Non-monotonicity in the episodic random utility model

The time trade-off (TTO) is widely used in population-based surveys to estimate health-state valuations. Typically, respondents may characterize states as being better than or worse than dead. However, worse-than-dead responses can produce strongly negative mean values, so various analytic transformations of these responses have been suggested. The episodic random utility model (eRUM), operationalized using a linear regression estimator, was proposed as an alternative to these transformations, in part because of its theoretical appeal. We analyzed the eRUM estimator's mathematical properties and found that it violates monotonicity under certain patterns of survey responses, such that improvement in some individual valuations would imply a lower overall valuation for a given health state. Consequently, it is possible that orderings of alternative strategies based on eRUM valuations could lead a decision-maker to choose a strictly dominated strategy. Re-analyzing data from a large population-based EQ-5D valuation survey in the United Kingdom, we found 27% of all TTO responses (63% of all worse-than-dead responses) met the conditions for violation of monotonicity, and 74% of all respondents had at least one such response. These results present some challenge to the use of the eRUM estimator in generating health-state valuations for population health measurement and economic evaluation.