Mapping Study

Mapping Study to Estimate Health State Utilities

Many clinical trials record a disease-specific or clinical outcome measure, such as the EORTC QLQ-C30 in cancer, but no generic preference-based measure, so their results cannot be turned into QALYs without a mapping study. Using an additional dataset in which the same people completed both the clinical measure and a preference-based measure such as the EQ-5D, the study estimates how the two relate, tests how well the estimated relationship predicts, and publishes the result so that later analysts can predict health state utility values for trials that never collected them. The mapping function is the published equation, while the mapping study covers every choice behind that equation, including the estimation data, the statistical model, the validation and the reporting. Dakin and colleagues counted 144 studies reporting 190 algorithms for 110 source instruments onto the EQ-5D in work published by December 2016, so an analyst often has to choose between published mappings by judging the studies behind them.

Why NICE accepts mapped utilities

NICE prefers the EQ-5D as the source of utility values, and mapping is the recognised fallback when a trial did not collect it. The NICE technology appraisal and highly specialised technologies manual (PMG36) states in section 4.3.9 that when EQ-5D data are not available, they can be estimated by mapping other health-related quality-of-life measures, or health-related benefits seen in the relevant clinical trials, to EQ-5D. NICE has consulted on replacement text for that section as part of a modular update on the EQ-5D-5L value set.

NICE's interim methods statement on implementing the EQ-5D-5L value set (PMG51), published on 27 August 2026 and applying to new topics that start after its publication, sets out what the output of a mapping study has to deliver for adults. The UK 5L value set should be used to derive all utility values for adults in reference-case analyses. When EQ-5D-5L data from a relevant study are not available and data from the EQ-5D-3L or a non-EQ-5D measure are used instead, these should be mapped to utility values based on the UK EQ-5D-5L value set, if necessary by mapping onto the 3L value set first and then onto the 5L value set. The statement adds that the mapping model should be fully described, its choice justified and its fit to the data properly demonstrated, and that sensitivity analyses should explore the impact of using different mapping models on the outputs.

Published work lags behind this rule. Dakin and colleagues found that only six of the 144 studies in their review mapped onto the EQ-5D-5L at all, four of them to the 5L alone and two to both versions, while the rest mapped onto the EQ-5D-3L.

What the study has to decide

Each decision in a mapping study can change the utilities that a later cost-utility analysis uses. The ISPOR Good Practices for Outcomes Research Task Force, reported by Wailoo and colleagues in 2017, wrote its recommendations for three audiences, namely analysts who undertake mapping studies, those who use the results in cost-utility analysis, and those who critically review such studies. Its recommendations span the selection of datasets for the mapping estimation, model selection and performance assessment, reporting standards, and the use of results, including the appropriate reflection of variability and uncertainty.

The NICE Decision Support Unit's Technical Support Document 22 (TSD 22), by Wailoo, Hernández Alava and Pudney, updates and replaces TSD 10, the earlier document on mapping by Longworth and Rowen. TSD 22 notes that health utility data have several statistically challenging features, so the choice and performance of statistical models need careful assessment.

Choosing the estimation dataset

The limits of the estimation dataset pass into every prediction. The two measures have to come from the same people at the same time, and the people need to cover the range of severity found in the population to which the mapping will later be applied. A mapping estimated mainly in mild disease has little information about the severe states that often drive a cost-effectiveness result.

Gray, Rivero-Arias and Clarke estimated a mapping of the SF-12 onto the EQ-5D using 12,967 adult survey responses from the 2000 US Medical Expenditure Panel Survey, and tested it out of sample on 13,304 adults from the 1996 Health Survey for England. Testing in another country and survey shows whether the relationship travels.

Statistical models for bounded and lumpy utility data

Utility data break the assumptions of ordinary regression in predictable ways. Hernández Alava, Wailoo and Ara described EQ-5D utility values as bounded above at 1 with a substantial gap before the next feasible values, bounded below, and multimodal. Their adjusted limited dependent variable mixture models build the upper bound and the gap into the model and use a mixture to capture the several peaks, and they compared these with the linear and Tobit models then common in the literature, using rheumatoid arthritis trial data.

The main model families seen in mapping studies differ in what they predict and in how they treat the bounds.

A two-part model joins a first part, often a logit regression, for the probability of full health with a second part for utility among people below full health, and combines them into one expected value.

$$\hat{U}_i = \hat{p}_i \times 1 + (1-\hat{p}_i) \times \hat{m}_i$$

where $\hat{U}_i$ is the predicted utility for patient $i$, $\hat{p}_i$ is the predicted probability that the patient reports full health (a utility of 1) from the first part, and $\hat{m}_i$ is the predicted mean utility for the patient given that the patient is below full health, from the second part.

Response mapping takes a different route. Gray, Rivero-Arias and Clarke used multinomial logit regression to estimate the probability of each EQ-5D response level on each question from SF-12 answers, then used Monte Carlo simulation to generate predicted EQ-5D responses that were converted into utility scores. Because the prediction is a set of EQ-5D responses, a different value set can be applied later without re-estimating the mapping.

Hernández Alava and colleagues compared these approaches in case studies for an NIHR report in 2020. They concluded that, theoretically, linear regression is inappropriate for mapping, and that the case studies confirmed this. Flexible direct mapping methods based on variants of mixture models with appropriate underlying distributions performed very well for all the preference-based measures studied, and beta-based mixtures performed similarly but required detailed thought about the number and location of probability masses.

Validation and performance assessment

A mapping is judged by predictive accuracy in data that played no part in estimation, rather than by fit to the estimation sample. The usual summary statistics are the mean absolute error and the root mean square error of predicted against observed utilities, computed in data held back from estimation or by cross-validation.

Average error statistics can hide bias that matters for decisions. A sample made up mostly of people in good health can give a small mean absolute error while the model predicts too high in poor health. Comparing mean predicted and observed utilities within bands of severity shows whether the mapping keeps the spread of utilities that the economic model needs.

Reporting a mapping study with the MAPS statement

Reporting standards let a reviewer see what a mapping study did and let a later user judge whether its mapping fits a new decision problem. Petrou and colleagues published the MAPS statement (Preferred Reporting Items for Studies Mapping onto Preference-Based Outcome Measures) in 2015 for this purpose, aimed at researchers, funders, peer reviewers and editors.

A working group of six health economists and one Delphi methodologist drafted 29 candidate items, and a two-round modified Delphi survey among academics, consultants, HTA agency staff and journal editors reduced them to 23 reporting items in six sections, covering the title and abstract, introduction, methods, results, discussion and other information. A companion explanation and elaboration paper illustrates each item with an example of good reporting practice.

Dakin and colleagues later applied the MAPS checklist to recent EQ-5D mapping studies when they updated the systematic review behind the online mapping database of the Health Economics Research Centre (HERC) at the University of Oxford.

Illustrative worked example comparing two mapping models

All numbers in this example are illustrative and do not come from any published mapping. A mapping study estimates two models that predict EQ-5D utility from a disease score $S$ running from 0 (no symptoms) to 50 (worst). A trial reports a typical patient at $S = 40$ without treatment and $S = 5$ with treatment, for one year, and treatment costs GBP 8,400 more.

Step 1 (linear model). The fitted linear model is $\hat{U} = 0.95-0.012 S$. At $S = 40$ the decrement is $d_{40} = 0.012 \times 40 = 0.48$, so $\hat{U}_{40} = 0.95-0.48 = 0.47$. At $S = 5$ the decrement is $d_{5} = 0.012 \times 5 = 0.06$, so $\hat{U}_{5} = 0.95-0.06 = 0.89$.

Step 2 (two-part model). At $S = 40$ the first part gives $\hat{p} = 0.02$ and the second part gives $\hat{m} = 0.38$, so with $q = 1-\hat{p} = 0.98$ the second term is $b_{40} = 0.98 \times 0.38 = 0.3724$ and $\hat{U}_{40} = 0.02 + 0.3724 = 0.3924$. At $S = 5$ the model gives $\hat{p} = 0.40$ and $\hat{m} = 0.80$, so with $q = 1-\hat{p} = 0.60$ the second term is $b_{5} = 0.60 \times 0.80 = 0.48$ and $\hat{U}_{5} = 0.40 + 0.48 = 0.88$.

Step 3 (QALY gain over one year). The linear model gives $\Delta Q_{L} = 0.89-0.47 = 0.42$ QALYs and the two-part model gives $\Delta Q_{T} = 0.88-0.3924 = 0.4876$ QALYs.

Step 4 (cost per QALY). The linear model gives $ICER_{L} = 8{,}400 / 0.42 = 20{,}000$, or GBP 20,000 per QALY. The two-part model gives $ICER_{T} = 8{,}400 / 0.4876 = 17{,}227$, or GBP 17,227 per QALY, a difference of GBP 2,773.

The two models agree closely for the treated state and differ for the severe untreated state, where the estimation data are usually thinnest. Which model is right is a question for validation in the estimation sample, and sensitivity analyses using different mapping models, which PMG51 asks for, expose differences of this kind.

Using a published mapping in a cost-utility analysis

The analyst who applies a mapping inherits its assumptions. The estimation population should resemble the trial population in condition and severity, and the target value set should be the one the decision maker requires.

A mapping predicts the expected utility for a given set of source scores. Patients with the same scores report different utilities, so mapped values are less dispersed than observed ones. The Wailoo report's recommendations on using results include the appropriate reflection of variability and uncertainty. Sampling the mapping coefficients in a probabilistic analysis covers parameter uncertainty only, while reflecting variability between patients needs the individual-level dispersion, through the residual error or the full predicted distribution.

Mapping study, crosswalk and indirect utility assessment

Several nearby ideas share the vocabulary of mapping but answer different questions. A mapping study links two different measures through a statistical model estimated on data containing both.

A crosswalk is the version-to-version case of mapping, converting scores between versions of one instrument such as the EQ-5D-3L and EQ-5D-5L. For that link, PMG51 says the mapping model developed by the Decision Support Unit and the Economic Evaluation Policy Research Unit should be used for mapping from 3L descriptive system data. Indirect utility assessment applies an existing value set to responses on a preference-based measure that was collected in the study itself, so no relationship between measures has to be estimated.

Where mapped utilities mislead

A mapping cannot recover information that the source measure does not hold. When the clinical measure omits a domain that the EQ-5D values, such as anxiety and depression in a measure of physical function, the predicted utilities will not respond to treatment effects in that domain, however good the statistical model.

1. Mapped utilities are sometimes treated as if they had been observed, although they are predictions with error.
2. Linear regression is sometimes treated as an acceptable default because it is simple. Hernández Alava and colleagues concluded in 2020 that linear regression is theoretically inappropriate for mapping.
3. A published mapping onto the EQ-5D-3L is sometimes read as directly usable, or as unusable, under PMG51. Where no model maps directly to the 5L value set, PMG51 allows mapping onto the 3L value set first and then onto the 5L value set with the DSU and EEPRU model.

Sources

• Wailoo AJ, Hernandez-Alava M, Manca A, Mejia A, Ray J, Crawford B, Botteman M, Busschbach J. 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;20(1):18-27. https://doi.org/10.1016/j.jval.2016.11.006
• Wailoo A, Hernández Alava M, Pudney S. Mapping to estimate health state utilities. NICE DSU Technical Support Document 22. Decision Support Unit, ScHARR, University of Sheffield; 2023, updated 2026. https://www.sheffield.ac.uk/nice-dsu/tsds/utilities
• Petrou S, Rivero-Arias O, Dakin H, Longworth L, Oppe M, Froud R, Gray A. Preferred reporting items for studies mapping onto preference-based outcome measures: the MAPS statement. PharmacoEconomics. 2015;33(10):985-991. https://doi.org/10.1007/s40273-015-0319-2
• Dakin H, Abel L, Burns R, Yang Y. Review and critical appraisal of studies mapping from quality of life or clinical measures to EQ-5D: an online database and application of the MAPS statement. Health and Quality of Life Outcomes. 2018;16:31. https://doi.org/10.1186/s12955-018-0857-3
• Hernández Alava M, Wailoo AJ, Ara R. Tails from the peak district: adjusted limited dependent variable mixture models of EQ-5D questionnaire health state utility values. Value in Health. 2012;15(3):550-561. https://doi.org/10.1016/j.jval.2011.12.014
• Hernández Alava M, Wailoo A, Pudney S, Gray L, Manca A. Mapping clinical outcomes to generic preference-based outcome measures: development and comparison of methods. Health Technology Assessment. 2020;24(34). https://doi.org/10.3310/hta24340
• Gray AM, Rivero-Arias O, Clarke PM. Estimating the association between SF-12 responses and EQ-5D utility values by response mapping. Medical Decision Making. 2006;26(1):18-29. https://doi.org/10.1177/0272989X05284108
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). 2022, updated 2026. Section 4.3.9. https://www.nice.org.uk/process/pmg36/chapter/economic-evaluation-2
• National Institute for Health and Care Excellence. Interim methods statement: implementing the EQ-5D-5L value set (PMG51). Published 27 August 2026. Sections 1.10 and 1.11. https://www.nice.org.uk/process/pmg51/chapter/statement-on-using-the-eq-5d-5l-value-set
• National Institute for Health and Care Excellence. The EQ-5D-5L, frequently asked questions. 2026. https://www.nice.org.uk/what-nice-does/faqs/the-eq-5d-5l