Mapping Function

Concept

Theoretically, Mapping Function is the mathematical relationship that transforms scores from a non-preference-based health outcome measure into predicted preference-based utility values. It represents the functional form of a mapping algorithm rather than the statistical procedure used to estimate it. The concept is founded on statistical prediction theory and exists to enable estimation of health utilities when direct preference-based measurements are unavailable.

Mathematically, mapping functions have no universally recognised canonical mathematical formula. They are expressed as fitted predictive equations in which utility is modelled as a function of one or more explanatory variables derived from the source instrument. The functional form depends on the selected statistical model and the estimated model parameters.

In practice, mapping functions are derived from datasets containing both the source instrument and a preference-based measure such as EQ-5D. Once validated, the published function is applied to independent datasets to predict health state utility values for quality-adjusted life year estimation, economic evaluation and health technology assessment. Predictive performance is evaluated using recognised goodness-of-fit and prediction error statistics.

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Purpose

Used to convert scores from non-preference-based health outcome measures into predicted preference-based utility values for cost-utility analysis when direct utility measurement is unavailable.

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Mathematical Formulae

Primary Formula

There is no universally recognised canonical mathematical formula.

Supporting Formulae

U? = f(X; ??)

where:

• U? = predicted health utility
• X = predictor variable or vector of predictor variables
• ?? = estimated model parameters
• f(�) = fitted mapping function

For a linear mapping function:

U? = ?? + ????? ??X?

Related Mathematical Methods

• Regression modelling
• Ordinary least squares regression
• Generalised linear models
• Beta regression
• Response mapping
• Cross-validation
• Root mean squared error (RMSE)
• Mean absolute error (MAE)

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Example

A published mapping function predicts EQ-5D utility from a disease-specific questionnaire:

U? = 0.91 ? 0.018(Disease Score)

For a patient with a disease score of 15:

U? = 0.91 ? 0.018 ? 15 = 0.640

The predicted utility value of 0.640 is subsequently used to estimate QALYs in a cost-utility analysis.

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Excel Implementation

Function	Example Formula	Health Economics Application
SUMPRODUCT	=SUMPRODUCT(B2:F2,$B$1:$F$1)+$A$1	Applies a published mapping function to predict utility values.
LINEST	=LINEST(Y2:Y201,B2:F201,TRUE,TRUE)	Estimates coefficients when developing a mapping function.
SQRT	=SQRT(AVERAGE((Y2:Y201-Z2:Z201)^2))	Calculates RMSE to evaluate predictive performance.
ABS	=ABS(Y2-Z2)	Calculates absolute prediction error for model validation.

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VBA (Optional)

Automate the application of validated mapping functions to patient datasets and generate predicted utility values with model validation statistics.

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Sources

• Wailoo AJ, Hernandez-Alava M, Manca A, et al. Mapping to Estimate Health-State Utility from Non-Preference-Based Outcome Measures: An ISPOR Good Practices for Outcomes Research Task Force Report. Value in Health. 2017.
• Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
• Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
• NICE. Health Technology Evaluation Manual.
• Brazier J, Ratcliffe J, Salomon JA, Tsuchiya A. Measuring and Valuing Health Benefits for Economic Evaluation. Oxford University Press.