Crosswalk

Crosswalk Between Versions of a Health Utility Instrument

A crosswalk lets utility values be produced for data collected with one version of an instrument when the values that a decision maker accepts belong to another version of the same instrument. The best known case is the EQ-5D, where the five-level EQ-5D-5L replaced the three-level EQ-5D-3L in many studies before value sets for the new version existed or were accepted. Because a crosswalk changes the utilities that enter a cost-utility analysis, the choice of crosswalk can change QALY gains and the ICER, and it needs to be reported and tested like any other model input.

Why crosswalks are needed when instruments are revised

Instruments are revised to describe health better, for example by adding response levels to reduce ceiling effects. Revisions create a gap, since trials begin collecting the new version while reimbursement bodies, historical evidence and existing models are built on values for the old one. A crosswalk fills the gap by expressing each health state described by the new version as a value on the old version's scale. It is a bridge between versions of one descriptive system, which separates it from mapping between different instruments.

How the EQ-5D-5L to EQ-5D-3L crosswalk was built

Van Hout and colleagues developed the interim scoring for the EQ-5D-5L by linking the two versions through respondents who completed both. They modelled how responses on the five-level scale relate to responses on the three-level scale in each dimension, and then assigned each five-level health state the expected three-level value under a country's existing 3L value set. The result is a value for every one of the 3,125 five-level states, available for each country with a 3L value set.

$$U_{3L}(h_{5L}) = \sum_{h_{3L}} \Pr\left(h_{3L} \mid h_{5L}\right) \times V_{3L}(h_{3L})$$

where $h_{5L}$ is a five-level health state, $h_{3L}$ runs over the 243 three-level states, $\Pr(h_{3L} \mid h_{5L})$ is the estimated probability that a person describing $h_{5L}$ would describe $h_{3L}$, $V_{3L}$ is the 3L value set, and $U_{3L}(h_{5L})$ is the crosswalk value. Hernández Alava, Wailoo and Pudney later estimated an alternative mapping between the two versions that also allows for age and sex, for use in technology appraisal.

Worked example of a crosswalk value

The figures in this example are illustrative and do not come from a published crosswalk. Suppose a five-level state is estimated to correspond to three-level states A, B and C with probabilities 0.60, 0.30 and 0.10, and the 3L value set gives those states values of 0.85, 0.72 and 0.52.

$$U = 0.60 \times 0.85 + 0.30 \times 0.72 + 0.10 \times 0.52 = 0.510 + 0.216 + 0.052 = 0.778$$

where 0.778 is the crosswalk value assigned to the five-level state. A patient reporting that state in a trial would contribute 0.778 per year to QALYs on the 3L scale. The value lies between the 3L values it averages, which is why crosswalk values tend to be smoother than direct values.

Assumptions behind a crosswalk

A crosswalk assumes that the relation between the two versions estimated in the linking sample holds in the population where it is applied. It also assumes that the old version's value set is the right one to use, so any weakness in that value set passes through. Because the new version describes health in finer steps, a crosswalk cannot recover preferences for the distinctions the old version cannot express, and it can compress differences between treatments.

Use in cost-utility analysis and HTA

In a cost-utility analysis the crosswalk value replaces a directly valued utility for each patient and time point, and QALYs are then computed in the usual way. When a body prefers values on the old scale, the crosswalk keeps results comparable with earlier appraisals, and when a value set for the new version becomes available, results computed both ways show whether the choice matters. Reporting which crosswalk, which country's value set and which software were used allows the result to be reproduced.

Crosswalks, mapping studies and value sets

A crosswalk links versions of one instrument. A mapping study instead predicts utilities on a preference-based measure from a different instrument, such as a disease-specific questionnaire or the SF-12, using regression or response models, and its error is usually larger because the two descriptive systems overlap less. A native value set for the new version, valued directly by the population, makes a crosswalk unnecessary for that country.

Common misreadings of crosswalk values

Treating crosswalk values as directly elicited preferences overstates their precision. Applying a crosswalk built with one country's value set to another country's decision problem mixes populations. Calling any regression between different instruments a crosswalk confuses it with mapping, and ignoring the uncertainty in the crosswalk in probabilistic analysis understates decision uncertainty.

Sources

• van Hout B, Janssen MF, Feng YS, Kohlmann T, Busschbach J, Golicki D, Lloyd A, Scalone L, Kind P, Pickard AS. Interim scoring for the EQ-5D-5L: mapping the EQ-5D-5L to EQ-5D-3L value sets. Value in Health. 2012;15(5):708-715.
• Hernández Alava M, Wailoo A, Pudney S. Methods for mapping between the EQ-5D-5L and the 3L for technology appraisal. NICE Decision Support Unit report. University of Sheffield; 2017.
• Brazier J, Ratcliffe J, Salomon JA, Tsuchiya A. Measuring and Valuing Health Benefits for Economic Evaluation. 2nd ed. Oxford University Press; 2017.
• Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press; 2015.