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Scaling Session. Measurement implies “assigning numbers to objects or events…”

Scaling Session

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Scaling Session

Measurement implies “assigning numbers to objects or events…”

Distinguish two levels: we can assign numbers to the response levels for a single question (mild, moderate or severe pain), and we can also assign different numerical weights to each question. Thus, saying ‘No’ to “Can you get out of bed?” might get a higher score than ‘No’ to “Can you run a mile?”

The purpose of scaling is to select appropriate numbers for these two purposes to represent amounts of health.

Where do these numbers come from?

- You can assign the same weight to each question: e.g., one point for each affirmative response
- You could assign arbitrary values to response levels (mild pain = 1, moderate = 2, severe = 3)
- You might base these numbers on some type of conceptual model of the phenomenon
- Or infer weights from administrative, legal, or social decisions (how much compensation is paid for this type of disability?)
- Or you can calculate weights through a scaling task.

- These produce weights through an empirical procedure.
- Scaling is undertaken by people who are asked to provide their personal judgment; this measures their ‘preferences’ (or aversion) for specified health states;
- Two categories of preferences can be distinguished: ‘values’ and ‘utilities’.
- These correspond to two contrasting historical traditions that have influenced the way we assign numbers in health measurement: psychometrics and econometrics.

- Psychometrics deals with feelings, opinions and perceptions, and is appropriate in judging single items; it measures “values”.
- The econometric tradition derives from studies of consumption and choices between goods; it focuses on making decisions under conditions of uncertainty (as with investing). It measures “utilities”: choice given risk.
- “Utilities are the numbers that represent the strength of a person’s preferences for particular outcomes when faced with uncertainty” (George Torrance)

- Hence the econometric approach is suitable for weighting health states for clinical decision analysis and the patient’s choice of therapy, where there is uncertainty. Used in planning care & anything to do with future health.
- The psychometric approach is good for valuing current health states.
- In general, utility scores are higher than value judgments, although the difference may not be great.

Psychometric

- Paired comparisons method
- Equal-appearing interval scaling
- Likert scaling
- Magnitude estimation methods
Utility Methods

- Standard gamble
- Time tradeoff
- Willingness to pay

Many variants. For example:

- Thurstone ‘equal-appearing interval scaling’. Cards with descriptions of health states (the items) written on each; raters place these on a scale representing intensity of the relevant concept (e.g., disability). Typically 15 spaces on scale. The item weights come from the average of individual judgments. High SD suggests ambiguous item.
- Magnitude estimation: Raters compare the health states with a standard state and are asked to provide a number or ratio indicating how much worse or better each is than the standard.

- ‘Standard Gamble’. Respondent chooses between a certain outcome (e.g., living in the restricted health state for 10 years and then dying) and a gamble (e.g., 90% chance of immediate cure, but with a 10% chance of immediate death). The more severely they judge the current state, the higher the risk of death they will accept (12% or 15%, etc) to avoid it.
- Time trade-off. Respondent asked to imagine being in the health state being rated and is then asked how many years of life hw will give up to be cured from it.

- Choose people to make the judgments. Think carefully about the sample!
- Choose the health states to be rated (often a brief description)
- Select a scaling method (psychometric or econometric)
- Collect the preference judgments
- Analyze the data and calculate weights for each health state

- All of that seems quite a bother to do!
- An alternative is to derive weights from the pattern of responses from a representative sample of people on the health measure.
- This fits within the classical test theory approach to measurement.
- It is ‘norm referenced’ – compared to a distribution.
- One example is Likert scaling: next slide

* Half p for that category plus p for category below

People

A B C D E F

I can use the toilet without assistance yes yes yes yes yes no

I can rise from an armchair yes yes yes yes nono

I can walk one block yes yes yes no no no

I can do the grocery shopping yes yes no no no no

I can run a mile yesno no no no no

score 5 4 3 2 1 0

This generates an ordinal scale in which all items fall on one dimension.

- Is scaling worth the effort? The weighted and unweighted versions of many health measures often correlate > 0.9
- Where a scale has different sections, the overall score is weighted by the number of items in each section.
- Think about unidimensionality. Is a notion such as “independence” really a single dimension?
- Do overall scores make sense? Should we add incontinence to mobility?
- Is Hi + Lo equivalent to Med + Med?

- Note that numerical ratings can represent many different aspects of a health state:
- frequency of occurrence of the symptom
- probability it will occur
- unpleasantness of the symptom
- utility (or undesirability, given its probability)

- Do interval scales necessarily represent conceptually equal intervals? (Is age an interval scale when you are using it to represent maturity?)