Crosswalk

Concept

Theoretically, Crosswalk is a statistical mapping method used to estimate health utility values for one preference-based health-related quality of life instrument from responses obtained using another instrument. It exists to improve comparability between studies, facilitate economic evaluation when direct utility data are unavailable, and enable the application of value sets developed for different descriptive systems. Crosswalk methods are founded on regression modelling and statistical prediction rather than direct valuation.

Mathematically, Crosswalk is represented as a predictive mapping function in which utility values from the target instrument are estimated from responses or scores on the source instrument. The mathematical framework consists of regression-based prediction models, including ordinary least squares, Tobit, censored least absolute deviations, response mapping, multinomial logistic regression or mixture models, depending on the characteristics of the instruments and utility distribution. The resulting model estimates expected utility values conditional on observed health states.

In practice, Crosswalk algorithms are developed using datasets in which respondents complete both instruments simultaneously. Alternative statistical models are estimated, internally and externally validated, and assessed using measures such as mean absolute error (MAE), root mean squared error (RMSE) and prediction bias. The selected mapping function is then applied to datasets lacking direct utility measurements to estimate utilities for cost-utility analysis.

---

Purpose

Used to estimate preference-based health utility values from alternative health status instruments, enabling QALY estimation, economic evaluation, evidence synthesis and comparability across studies when direct utility measurement is unavailable.

---

Mathematical Formulae

Primary Formula

? = f(X; ?)

where:

• ? = predicted utility value for the target instrument
• X = observed responses or scores from the source instrument
• ? = estimated model parameters

Supporting Formulae

For a linear crosswalk model:

? = ?? + ????? ??X? + �

Prediction error:

RMSE = �((1/n) ????� (U? ? ??)�)

Mean absolute error:

MAE = (1/n) ????� |U? ? ??|

Related Mathematical Methods

• Ordinary least squares regression
• Tobit regression
• Response mapping
• Multinomial logistic regression
• Finite mixture modelling
• Model validation
• Root mean squared error
• Mean absolute error

---

Example

A clinical study collected only SF-12 responses from 600 patients. A published crosswalk algorithm predicts EQ-5D-5L utilities using the regression equation:

? = 0.182 + 0.0095 ? PCS + 0.0068 ? MCS

For a patient with PCS = 42 and MCS = 48:

? = 0.182 + (0.0095 ? 42) + (0.0068 ? 48) = 0.182 + 0.399 + 0.326 = 0.907

The predicted EQ-5D-5L utility of 0.907 is subsequently used to estimate QALYs in a cost-utility analysis.

---

Excel Implementation

Function	Example Formula	Health Economics Application
SUMPRODUCT	=Intercept+SUMPRODUCT(B2:F2,$B$10:$F$10)	Calculates predicted utility using estimated regression coefficients.
ABS	=ABS(Observed-Predicted)	Calculates absolute prediction error (MAE).
SQRT	=SQRT(AVERAGE(ErrorRange^2))	Calculates RMSE for model validation.
AVERAGE	=AVERAGE(PredictedUtilities)	Summarises predicted utilities for economic evaluation.

---

VBA (Optional)

Automate application of a published crosswalk algorithm to large patient datasets and generate predicted utility values with validation statistics.

---

Sources

• NICE. Health Technology Evaluation Manual.
• Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
• ISPOR Good Practices for Outcomes Research Task Force reports on mapping to health utility measures.
• van Hout B, Janssen MF, Feng YS, et al. Interim Scoring for the EQ-5D-5L: Mapping the EQ-5D-5L to EQ-5D-3L Value Sets. Value in Health. 2012.