, HUI3 shows the best results on absolute informativity but the lowest on relative informativity while EQ-5D shows highest relative informativity and lowest absolute informativity. HUI2 seems to be the optimal compromise. The importance of differences in the Shannon indices ultimately requires empirical evidence over a wider range of populations, conditions and instruments, including evidence on discriminant validity. As Shannon’s indices are new in the field of health status measurement, some methodological issues need to be addressed, taking into account that their principal focus is on classifications with mutually exclusive categories, rather than conventional (health status) measures which by design contain multiple partially overlapping items. The Shannon indices share some properties with reliability coefficients. Like reliability indices, they express discriminatory power. Furthermore, they are also non-dimensional, i.e. they have no relation to the content, meaning or clinical relevance of what the instrument aims to measure, which make them suitable for comparability, between instruments as well as between populations. However, reliability reflects two different concepts: discriminatory power as such, and consistency, e.g. consistency between raters (inter-rater reliability) or consistency over time (test-retest reliability). This requires a repeated measurement (repetition ‘over raters’ or over time) which introduces an error component in case of a difference among the repeated measurements. Shannon’s indices solely reflect discriminatory power, and need only a single measurement. Furthermore, the Shannon indices are non-parametric measures and therefore highly suitable for nominal or ordinal measurement scales. in that particular population Previously, the common approach to investigate discriminatory power was examining the frequency distributions of responses, e.g. for ceiling or floor effects. A comprehensive, formal measure to express discriminatory power such as Shannon’s indices seems clearly superior to such a ‘face-value’ method. Furthermore, when the number of categories is large (e.g. when comparing MAUIs as a whole), it becomes very difficult to make a sound comparison by just looking at the distributions. We have demonstrated the use of the Shannon indices to compare the discriminatory power of different MAUIs, to show which instrument is more sensitive in differentiating between levels of health in the population at hand. But they may also be used to guide the development of new, or optimization of existing MAUIs, by helping determine how many levels are efficient for each dimension. This is a particularly relevant consideration for MAUIs, since adding extra levels in a descriptive system makes it increasingly complex, and the derivation of a robust set of preference weights more challenging. Apart from MAUIs, the Shannon indices can also be used in a wide range of other classifications in the medical domain (e.g. the Karnofsky scale, the Spitzer QL index) and in the clinical domain (e.g. the APGAR score, the Child-Pugh classification). A practical weakness of the Shannon approach is that when the sample size is exceeded by the total number of health states described by all permutations across all dimensions of a MAUI, informativity (for the instrument as a whole) has to be estimated. This implies that using the Shannon Evenness index by instrument is not very practical when a health classification system has a large number of permutations as was the case in HUI3 (972,000 permutations). This however is not a disadvantage of the Shannon methodology per se, but also a matter of classification design (overload of dimensions with detailed response options producing an excessive amount of ‘empty’ permutations), or a practical problem (excessive data collection). H J H J How the Shannon indices will behave in a different population, such as patient populations, remains to be investigated. So far, Shannon’s indices proved to be useful in showing weaknesses of level gradings used in EQ-5D, HUI2 and HUI3, and offers leads for improvement, establishing their practical psychometric value.