Exploring the Benefits of Transformations in Health Utility Mapping

Background. Quality-of-life research and cost-effectiveness analyses frequently require data on health utility, a global measure of health-related quality of life. When utilities are unavailable, researchers have "mapped" descriptive instruments to utility instruments, using samples of responses to both instruments. Health utilities have an idiosyncratic distribution, with upper bound and probability mass at 1, left skewness, and kurtosis. Estimation of mean utility values conditional on covariates is of interest, particularly in health utility mapping applications. Traditional linear regression may be unsuitable because fundamental assumptions are violated. Complex statistical methods come with deficiencies that may outweigh their benefits. Aim. To investigate the benefits of transforming the health utility response variable before fitting a linear regression model. Methods. We compared log, logit, arcsin, and Box-Cox transformations with an untransformed model, using several measures of model accuracy. We made our evaluation by designing and conducting a simulation study and reanalyzing data from 2 published studies, which "mapped" a psychometric descriptive instrument to a utility instrument. Results. In the simulation study, log transformation with smearing estimator had in most cases the lowest bias but one of the highest variances, especially for estimating low utility values under small sample size. The untransformed model was outperformed by the transformed models. Findings were inconclusive for the analysis of real data, where arcsin gave the lowest error for one of the data sets, while the untransformed model had the best performance for the other. Conclusions. We identified the benefits of transformations and offered suggestions for future modeling of health utilities. However, the benefits were moderate and no single transformation appeared to be universally optimal, suggesting that selection requires examination on a case-by-case basis.