A threshold explanation for the lack of variation in negative composite time trade-off values

BACKGROUND: Recent studies concluded that for health states considered worse than dead (WTD), as measured with the time trade-off (cTTO) method, negative mean values were insensitive to health state severity, which represents a validity problem for the cTTO. However, the aforementioned studies analysed negative values in isolation, which causes selection bias as the value distribution is truncated. AIM: To investigate the validity of aforementioned studies and of negative values in general. METHODS: The ‘threshold explanation’ was formulated: beyond a certain severity threshold, preferences change from better than dead (BTD) to WTD. This threshold differs between respondents. Thus, negative values across severity are obtained from different respondents, and responses added for higher severity contribute negative values close to zero, explaining the aforementioned insensitivity. This explanation was tested using data from the Dutch EQ-5D-5L valuation study. Respondents valued 10 health states. Based on respondents’ number of WTD preferences, segments were constructed, containing respondents with similar severity thresholds. Using regression models for each individual respondent, we examined the relation between values and severity and compared respondents between segments. RESULTS: Negative values, when analysed in isolation, were insensitive to severity. However, for individual respondents and within most segments, cTTO values and severity were negatively related. For individual respondents, negative slopes were steeper for segments with more WTD preferences, as predicted by the threshold explanation. DISCUSSION: Analysing negative values in isolation leads to biased estimates. Analyses of cTTO values for individual respondents refute the insensitivity of negative cTTO values. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s11136-022-03155-6.