Calculating utility decrements associated with an adverse event: marginal Tobit and CLAD coefficients should be used...

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.

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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.

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.

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.