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Background: Parameter uncertainty in EQ-5D-5L value sets often exceeds the instrument's minimum important difference, yet this is routinely ignored. Multiple imputation (MI) accounts for parameter uncertainty in the value set; however, no valuation study has implemented this methodology. Our objective was to create a Canadian MI value set for the EQ-5D-5L, thus enabling users to account for parameter uncertainty in the value set., Methods: Using the Canadian EQ-5D-5L valuation study ( N  = 1,073), we first refit the original model followed by models with state-level misspecification. Models were compared based on the adequacy of 95% credible interval (CrI) coverage for out-of-sample predictions. Using the best-fitting model, we took 100 draws from the posterior distribution to create 100 imputed value sets. We examined how much the standard error of the estimated mean health utilities increased after accounting for parameter uncertainty in the value set by using the MI and original value sets to score 2 data sets: 1) a sample of 1,208 individuals from the Canadian general public and 2) a sample of 401 women with breast cancer., Results: The selected model with state-level misspecification outperformed the original model (95% CrI coverage: 94.2% v. 11.6%). We observed wider standard errors for the estimated mean utilities on using the MI value set for both the Canadian general public (MI: 0.0091; original: 0.0035) and patients with breast cancer (MI: 0.0169; original: 0.0066)., Discussion and Conclusions: We provide 1) the first MI value sets for the EQ-5D-5L and 2) code to construct MI value sets while accounting for state-level model misspecification. Our study suggests that ignoring parameter uncertainty in value sets leads to falsely narrow SEs., Highlights: Value sets for health state utility instruments are estimated subject to parameter uncertainty; this parameter uncertainty may exceed the minimum important difference of the instrument, yet it is not fully captured using current methods.This study creates the first multiply imputed value set for a multiattribute utility instrument, the EQ-5D-5L, to fully capture this parameter uncertainty.We apply the multiply imputed value set to 2 data sets from 1) the Canadian general public and 2) women with invasive breast cancer.Scoring the EQ-5D-5L using a multiply imputed value set led to wider standard error estimates, suggesting that the current practice of ignoring parameter uncertainty in the value set leads to falsely low standard errors.Our work will be of interest to methodologists and developers of the EQ-5D-5L and users of the EQ-5D-5L, such as health economists, researchers, and policy makers., Competing Interests: The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Financial support for this study was provided in part by the Mitacs Accelerate Postdoctoral Fellowship, the Canadian Statistical Science Institute (Ontario) Top-up Award for Postdoctoral Fellows in Data Science, and the Canadian Centre for Applied Research in Cancer Control (ARCC). The funding agreement ensured the authors’ independence in designing the study, interpreting the data, writing, and publishing the report.

Introduction. The EQ-5D-5L valuation protocol contains both time tradeoff (TTO) tasks and discrete choice experiments (DCE), raising the question of how to best use these in creating a value set. The hybrid model, which combines TTO and DCE data, has emerged as a commonly used approach. However, this model assumes independence among responses from the same individual, a linear relationship between TTO and DCE utilities, and, in many implementations, homoscedastic residuals. The aims of this study are to examine alternatives to these assumptions and determine the impact of misspecification on value sets. Methods. We performed a simulation study, parameterized using the US EQ-5D-5L valuation study, to assess the impact of model misspecification. We simulated TTO and DCE data with nonlinear relationships between TTO and DCE utilities, heteroscedastic errors, and correlated responses. Simulated data were analyzed using hybrid models with and without heteroscedasticity, Tobit models with and without heteroscedasticity, a latent class model, and a mixed model. Results. Mean absolute errors (MAEs) for correctly specified models were <0.05, whereas models that incorrectly assumed a linear relationship between TTO and DCE utilities or homoscedasticity of TTO responses featured states with an MAE >0.1. When a linear relationship between TTO and DCE utilities held, using both TTO and DCE data under correct specification yielded smaller MAEs compared with using TTO data alone but yielded larger MAEs when a linear relationship did not hold. Mistakenly assuming homoscedasticity led to increased MAEs, whereas ignoring dependence did not. Conclusions. Because heteroscedasticity in TTO utilities and nonlinear associations between DCE and TTO utilities have been noted, we recommend careful assessment of scedasticity and linearity to ascertain the suitability of a hybrid model.

Background . Scoring algorithms of multi-attribute utility instruments (MAUI) are developed in valuation studies and are hence estimated subject to uncertainty. Valuation studies need to be designed to achieve reasonable accuracy. We aim to provide the first closed-form mathematical formula for the mean square error (MSE) of an additive MAUI as a function of sample size that acknowledges that the MAUI model for the mean utility is not a perfect fit. Methods . Based on the design of the EQ-5D valuation study, we derived our closed-form formula in terms of sample size and number of directly valued health states overall and per subject. We validated our formula by conducting a simulation study using the US EQ-5D-3L valuation data set and examined the effect of using a random-effects versus an ordinary least-squares model and the effect of heteroscedasticity. We explored the effect of sample size and number of valued health states. Results . The simulation study validated our MSE-based closed-form formula regardless of whether assuming a random-effects model versus an ordinary least squares model or heteroscedasticity versus homoscedasticity. As the sample size approaches infinity, the MSE does not approach zero but levels off asymptotically. The improvement based on increasing sample is more prominent when the sample is small. When the sample size is greater than 300 to 500, further increases do not meaningfully improve the MSE, while increasing the number of health states can further improve the MSE. Conclusion . We have derived a closed-form formula to calculate the MSE of an additive MAUI scoring algorithm based on sample size and number of health states, which will enable the developers of MAUI valuation studies to calculate the required sample size for their desired predictive precision.

Background. In health economics, there has been interest in using discrete-choice experiments (DCEs) to derive preferences for health states in lieu of previously established approaches like time tradeoff (TTO). We examined whether preferences elicited through DCEs are associated and agree with preferences elicited through TTO tasks. Methods. We used data from 1073 respondents to the Canadian EQ-5D-5L valuation study. Multivariate mixed-effects models specified a common likelihood for the TTO and discrete-choice data, with separate but correlated random effects for the TTO and DCE data, for each of the 5 EQ-5D-5L dimensions. Multivariate latent class models allowed separate but associated latent classes for the DCE and TTO data. Results. Correlation between the random effects for the 2 tasks ranged from -0.12 to 0.75, with only pain/discomfort and anxiety/depression having at least a 50% posterior probability of strong (>0.6) correlation. Latent classes for the TTO and DCE data both featured 1 latent class capturing participants attaching large disutilities to pain/discomfort, another capturing participants attaching large disutility to anxiety/depression, and the third class capturing the remainder. Agreement in class membership was poor (κ coefficient: 0.081; 95% credible interval, 0.033-0.13). Fewer respondents expressed strong disutilities for problems with anxiety/depression or pain/discomfort in the TTO than the DCE data (17% v. 55%, respectively). Conclusions. Stated preferences using TTO and DCEs show association across dimensions but poor agreement at the level of individual health states within respondents. Joint models that assume agreement between DCE and TTO have been used to develop national value sets for the EQ-5D-5L. This work indicates that when combining data from both techniques, methods requiring association but not agreement are needed.

Background: Resource-constrained countries have difficulty conducting large EQ-5D valuation studies, which limits their ability to conduct cost-utility analyses using a value set specific to their own population. When estimates of similar but related parameters are available, shrinkage estimators reduce uncertainty and yield estimators with smaller mean square error (MSE). We hypothesized that health utilities based on shrinkage estimators can reduce MSE and mean absolute error (MAE) when compared to country-specific health utilities., Methods: We conducted a simulation study (1,000 iterations) based on the observed means and standard deviations (or standard errors) of the EQ-5D-3L valuation studies from 14 counties. In each iteration, the simulated data were fitted with the model based on the country-specific functional form of the scoring algorithm to create country-specific health utilities ("naïve" estimators). Shrinkage estimators were calculated based on the empirical Bayes estimation methods. The performance of shrinkage estimators was compared with those of the naïve estimators over a range of different sample sizes based on MSE, MAE, mean bias, standard errors and the width of confidence intervals., Results: The MSE of the shrinkage estimators was smaller than the MSE of the naïve estimators on average, as theoretically predicted. Importantly, the MAE of the shrinkage estimators was also smaller than the MAE of the naïve estimators on average. In addition, the reduction in MSE with the use of shrinkage estimators did not substantially increase bias. The degree of reduction in uncertainty by shrinkage estimators is most apparent in valuation studies with small sample size., Conclusion: Health utilities derived from shrinkage estimation allow valuation studies with small sample size to "borrow strength" from other valuation studies to reduce uncertainty.

Background: Parameter uncertainty in value sets of multiattribute utility-based instruments (MAUIs) has received little attention previously. This false precision leads to underestimation of the uncertainty of the results of cost-effectiveness analyses. The aim of this study is to examine the use of multiple imputation as a method to account for this uncertainty of MAUI scoring algorithms., Method: We fitted a Bayesian model with random effects for respondents and health states to the data from the original US EQ-5D-3L valuation study, thereby estimating the uncertainty in the EQ-5D-3L scoring algorithm. We applied these results to EQ-5D-3L data from the Commonwealth Fund (CWF) Survey for Sick Adults ( n = 3958), comparing the standard error of the estimated mean utility in the CWF population using the predictive distribution from the Bayesian mixed-effect model (i.e., incorporating parameter uncertainty in the value set) with the standard error of the estimated mean utilities based on multiple imputation and the standard error using the conventional approach of using MAUI (i.e., ignoring uncertainty in the value set)., Result: The mean utility in the CWF population based on the predictive distribution of the Bayesian model was 0.827 with a standard error (SE) of 0.011. When utilities were derived using the conventional approach, the estimated mean utility was 0.827 with an SE of 0.003, which is only 25% of the SE based on the full predictive distribution of the mixed-effect model. Using multiple imputation with 20 imputed sets, the mean utility was 0.828 with an SE of 0.011, which is similar to the SE based on the full predictive distribution., Conclusion: Ignoring uncertainty of the predicted health utilities derived from MAUIs could lead to substantial underestimation of the variance of mean utilities. Multiple imputation corrects for this underestimation so that the results of cost-effectiveness analyses using MAUIs can report the correct degree of uncertainty.

Background: Health state preferences vary among countries, and country-specific value sets are important in health care reimbursement decisions. When decisions are made at the regional level, regional variation in health state preferences may be important. We propose that shrinkage analysis and Bland-Altman plots can be a helpful way to investigate regional variation., Methods: The presence of regional variation can be investigated by introducing interactions between regions and the regression coefficients in the scoring algorithm. When variation is present, regional scoring algorithms can be derived through shrinkage analysis. The impact of using regional algorithms in place of the national algorithm can be investigated using simulation and illustrated using Bland-Altman plots. We applied this methodological approach to the Canadian EQ-5D-5L valuation study, which used time-tradeoff (TTO) tasks to elicit health state preferences from 1073 participants from 4 regions (Alberta, British Columbia, Ontario, and Quebec)., Results: There were statistically significant interactions between the fixed effects of the scoring algorithm and region. On computing regional scoring algorithms and applying them to the EQ-5D-5L health states reported by our population, the mean utility using the Canada-wide scoring algorithm was 0.87 (standard error, 0.0013), compared to 0.85 (0.0013) on using the algorithm for Alberta, 0.80 (0.0013) on using the algorithm for British Columbia, 0.91 (0.0013) for Ontario, and 0.89 (0.0014) for Quebec., Conclusions: When health care falls under regional jurisdiction, shrinkage estimators can be used to generate regional scoring algorithms for the EQ-5D-5L and Bland-Altman plots used to assess the importance of regional variation in health state preferences. Our results suggest that mean health state preferences vary among Canada's regions and make a sizable impact on estimates of population mean utility.

Background: . Parameter uncertainty in EQ-5D value sets is routinely ignored. Sources of parameter uncertainty include uncertainty in the estimated regression coefficients of the scoring algorithm and uncertainty that arises from the need to use a nonsaturated functional form when creating the scoring algorithm. We hypothesize that this latter source is the major contributor to parameter uncertainty in the value sets., Methods: . We used data from the United States EQ-5D-3L valuation study to assess the extent of parameter uncertainty in the value set. We refitted the US scoring algorithm to quantify contributors to the mean square prediction errors and used a Bayesian approach to estimate the predictive distribution of the mean utilities. The impact of parameter uncertainty in the value set was assessed using survey data., Results: . Parameter uncertainty in the estimated regression coefficients explained 16% of the mean squared prediction error; uncertainty in the functional form explained the remaining 84%. The median width of the 95% credible intervals for the mean utilities was 0.15. In estimating mean utility in our survey population, parameter uncertainty in the value set was responsible for 93% of the total variance, with sampling variation in the survey population being responsible for the remaining 7%., Conclusion: . EQ-5D-3L value sets are estimated subject to considerable parameter uncertainty; the median credible interval width is large compared with reported values of the minimum important difference for the EQ-5D-3L, which have been reported to be as small as 0.03. Other countries' scoring algorithms are based on smaller studies and are hence subject to greater uncertainty. This uncertainty should be accounted for when using EQ-5D health utilities in economic evaluations., (© The Author(s) 2015.)

Background: Bayesian methods have been proposed as a way of synthesizing all available evidence to inform decision making. However, few practical applications of the use of Bayesian methods for combining patient-level data (i.e., trial) with additional evidence (e.g., literature) exist in the cost-effectiveness literature. The objective of this study was to compare a Bayesian cost-effectiveness analysis using informative priors to a standard non-Bayesian nonparametric method to assess the impact of incorporating additional information into a cost-effectiveness analysis., Methods: Patient-level data from a previously published nonrandomized study were analyzed using traditional nonparametric bootstrap techniques and bivariate normal Bayesian models with vague and informative priors. Two different types of informative priors were considered to reflect different valuations of the additional evidence relative to the patient-level data (i.e., "face value" and "skeptical"). The impact of using different distributions and valuations was assessed in a sensitivity analysis. Models were compared in terms of incremental net monetary benefit (INMB) and cost-effectiveness acceptability frontiers (CEAFs)., Results: The bootstrapping and Bayesian analyses using vague priors provided similar results. The most pronounced impact of incorporating the informative priors was the increase in estimated life years in the control arm relative to what was observed in the patient-level data alone. Consequently, the incremental difference in life years originally observed in the patient-level data was reduced, and the INMB and CEAF changed accordingly., Conclusions: The results of this study demonstrate the potential impact and importance of incorporating additional information into an analysis of patient-level data, suggesting this could alter decisions as to whether a treatment should be adopted and whether more information should be acquired.

Background: Measured utility data have a discrete distribution, and the discreteness is particularly pronounced for EQ-5D utilities. Given the discreteness of the data, modeling the distribution parametrically is likely to be difficult. Moreover, since the distribution is bounded, the linearity assumptions made by many models are questionable. This article suggests using semi-parametric models and illustrates the use of generalized additive models (GAMs) for handling nonlinear associations., Methods: A simulation study is used to explore whether bias arises when applying parametric models to discrete utility data. A further simulation investigates the bias in semi-parametric linear and quasi-beta regression models when the assumed linearity does not hold and also investigates the use of GAMs. The use of GAMs in practice is shown through a recent study of health utilities among patients with diabetes., Results: Using parametric beta models to analyze discrete EQ-5D utility data led to substantial bias. Both semi-parametric linear regression and quasi-beta regression led to biased estimates of marginal and incremental effects when the mean model was misspecified. The use of GAMs reduced these biases., Conclusions: Parametric models for EQ-5D utility data should be used with caution. Semi-parametric modeling of utility data should check for nonlinearity. GAMs can help in diagnosing and accommodating nonlinearity.

Background: When calculating the decreases in health utility associated with adverse events, often a number of respondents achieve the upper utility bound of 1. "Marginal" Tobit or CLAD coefficients have been used to account for this. These are calculated by using a Tobit or a CLAD model to estimate the decrease in a latent unbounded variable associated with the event or condition, then to multiply by the proportion of respondents falling below 1 in order to transform back to the utility scale., Objective: &, Methods: Starting with the Tobit model, we show mathematically that this procedure is not valid, when calculating decreases in utility associated with binary events. We then generalize the result to the CLAD model. A selection of published studies is used to illustrate the bias in the marginal Tobit decrements., Results: The degree of bias is more severe the greater the decrease in utility associated with the event, and the larger the proportion of individuals at the upper ceiling.In the examples studied, the degree of bias was often greater than 10%. We provide the correct formula for calculating the utility decrement., Conclusions: The marginal Tobit and CLAD coefficients should not be used as estimates of a utility decrement corresponding to an adverse event or health condition unless the coefficients are small in absolute value, or if the proportion of individuals at the upper utility bound is small. In other settings, the corrected formula or alternative regression methods (e.g. linear models of mean utility) should be considered.