OBJECTIVES: Mapping algorithms can translate disease-specific or generic health-related quality of life measurements into values obtained from preference-based instruments such as the EuroQol 5-dimension questionnaire (EQ-5D). The Oxford Hip Score (OHS) is a disease-specific instrument widely used by orthopaedic surgeons to assess outcomes from hip surgery. There is an algorithm for estimating mean EQ-5D scores from the OHS, but this was developed using early response mapping methods and has limited external validation. We have developed a new mapping algorithm to translate OHS results into EQ-5D domain responses and utilities in a large UK dataset using direct and response mapping methods.  METHODS: OHS and EQ-5D responses were extracted from the publicly available National Patient Reported Outcomes Measures (PROMs) database. The sample of complete data pairs (n=126 862) was split into estimating (n=51 800, years 2009–10) and external validation (n=75 062, years 2010–12) samples. EQ-5D utilities were estimated directly using ordinary least squares regression and two-part models. EQ-5D responses were estimated using ordered and multinomial logit models. For the two-part and the multinomial logit models, the expected value method was used to calculate utilities. Performance was evaluated using mean square error (MSE) and mean absolute error (MAE). RESULTS: The two-part models and the ordered or multinomial regressions performed better than ordinary least square regression. In external validation, the MSE (MAE) was 0.0319 (0.1286) for the two-part model and 0.0315 (0.1249) for response mapping. For EQ-5D index values >0.5 (better health states), response mapping predictions had a slightly smaller MSE and MAE than direct method predictions. Both indirect and direct approaches predicted higher MSE and MAE when EQ-5D <0.5. CONCLUSIONS: Response mapping between OHS and EQ-5D was similar or slightly more predictive than direct mapping. Further research is needed to improve the performance of these techniques in poorer health states.