Efficient Designs for Valuation Studies That Use Time Tradeoff (TTO) Tasks to Map Latent Utilities from Discrete Choice Experiments to the Interval Scale: Selection of Health States for TTO Tasks.

Background: In eliciting utilities to value multiattribute utility instruments, discrete choice experiments (DCEs) administered online are less costly than interviewer-facilitated time tradeoff (TTO) tasks. DCEs capture utilities on a latent scale and are often coupled with a small number of TTO tasks to anchor utilities to the interval scale. Given the costly nature of TTO data, design strategies that maximize value set precision per TTO response are critical.

Methods: Under simplifying assumptions, we expressed the mean square prediction error (MSE) of the final value set as a function of the number $J$ of TTO-valued health states and the variance $V_J$ of the states' latent utilities. We hypothesized that even when these assumptions do not hold, the MSE 1) decreases as $V_J$ increases while holding $J$ fixed and 2) decreases as $J$ increases while holding $V_J$ fixed. We used simulation to examine whether there was empirical support for our hypotheses a) assuming an underlying linear relationship between TTO and DCE utilities and b) using published results from the Dutch, US, and Indonesian EQ-5D-5L valuation studies.

Results: Simulation set (a) supported the hypotheses, as did simulations parameterized using valuation data from Indonesia, which showed a linear relationship between TTO and DCE utilities. The US and Dutch valuation data showed nonlinear relationships between TTO and DCE utilities and did not support the hypotheses. Specifically, for fixed $J$, smaller values of $V_J$ reduced rather than increased the MSE.

Conclusions: Given that, in practice, the underlying relationship between TTO and DCE utilities may be nonlinear, health states for TTO valuation should be placed evenly across the latent utility scale to avoid systematic bias in some regions of the scale.

Highlights: Valuation studies may feature a large number of respondents completing discrete choice tasks online, with a smaller number of respondents completing time tradeoff (TTO) tasks to anchor the discrete choice utilities to an interval scale.We show that having each TTO respondent complete multiple tasks rather than a single task improves value set precision.Keeping the total number of TTO respondents and the number of tasks per respondent fixed, having 20 health states directly valued through TTO leads to better predictive precision than valuing 10 health states directly.If DCE latent utilities and TTO utilities follow a perfect linear relationship, choosing the TTO states to be valued by weighting on the 2 ends of the latent utility scale leads to better predictive precision than choosing states evenly across the latent utility scale.Conversely, if DCE latent utilities and TTO utilities do not follow a linear relationship, choosing the states to be valued using TTO evenly across the latent utility scale leads to better predictive precision than weighted selection does.In the context of valuation of the EQ-5D-Y-3L, we recommend valuing 20 or more health states using TTO and placing them evenly across the latent utility scale.