Mapping Algorithm

Concept

Theoretically, Mapping Algorithm is a statistical prediction model used to estimate health state utility values from non-preference-based health outcome measures when direct utility data are unavailable. It is founded on regression modelling and statistical prediction theory and exists to enable quality-adjusted life year estimation from clinical studies that did not collect preference-based measures. Mapping algorithms are widely used in health economic evaluation when preference-based utility instruments such as EQ-5D were not administered.

Mathematically, mapping algorithms have no universally recognised canonical mathematical formula. They are represented by fitted statistical models that predict utility values from one or more explanatory variables derived from disease-specific or generic health measures. The mathematical framework estimates the expected utility conditional on observed patient characteristics or questionnaire scores.

In practice, mapping algorithms are developed using datasets containing both the source instrument and a preference-based utility measure. Regression coefficients are estimated using recognised statistical methods, internally and externally validated, and subsequently applied to new datasets to predict utility values for economic evaluation. Good practice recommends transparent reporting of predictive accuracy, model performance and uncertainty.

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Purpose

Used to estimate preference-based health utility values from non-preference-based health outcome measures when direct utility data are unavailable, thereby supporting cost-utility analysis and health technology assessment.

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Mathematical Formulae

Primary Formula

There is no universally recognised canonical mathematical formula.

Supporting Formulae

U? = ?? + ????? ??X? + �

where:

• U? = predicted health utility
• ?? = intercept
• ?? = estimated regression coefficients
• X? = predictor variables from the source instrument
• � = random error

RMSE = �[(1?n)????�(U? ? U??)�]

MAE = (1?n)????�|U? ? U??|

Related Mathematical Methods

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

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Example

A clinical study collected scores from a disease-specific quality of life questionnaire but did not administer EQ-5D. A published mapping algorithm predicts EQ-5D utility as:

U? = 0.92 ? 0.015(Symptom Score)

For a patient with a symptom score of 18:

U? = 0.92 ? 0.015 ? 18 = 0.650

The predicted utility of 0.650 is then 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	Calculates predicted utility from published regression coefficients.
LINEST	=LINEST(Y2:Y201,B2:F201,TRUE,TRUE)	Estimates regression coefficients when developing a mapping algorithm.
SQRT	=SQRT(AVERAGE((Y2:Y201-Z2:Z201)^2))	Calculates RMSE for model validation.
ABS	=ABS(Y2-Z2)	Calculates absolute prediction error for MAE estimation.

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VBA (Optional)

Automate the application of published mapping algorithms to patient datasets and generate predicted utility values with model performance 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.