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Response mapping to the EQ-5D: methods and comparative performance

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Response mapping to the EQ-5D: methods and comparative performance

Oliver Rivero-Arias, Alastair Gray and Helen Dakin

iHEAorganised session 9th July 2013

- In response mapping, 5 categorical models (e.g. mlogit) predict the probability or odds that a participant is at level j on each EQ-5D domain
- Combine predicted responses with tariff to estimate utilities
- Advantages:
- Response mapping algorithm can be used with any national EQ-5D tariff
- Provides data on the distribution of patients across EQ-5D states
- Gives insights into the nature of the relationship between instruments
- May give better utility predictions by reflecting the distribution better

- Disadvantages:
- Models are more complicated to estimate: larger sample size needed?
- More complicated to estimate utilities from predicted probabilities

Pain/discomfort

Self care

Anxiety/depression

Mobility

Usual activities

- Highest probability: Assume patient is at the level with the highest predicted probability
- Monte Carlo: Randomly assign patients to one level
- Expected value: Multiply predicted the probabilities with tariff values to obtain expected utility

Highest prob:

1

2

1

-.2*.104

-.1*.214

2

1

1

-.4*.036

-.32*.094

2

3

2

-.35*.123

-.3*.386

2

1

1

-.32*.071

-.12*.236

2

1

1

=0.883

=0.760

=0.312

=0.305

1-.3*.069

-.17*.314

Monte Carlo 1:

Expected

value:

2:

-.17*.1*.32*.3*.12*.269 -(1-(1-.53)*(1-.7)*(1-.27)*(1-.35)*(1-.66)*.081

- Highest probability
- Underestimates % of patients in rare health states (e.g. level 3)
Overestimates predicted utility

- Underestimates % of patients in rare health states (e.g. level 3)
- Monte Carlo (MC)
- ≥1000 draws normally needed
- Some studies use only one draw random variability

- Expected value (EV)
- Equivalent to Monte Carlo with infinite draws
- Gives exact result instantly with one equation

- To review how response mapping to EQ-5D has been used to date
- To compare the performance of response mapping with other methods

- A systematic review was conducted to identify studies using response mapping to predict EQ-5D responses from responses/scores on other QoL instruments
- Included published and available unpublished studies

- Searched Medline, Centre for Reviews and Dissemination (CRD), the Health Economists’ Study Group (HESG) website and HERC database of mapping studies (http://www.herc.ox.ac.uk/downloads/mappingdatabase)
- Extracted data on:
- Source instrument, models estimated
- How prediction accuracy varied between models
- Methods used to calculate utilities from predicted probabilities
- Highest probability, expected value (EV) or Monte Carlo (MC)

- 21 studies identified
- Source instrument: SF-12 in 4 studies; EQ-5D-5L in 1 & disease-specific in 16
- 75% (6/8) of studies found predictions errors from both direct & response mapping higher for patients with utilities <0.5 than those with good health

- OLS was most common direct mapping method
- Multinomial logit was most common response mapping model

Direct mapping models

Response mapping models

Bayesian

networks: 2

Mlogit: 14

CLAD: 7

11

2

Other: 5

3

2

2

1

3

2

9

Oprobit or generalised oprobit: 2

2

1

2

Ologit: 6

1

2-part: 5

OLS or

GLS: 20

Cross-tabulation: 1

- Monte Carlo, expected value and highest probability methods all commonly used to estimate utilities
- 3 studies compared different methods

Expected value: 9

Monte Carlo (n=1 or 11): 7

6

1

6

1

1

2

Highest probability: 5

Monte Carlo (n>100): 3

- 55% of studies using EV or ≥100 Monte Carlo found response mapping gave similar or more accurate prediction errors
- V.s 17% of those using highest probability or ≤11 Monte Carlo draws

Predictions from

response mapping are:

Highest probability

or ≤11 Monte Carlo

Expected value or

≥100 Monte Carlo

- Response mapping and direct mapping have similar prediction errors when EV or MC (n>100) are used to calculate utilities
- Highest probability method and n=1 Monte Carlo should be avoided

- All mapping models perform poorly in patients with poor QoL
- Response mapping has additional advantages
- Insights into relationships between instruments
- Gives domain-level predictions
- Can be used with any EQ-5D valuation tariff

- Distribution of Excel or Stata commands to estimate predictions can simplify the process for users
- mrs2eq and oks2eq commands accepted for publication in Stata Journal

- Many thanks to Jason Madan, Kamran Kahn, Aki Tsuchiya and Richard Eldin for allowing us to cite their unpublished work