Mapping the Oxford Shoulder Score onto the EQ-5D utility index

In order to enable cost-utility analysis of shoulder pain conditions and treatments, this study aimed to develop and evaluate mapping algorithms to estimate the EQ-5D health index from the Oxford Shoulder Score (OSS) when health outcomes are only assessed with the OSS.

5437 paired OSS and EQ-5D questionnaire responses from four national multicentre randomised controlled trials investigating different shoulder pathologies and treatments were split into training and testing samples. Separate EQ-5D-3L and EQ-5D-5L analyses were undertaken. Transfer to utility (TTU) regression (univariate linear, polynomial, spline, multivariable linear, two-part logistic-linear, tobit and adjusted limited dependent variable mixture models) and response mapping (ordered logistic regression and seemingly unrelated regression (SUR)) models were developed on the training sample. These were internally validated, and their performance evaluated on the testing sample. Model performance was evaluated over 100-fold repeated training-testing sample splits.

For the EQ-5D-3L analysis, the multivariable linear and splines models had the lowest mean square error (MSE) of 0.0415. The SUR model had the lowest mean absolute error (MAE) of 0.136. Model performance was greatest in the mid-range and best health states, and lowest in poor health states. For the EQ-5D-5L analyses, the multivariable linear and splines models had the lowest MSE (0.0241-0.0278) while the SUR models had the lowest MAE (0.105-0.113).

The developed models now allow accurate estimation of the EQ-5D health index when only the OSS responses are available as a measure of patient-reported health outcome.