Analysis of Health Utility Data When Some Subjects Attain the Upper Bound of 1: Are Tobit and CLAD Models Appropriate?
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BACKGROUND: Health utility data often show an apparent truncation effect, where a proportion of individuals achieve the upper bound of 1. The Tobit model and censored least absolute deviations (CLAD) have both been used as analytic solutions to this apparent truncation effect. These models assume that the observed utilities are censored at 1, and hence that the true utility can be greater than 1.We aimed to examine whether the Tobit and CLAD models yielded acceptable results when this censoring assumption was not appropriate. METHODS: Using health utility (captured through EQ5D) data from a diabetes study, we conducted a simulation to compare the performance of the Tobit, CLAD, ordinary least squares (OLS), two-part and latent class estimators in terms of their bias and estimated confidence intervals. We also illustrate the performance of semiparametric and nonparametric bootstrap methods. RESULTS: When the true utility was conceptually bounded above at 1, the Tobit and CLAD estimators were both biased. The OLS estimator was asymptotically unbiased and, while the model-based and semiparametric bootstrap confidence intervals were too narrow, confidence intervals based on the robust standard errors or the nonparametric bootstrap were acceptable for sample sizes of 100 and larger. Two-part and latent class models also yielded unbiased estimates. CONCLUSIONS: When the intention of the analysis is to inform an economic evaluation, and the utilities should be bounded above at 1, CLAD, and Tobit methods were biased. OLS coupled with robust standard errors or the nonparametric bootstrap is recommended as a simple and valid approach.
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