اعتبار ارزش زمان تجارت کردن در محاسبه QALYs: ثابت زمانی نسبی تجارت کردن در مقابل اکتشافی متناسب

In order to calculate quality adjusted life years (QALYs) from time trade-off (TTO) responses, individual preferences are required to satisfy the constant proportional time trade-off (CPTTO) assumption. Respondents who use a simple proportional heuristic may appear to satisfy CPTTO but will in fact generate preference reversals for states that are associated with a maximal endurable time (MET). Using data from 91 respondents, the study reported here examines the extent to which valuations satisfy the CPTTO assumption and the extent to which they might be generated by the proportional heuristic. The results suggest that respondents are using a proportional heuristic that casts doubt on the validity of using the TTO method to calculate QALYs for health states that are associated with MET preferences.

As a very simple example of how QALYs would be calculated using any tariff of health state values, consider an intervention that has known effects on health status and life expectancy. Assume also that health status does not vary over time. The QALY gain to an individual from this intervention will be View the MathML source where Q1 and Q0 represent pre- and post-intervention health status and T1 and T0 represent pre- and post-intervention life expectancy, respectively. A number of authors have shown, in various ways, that quite stringent assumptions have to be made for this algorithm to fully represent individual preferences ( Pliskin et al., 1980, Miyamoto and Eraker, 1985 and Bleichrodt et al., 1997). At a general level, for the QALY algorithm to be a valid representation of the individual utility from changes in health, all of these models require that preference theory is satisfied; that is, they assume that individuals have clear well-defined preferences and are rational according to some set of axioms (such as those required in consumer theory, namely, completeness, reflexivity and transitivity). If preference theory is not satisfied, then the number of QALYs generated by an intervention cannot be assumed to represent utility, and so it may be possible that, under certain circumstances (such as when a health state becomes increasingly intolerable over time), less QALYs are preferred to more. So that QALYs can be calculated from health state values generated by the TTO method, preferences are required to satisfy the constant proportional time trade-off (CPTTO) assumption. CPTTO entails that an individual is willing to sacrifice a constant proportion of her remaining life years in order to achieve a given improvement in her health, irrespective of the number of life years that remain. CPTTO may not be a very good representation of people’s preferences in that the value of some less severe states may increase over time and the value of some more severe states may decrease over time, but it is required for the QALY model to hold when values have been elicited using the TTO method. CPTTO implies that respondents in the EQ-5D study would have been willing to trade-off the same fraction of life years whether the states were described as lasting for 5 or 20 years instead of for 10 years. In this way, the same set of tariff values would have been generated irrespective of the specified duration. The evidence relating to CPTTO is somewhat mixed. The early work in this area suggests that people trade-off a larger fraction of their remaining years of life as the number of these years increases (Sackett and Torrance, 1978, Pliskin et al., 1980 and McNeil et al., 1981). More recent studies, however, have found that the largest trade-offs are for the shortest durations of life expectancy (Stalmeier et al., 1996, Stalmeier et al., 2001 and Unic et al., 1998). Encouragingly for the QALY model, there is also evidence that CPTTO might provide a reasonably good approximation of preferences. Stalmeier et al. (1996) found that the values for states lasting 10, 25 and 50 years were remarkably similar and Bleichrodt and Johannesson (1996) found that the mean values for states lasting 10 years and for states lasting 30 years were almost identical to one another. If, on average, CPTTO does hold, it would only be applicable to those states for which more time is always preferred to less, and there is some evidence that this may not always be the case. For example, Sutherland et al. (1982) having found from a sample of 20 colleagues that the proportion preferring death to varying durations in each of five health states increased as the duration of the states increased, postulate that for some states there exists a maximum endurable time (MET) beyond which people do not wish to live. In other words, the value of those states becomes negative after some threshold. This concept has been reinforced by the results from a much larger general population study ( Dolan, 1996). These results suggest that it might be inappropriate to calculate QALYs using TTO values of states for which there might come a point at which death would be preferred to any more time in those states, despite (positive) TTO values that suggest otherwise. However, it is difficult to know precisely how to interpret the results from these studies since they did not explore the reasons behind people’s responses. In a study designed to “get behind the numbers”, Robinson et al. (1997) conducted a qualitative follow-up to the ‘tariff study’ which was designed to explore why so many more states were rated as worse than dead using the TTO method than when using a visual analogue scale (VAS). The conclusion that “the 10-year duration of the health state is more salient in the TTO than the VAS” suggests that MET preferences might exist. In other words, respondents might think about a short duration in the VAS task and rate the state as better than dead but contemplate 10 years in that state in the TTO task and consequently rate it as worse than dead. For respondents with MET preferences, Stalmeier et al. (1997) show that preference reversals can occur. On average, respondents in their study were indifferent between 10 years with very frequent migraines and 4 years in full health, i.e. [10,M]∼[4,H]. They were also indifferent, on average, between 20 years with very frequent migraines and 8 years in full health, i.e. [20,M]∼[8,H]. If more years in full health are preferred to less, i.e. [8,H]>[4,H], then this implies that [20,M]>[10,M]. However, 103 (out of 176) respondents exhibited MET preferences, i.e. [20,M]<[10,M], and, of these, only 24 gave a lower number of equivalent healthy years to the longer duration. In other words, the majority of respondents who preferred 10 years of migraine to 20 years of migraine gave TTO responses that suggested the opposite preference ordering, and hence this results in a preference reversal. Such reversals falsify the assumptions underlying the QALY model, so that using a value of 0.4 (i.e. 8/20) for migraine has no valid interpretation within the QALY model for those with preference reversals. Preference reversals involving money gambles are now well documented in the economics literature (Grether and Plott, 1979 and Tversky et al., 1990). Here, out of two gambles, respondents tend to place a higher certainty equivalent value on the higher pay-off/smaller probability gamble but choose to play out the smaller pay-off/higher probability one. Respondents in the Stalmeier et al. (1997) study would not have committed a similar reversal if their preferences had been consistent with CPTTO. Instead, the authors conclude that most respondents with a MET preference use a proportional heuristic, whereby they trade-off a constant proportion of their remaining life expectancy, not because they satisfy CPTTO but because they simply double their stated number of years in full health as the number of years in the poor health state doubles. Since people’s health state valuations are likely to be rather imprecise and constructed partly during the process of elicitation (Dolan, 2000), the proportional heuristic provides respondents with a simple ‘rule of thumb’ to help them generate responses to quite difficult valuation questions. For those who use the proportional heuristic in combination with a preference reversal, values derived using the QALY model clearly have no valid interpretation within that model. However, for those who use the proportional heuristic in the absence of a preference reversal, values derived using the QALY model may have a valid interpretation within the QALY model. In the study reported here, we assess respondents’ trade-offs when asked to value one of the EQ-5D health states using the TTO method for durations of 10 and 20 years. By directly asking respondents whether they would prefer to live for 10 or 20 years in that state, we are able to examine the extent to which their valuations satisfy the CPTTO assumption and the extent to which they might be generated by the proportional heuristic. If CPTTO holds, then [10,P]∼[x,H], [20,P]∼[2x,H] and, crucially, [20,P]>[10,P], where P is the EQ-5D health state and x is the number of years in full health, H. We would have strong evidence of the proportional heuristic if the same set of TTO responses were generated (i.e. [10,P]∼[x,H] and [20,P]∼[2x,H]) but if [10,P]>[20,P]. This would show that MET preferences exist but that these are not reflected in people’s TTO responses. The study was designed specifically to provide qualitative insights into the reasons behind respondent preferences and to gain insights into why shorter or longer durations in the same health state might be preferred. This information would thus shed some light on the descriptive validity of the tariff for calculating QALYs.

The results from this study suggest that respondents with MET preferences are using a proportional heuristic when responding to TTO questions. Even though our data do not prove this, respondents without MET preferences might also be using the same heuristic. Therefore, the CPTTO-like patterns of responses reported elsewhere may be little more than the proportional heuristic in disguise. All of this suggests that TTO values may not fully comply with the preference theory upon which their interpretation for use in economic evaluations is based. Nevertheless, the TTO values that have been successfully elicited over the last couple of decades are still useful. If the proportional heuristic holds, the values can be used to rank health states and to provide information about the relative distances between them. Moreover, the number of QALYs estimated for profiles of health that contain relatively mild states (where MET preferences are less likely) provide a good approximation of the relative health benefits from alternative interventions. What the proportional heuristic does mean, however, is that the values may not fully comply with the properties required by the QALY model and could in some circumstances (e.g. for severe states that last for relatively long periods of time) lead to the wrong conclusions about the ordering of different profiles of health.