Methodological challenges in mapping a disease specific psychometric instrument to a disease specific utility instrument: The effect of alternate utility transformations and within-instrument sub-scale correlations on model fit

Abstract

OBJECTIVES: a) Determine the effect of utility transformations on the fit of linear regression used to map psychometric disease-specific instrument scores to disease-specific utility scores and b) determine whether the model fit is dependent upon the correlation between the disease specific and non-specific items of the preference-based instrument. METHODS: We compare regression models mapping scores from the UCLA Prostate Cancer Index (PCI), a psychometric instrument measuring Health Related Quality of Life for prostate cancer patients, to utility responses from PORPUS-U, a prostate cancer-specific utility instrument with disease-specific and generic subscales. Models were fitted using a dataset from prostate cancer patients, while fit was assessed on three separate datasets, using the Root Mean Squared Error (RMSE) in the retransformed scale. The often poor fit of regression-based mapping models may be due to limited overlap between the constructs addressed by preference-based and psychometric instruments. We investigated this hypothesis employing a simulation procedure where we: a) fitted a multivariate regression model estimating how the generic subscales depend on the disease-specific ones, b) used these estimates, with varying noise, to simulate generic subscale scores, c) calculated utility scores from the true disease-specific and simulated generic subscales, d) applied linear regression to map PCI scales to "semi"-simulated PORPUS-U utilities, and f) evaluated the mapping using RMSE, determining whether a "tighter" correlation structure improves the fit. RESULTS: The arcsin transformation appears to give the best fit, with RMSE values of 0.0405, 0.0605 and 0.0457 for the three test datasets. The simulation experiments showed that larger correlation between disease specific and non-disease specific instrument domains only yields a marginal benefit in the mapping. CONCLUSIONS: Transforming utility scores does affect model fit, and appears to be an important step in utility mapping. Limited construct overlap between disease-specific and generic items in prostate cancer quality of life instruments did not evidently explain suboptimal fit in our mapping models.