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This paper tests the internal consistency of time trade-off utilities. We find significant violations of consistency in the direction predicted by loss aversion. The violations disappear for higher gauge durations. We show that loss aversion can also explain that for short gauge durations time trade-off utilities exceed standard gamble utilities. Our results suggest that time trade-off measurements that use relatively short gauge durations, like the widely used EuroQol algorithm, are affected by loss aversion and lead to utilities that are too high.

This paper studies the consistency of time trade-off utilities. The time trade-off is a widely used technique to elicit health state utilities. The EuroQol algorithm, a frequently employed algorithm to compute health state utilities, is based on time trade-off valuations (Dolan, 1997). Several studies provide empirical evidence that the time trade-off captures individual preferences for health well (van Busschbach, 1994, Dolan et al., 1996 and Bleichrodt and Johannesson, 1997a). Richardson (1994) and Dolan (2000) give theoretical arguments in favor of the time trade-off. Inconsistencies in time trade-off measurements were found by Stalmeier in several studies. Stalmeier et al., 1996 and Stalmeier et al., 1997, and Dolan and Stalmeier (2003) observed preference reversals between direct choices and time trade-off judgments for health states of low quality, i.e. health states that are close to or worse than death. They attributed these reversals to a proportional heuristic that people use in answering time trade-off questions. These preference reversals do not occur for health states that are clearly preferred to death. The common endpoints in time trade-off measurements are full health and death. Stalmeier (2002) found inconsistencies in time trade-off utilities when the endpoints used in the elicitation vary. His findings indicate no problems for time trade-off measurements in which endpoints are held fixed, because he observed that the relative size of utility differences, which is the information used in cost–utility analyses, does not depend on the endpoints used. The above findings suggest that time trade-off measurements may be problematic for health states close to or worse than death and in analyses in which the endpoints in the elicitation task vary. Time trade-off measurements that use health states clearly preferred to death and that do not vary the endpoints, which is the common case in cost–utility analysis, appear to be on much firmer ground. The present paper will show, however, that inconsistencies also occur in the latter case. What is worse, these inconsistencies are systematic and cannot be explained by random error. We show that the systematic inconsistency can be explained by loss aversion (Kahneman and Tversky, 1979 and Tversky and Kahneman, 1991), the idea that people evaluate outcomes as gains and losses from a reference point and are more sensitive to losses than to equally sized gains. The inconsistencies in the time trade-off decrease with the gauge duration used. This finding has interesting implications for the use of the time trade-off in health utility measurement. It also suggests that the EuroQol algorithm leads to health state utilities that are affected by loss aversion. Two recent papers have also performed consistency tests of the time trade-off (Spencer, 2003 and Clarke et al., 2003). Both studies found less evidence of systematic inconsistencies in the direction predicted by loss aversion. These two studies used different designs than ours, however, which may partly explain the difference in findings. We discuss these studies in Section 5 of the paper. The paper is structured as follows. In Section 2 we describe the consistency test used in the paper. In Section 3 we explain how loss aversion can explain why the time trade-off might violate the consistency test in a systematic manner. Section 4 describes the design and results of two experiments that test the consistency of time trade-off measurements. Section 5 concludes the paper.

5.1. Main findings We find inconsistencies in time trade-off utilities. These inconsistencies are in the direction predicted by loss aversion, but arise only when the gauge duration in the time trade-off is relatively low. For longer gauge durations, the time trade-off utilities are consistent. These findings appear robust with respect to the health state used. We are able to replicate Dolan et al.’s (1996) finding that for short gauge durations conventional time trade-off utilities exceed standard gamble utilities. For longer gauge durations standard gamble utilities exceed conventional time trade-off utilities as is commonly observed in the literature. These results are consistent with the hypothesis that loss aversion was the cause of Dolan et al.’s finding. Our findings on constant proportional trade-offs are rather negative. We find mixed evidence on constant proportional trade-offs in conventional time trade-off measurements. In alternative time trade-off measurements, constant proportional trade-offs is violated. Utility independence is violated in both tests that we performed. 5.2. Explanations An explanation why the difference between conventional and alternative time trade-off utilities decreases with duration can be that duration and health status become closer substitutes for higher durations. Several studies have shown that the effect of loss aversion decreases when attributes become closer substitutes (Ortona and Scacciati, 1992 and Chapman, 1998). McNeil et al. (1981) found that that health status and duration became closer substitutes for higher durations. They observed that people are unwilling to trade life duration for health status if duration is low. That is, for low durations preferences are lexicographic. If duration increases beyond a certain duration, people are willing to give up life duration for improved health status and this willingness increases with duration (see also Pliskin et al., 1980 and Miyamoto and Eraker, 1988). Our findings on constant proportional trade-offs are to some extent consistent with the proportional heuristic. As expected under the proportional heuristic, we find less support for constant proportional tradeoffs than in other studies that used multiples of 10 as gauge durations. Nevertheless, we find some support for constant proportional trade-offs in the conventional time trade-off measurements. The clear violations of constant proportional trade-offs in the alternative time trade-off measurements suggest that the proportional heuristic plays no role there. 5.3. Possible objections An objection against our study is that in both experiments we elicited the conventional time trade-off before the alternative time trade-off. This may have led to an order effect if people had no clearly defined preferences before coming to the experiment, but constructed their preferences during the elicitation task and benefited in the second session from their experience in the first session. We took some care to avoid the problem of preference construction. In both experiments, subjects received practice questions at recruitment. These questions were intended to induce subjects to think about trading-off life-years against health status. We are inclined to believe that our results are not seriously affected by an order effect. If the problem of preference construction occurred then it is less likely to have affected the results of the second experiment, because in the second experiment subjects answered the standard gamble questions first. They, therefore, already had opportunity to construct their preferences regarding the trade-off between life-years and health status before they answered the conventional time trade-off questions. The results from the second experiment were, however, similar to those from the first experiment. Moreover, it is hard to conceive of a systematic bias arising from an order effect. If anything, we would expect preferences to be less precise in the conventional time trade-offs, but not systematically biased. We observe, however a systematic difference between conventional and alternative time trade-off utilities. That having said, it would clearly have been better to include both conventional and alternative time trade-off questions in the first experimental session. Another possible objection against our study is that we used a young population of students and that it is not clear whether our results can be generalized to the population at large. It is plausible that older people value remaining life duration differently from younger people. Such criticism emphasizes the need to try and replicate our findings in a more representative group of participants. While we agree with the need to replicate our findings, we do not consider the unrepresentativeness of our sample to be an important problem. Many studies show that health state valuations are robust and do not depend in a significant way on the representativeness of the study sample (see de Wit et al., 2000 for a review). An indication that our results are robust is that, in spite of the unrepresentativeness of our sample, we were able to replicate the finding by Dolan et al., who used a representative sample, that for short gauge durations conventional time trade-off utilities exceed standard gamble utilities. For longer gauge durations we find the common pattern that standard gamble utilities exceed conventional time trade-off utilities. 5.4. Other studies As noted in Section 1, two other recent studies also examined the consistency of time trade-off measurements. Spencer (2003) found mixed evidence: in one test the time trade-off measurements were consistent, in the other test there were inconsistencies in the direction of loss aversion. Clarke et al. (2003) found no evidence of systematic inconsistencies in the direction predicted by loss aversion. Spencer (2003), like us, used a series of choices to elicit indifference durations. The conventional and the alternative time trade-off measurements in her study were not linked, however, and, as Spencer explains, besides loss aversion, time preference, scale compatibility, and maximal endurable time affect the difference between conventional and alternative time trade-off utilities. Moreover, these factors exert opposing influences on the difference between conventional and alternative time trade-off utilities. In our test, time preference and scale compatibility do not affect the results, as we have explained before, and we corrected for maximal endurable time by deleting those subjects who did not satisfy monotonicity with respect to life-years. Clarke et al. (2003) used a discrete choice experiment in which each subject got only one choice. The most plausible reason for the difference in findings between our study and that of Clarke et al. is the difference in elicitation method. Even though we used a series of choices to elicit indifference, our procedure is closer to matching than Clarke et al.’s who used just one choice. It is well known that people use different evaluation processes in choice tasks than in matching tasks (Tversky et al., 1988). Perhaps, loss aversion is more important in matching than in choice. 5.5. Implications Many practical studies use relatively short gauge durations and our results suggest that the resulting time trade-off utilities are affected by loss aversion. For example, the widely used EuroQol algorithm is based on time trade-off questions that used a gauge duration of 10 years (Dolan, 1997). Based on our findings we therefore have reason to believe that the EuroQol algorithm is affected by loss aversion. This belief is sustained by the fact that we were able to replicate Dolan et al.’s (1996) findings for a short gauge duration, but not for longer gauge durations. The question is then whether we should strive to avoid the effect of loss aversion on time trade-off utilities. We are inclined to answer this question in the affirmative and to consider loss aversion a bias that should be avoided in health utility measurement. Health utility measurement yields inputs for economic evaluation and medical decision making. The aim of economic evaluations and medical decision making is to help policy makers and patients to make better decisions. That is, economic evaluation and medical decision making are prescriptive techniques and health utility measurement serves to yield inputs for prescriptive decision making. A crucial requirement for prescriptive decision making is that the results of the decision process should not depend on the method that was used to generate the utilities. Equivalent ways to elicit health state utilities should give the same results. Our consistency tests examined this requirement for time trade-off utilities. As noted, we found that the time trade-off only satisfies the requirement for longer gauge durations. On the other hand, loss aversion is probably not the only bias that affects the time trade-off. An indication that other factors are also at work is that even though the effect of loss aversion (and hence the upward bias in conventional time trade-off measurements) is strongest for short reference durations, conventional time trade-off utilities are not significantly higher for shorter reference durations. Bleichrodt (2002) argued that some effect of loss aversion on the time trade-off utilities may be desirable to offset other biases in time trade-off measurements. The question of how much loss aversion to allow is not easy to answer. Future research should aim to identify and quantify the biases in time trade-off measurements. We hope that the results from this paper will be helpful in designing such future work. We should simultaneously strive for the development of new utility measurement instruments. Because the effects and sizes of biases are hard to predict, economic evaluation and medical decision making should ideally use utility elicitation techniques that are not susceptible to biases such as loss aversion. Finally, several studies have suggested that there exists a concave relationship between the standard gamble and the time trade-off and that it might be possible to obtain standard gamble utilities by adjusting time trade-off utilities for risk attitude (Miyamoto and Eraker, 1985 and Stiggelbout et al., 1994). The results from our paper suggest that the relationship between time trade-off utilities and standard gamble utilities is complex and depends, among other things, on the gauge duration used. Acknowledgements Two anonymous referees gave very helpful comments. Han Bleichrodt’s research was made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences and by a grant from the Netherlands Organisation for Scientific Research (NWO). Financial support for the experiments reported in the paper was obtained from SEC 2000-1087.