UNDERESTIMATION OF VARIANCE OF MEAN UTILITIES DERIVED FROM MULTI-ATTRIBUTE UTILITY INSTRUMENTS: THE USE OF MULTIPLE IMPUTATION AS A POTENTIAL SOLUTION

Monday, October 20, 2014
Poster Board # PS2-23

Candidate for the Lee B. Lusted Student Prize Competition

Kelvin Chan, MD, MSc., Sunnybrook Odette Cancer Center, Toronto, ON, Canada, Feng Xie, PhD, McMaster University, Hamilton, ON, Canada and Eleanor Pullenayegum, PhD, The Hospital for Sick Children, Toronto, ON, Canada
Purpose:

The issue of underestimation of variance of mean utilities derived from multi-attribute utility instruments has received little attention previously.  This false precision can lead to incorrect estimation of the precision of the results of cost-effectiveness analyses. This study aimed to illustrate this underestimation and to propose a method using multiple imputation to account for it.

Method:

The dataset from the original US EQ-5D-3L valuation study was randomly divided into two datasets: a derivation set (n=3273) and an application set (n=500).  Using the derivation set, a D1 model was fitted using a Bayesian mixed effect model with random effect by respondents and health states in WinBUGs.  Using the coefficients of this D1 model, the mean utilities of the respondents in the application set and its variance were calculated.  These were compared with the mean utilities and its variance using the predictive distribution from the Bayesian mixed effect model on the application set.  Furthermore, using the Monte Carlo Markov Chain method, multiple imputation was used to approximate the posterior distribution of the mean utilities attached to the health states.  Random imputed sets of all 243 health states were drawn from their posterior distributions. Using these imputed sets, the mean utilities of the respondents in the application set and its variance were calculated using Rubin’s rule.

Result:

The mean utilities based on the predictive distribution of the Bayesian mixed effect D1 model on the application set was 0.873 with a standard error (SE) of 0.0109 (variance=1.19x10-4).  When utilities were derived from coefficients of D1 model only, the mean derived utilities in the application set was 0.873 with a SE of 0.00728 (variance=5.30x10-5), which is only 44% of the variance based on the full predictive distribution of the mixed effect model.  Using the method based on multiple imputation with 20 imputed sets, the mean utilities in the application set was 0.876 with a SE of 0.0111 (variance=1.23x10-4), which is similar to the variance based on the full predictive distribution.

Conclusion:

Using multi-attribute utility instruments to derive utilities can lead to substantial underestimation of the variance of mean utilities. Multiple imputation can help correct for this underestimation so that the results of cost-effectiveness analyses using multi-attribute utility instruments can have the correct degree of precision.

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