Eliciting discounting model and direction at the individual level with time trade-off follow-up questions

Abstract

Objective

Time preference is increasingly considered in health state valuation. As its inclusion impacts the produced value sets, it is important to account for it using the correct specification. Various discounting functions have been used, and both directions of time preference have been identified. I aimed to extend the composite time-trade off task (composite TTO, cTTO) by follow-up questions (TTOFUs) to identify the discounting function and direction for individual respondents.

Methods

Respondents completed cTTO tasks for 6 EQ-5D-5L health states. If utility exceeded 0.1, three TTOFUs (Q1–Q3) were posed. Each TTOFU modified the indifference-yielding alternative by halving durations (Q1) or adding a 5-year lead-time in full health (Q2) or a 5-year lag-time in the valued state (Q3). As shown in the paper, the pattern of Q1–Q3 answers unambiguously discerns the discounting function (exponential, power, or hyperbolic) and direction.

Results

Data from 148 respondents, 16 health states, and 577 respondent-state pairs were analysed. Only 20.4% of pairs yielded theoretically-plausible patterns, and among those 60% imply no time preference. For Q2 and Q3, responses mostly implied negative () and positive () time preference, respectively. Majority-rule pooling within respondents produced a pattern not matching the considered discounting models but that can arise when quality-of-life and longevity are combined additively, not multiplicatively as in the quality-adjusted life years (QALY) model.

Conclusions

Standard discounting models poorly fit observed choices in TTO-like questions. The discounting parameters measured in other studies may be driven by other phenomena, including departures from the QALY model. Hence, careful interpretation of estimated parameters is warranted, and future studies are recommended.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10198-025-01866-4.

Introduction

To inform decisions on reimbursement of health technologies, cost-utility analysis (CUA) is often used. In CUA, the total clinical effect is calculated based on changes in longevity and in health-related quality of life (HRQoL). To quantify the latter, health states are assigned numbers, QALY weights (QALY = quality-adjusted life years), based on preferences for health states elicited in valuation studies [1–3]. Health states are often defined using one of the EQ-5D family of instruments [4], for instance, the EQ-5D-5L, which is used in this paper and is introduced in the next section [5].

The preferences for EQ-5D-5L states are predominantly elicited using the composite time trade-off method (composite TTO, cTTO) [6, 7]. In the elicitation, commonly, the standard QALY model is assumed: living in state H for T years and dying afterwards is assigned the utility equal to [8, 9]. When states vary over time, the utility values of sub-periods are added. The utility u(H) is elicited by establishing indifference between two alternatives characterized by different duration and living in either H or full health (FH). In the standard QALY model, the total utility is linear in time, i.e., the life years distant in the future are as important as the life years near to now, or — in other words — the future life years are not discounted. Recently, it has been increasingly suggested that discounting should be accounted for in valuation studies, for instance, for SF-6D descriptive system [10], and discounting was included in some valuation studies using EQ-5D instruments [11, 12]. It is important to distinguish the discounting of future QALY benefits in CUA and the discounting in the elicitation of health state utilities in valuation studies. The former has been used for many years and in many countries (for a review of guidelines, see Attema et al. [13]). Typically, the exponential discounting is used with annual discount rates in the range 3–5%, usually equal for future QALYs and for future costs, typically close to the annual long-term government bond yields. This discounting aims to represent the public decision maker attributing larger importance to the effects and cost occurring sooner (i.e., positive time preference). Meanwhile, the latter, i.e., accounting for discounting in the elicitation task, aims to remove the possible impact of time preference of individual performing the elicitation task on the elicited utility values [14]. This paper focuses on the latter type of discounting.

Accounting for discounting in the elicitation of preference for health states poses several challenges. First, to facilitate estimation, parametric approaches are usually used. In such approaches, different models can be used to represent the discounting. In the health preference literature, either exponential, hyperbolic, or power models prevail (presented more formally in the next section). The exponential function is the classic approach to discounting used in economics or finance [15], and which is also used in CUA. The hyperbolic function was proposed as more behaviourally plausible [16]; this function fitted the data best in a valuation study [10]. The power function was also used in a valuation study [11] and in some approaches in a predictive modelling competition in health preference research [17]. Importantly for the motivation behind the present paper, the choice of the specific function matters for the estimated QALY weights: for SF-6D instrument, the proportion of worse than dead (WTD) states ranges from 4.7% for hyperbolic discounting, through 7.1% for exponential discounting, to 13.1% with no discounting, and the QALY weight for the worst possible state amounts to , , and , respectively [10]. In many studies, insufficient information is available at the individual level and discounting is accounted for by making parametric assumptions on the whole population level. Therefore, understanding how credible various discounting models are is useful.

Second, there is a large heterogeneity in the estimated discount rates and direction of discounting. In published studies, both positive (i.e., treating future life years as less important than present life years) and negative time preferences were identified in substantial subgroups of respondents (>30%), and more respondents demonstrated negative than positive time preference [18, 19]. This heterogeneity makes it challenging to include time preferences in analysis, as a single population-level parameter may not capture individual behaviour with sufficient precision. Hence, it is warranted to develop methods allowing for an estimation of the discount function at the individual respondent level. The large proportion of negative time preference is surprising when contrasted with the value of discount rates observed beyond health preference: a meta-analysis of multiple studies only reports rare cases of such negative time preference [20]. Hence, a better understanding of discounting at the individual level is required to confirm the validity of estimated discount rates. It is important to stress that the inclusion of time preference in valuation studies matters for the obtained QALY weights, and that it can change the results in both directions: there was an increase in Jonker et al. [10] and a decrease in Lipman et al. [18].

Third, the estimation of the parameters of discounting function may be confounded with other phenomena, as illustrated by the following example. Let us assume that the following cTTO outcomes (number of years in full health that yielded indifference) are observed for EQ-5D-5L health states 31111 (moderate problems in mobility), 13111 (moderate problems in self-care), and 33111 (moderate problems in both): 4 years (i.e., 6 years traded), 4 years, and 1 year, respectively. These outcomes can be obtained in either of two scenarios: (I) the preferences are linear in time and the utilities of the health states are, respectively, 0.4, 0.4, and 0.1, so the disutilities are 0.6, 0.6, 0.9, respectively (mobility and self-care dimensions are not combined in an additive way but they interact preferentially, i.e., they are complements), or (II) the instantaneous utility values are, respectively, 0.6, 0.6, and 0.2 (i.e., no preferential interaction) but the future life years are discounted exponentially with the annual discount rate of 0.165. The mechanism underlying this example is as follows. Negative interactions (i.e., if combining health problems has smaller total effect than the simple sum of individual health problems) reduces the number of life years in full health traded in TTO as compared with what would be expected based on the TTO results for individual problems. Meanwhile, the same effect, i.e., diminished willingness to trade, may be observed for positive discounting: the more life years have already been traded, the more valuable the remaining life years are and the greater the reluctance to trade is. Jonker and Donkers [21] included both the interaction and discounting in the model specification used with discrete choice experiment (DCE) data, which helps to avoid the above confounding. However, for DCE data estimating the individual level discounting is not possible and to draw the population-wise conclusions, parametric assumptions must be made (e.g., the discounting function or the function linking the utility difference to the probability of choice), which may be challenging in view of the heterogeneity discussed in the preceding paragraph.

A so-called direct method has been proposed to elicit the discounting function at the individual respondent level without relying on parametric assumptions [22]. In this method, the respondent is asked to compare two health profiles, each composed of a subperiod of worsened health and a subperiod of full health, but in a reverse order. The durations of subperiods are varied to establish indifference and approximate the shape of the discounting function. A possible shortcoming of the direct method is that it makes the ordering of the two subperiods involving the two health states focal in the task. Hence, the respondents may focus on this ordering in a way that confounds the estimated discounting function: for instance, if the respondents want to avoid emotional impact of knowing that their health will deteriorate, they may prefer to get over the health problems sooner, which will result in negative time preference. This ordering effect would explain the predominantly negative discounting obtained using the direct method [18, 19]. A certainty-equivalent approach to lotteries involving various durations was also proposed to elicit discounting parameter at the individual respondent level [23]. However, the results of this method can be distorted if respondents use probability weighting for cumulative probabilities [24]. Therefore, testing alternative methods to understand the individual-level discounting may be useful.

The aim of this paper is to propose an alternative method to detect the discounting function form and direction of time preference at the individual level. The proposed method allows for an identification of discount function form (among the three discount models introduced above) and the direction of time preference or lack thereof. The second goal is to test the method empirically in a convenience sample of respondents valuing EQ-5D-5L health states. The method entails asking additional TTO-type questions after indifference has been reached in the usual cTTO procedure with the details presented in the next section. The paper makes two kinds of contribution. First, it offers a methodological contribution by showing how different modifications of TTO task can help to identify different discounting models within an individual just based on the pattern of answers to three choice tasks, which do not require proceeding until indifference is established. Second, it offers an empirical contribution by showing that the usual discounting models poorly match the empirical data and by discussing the possible explanations and implications.

Methods

Overall experiment design

Six interviewers (graduate students of SGH Warsaw School of Economics, Poland) invited and interviewed a convenience sample of peers and older relatives or acquaintances between November 2022 and March 2023. This strategy was used to make sure various age groups are included as the attitude towards the future may depend on the respondent’s age. Interviews were performed in online sessions, using screen sharing and a software to illustrate the tasks.

Each respondent provided informed consent, answered basic demographic questions, evaluated own health using the EQ-5D-5L descriptive system and a visual analogue scale (EQ-VAS), answered the TTO tasks, and answered some debriefing questions. In the TTO part, the respondents first answered warm-up questions with three health states: living in a wheelchair and two health states using EQ-5D-5L descriptions (a mild one and a severe one). In this warm-up, the regular cTTO procedure was used [see 6] with no follow-up TTO questions. I briefly describe the parts of cTTO important for the present paper.

When valuing health state H, the respondent is first asked to compare living in for 10 years with living in H for 10 years, both followed by death, denoted by vs (H, 10). Typically is preferred, and the respondent is asked to compare immediate death with (H, 10). If the former is preferred, then H is considered WTD and lead-time TTO (LT-TTO) is used: 10 years in FH are added to both alternatives to allow for further trading. The LT-TTO part of cTTO is not important in the context of the present study. If (H, 10) is preferred over immediate death, then H is considered better-than-dead and the respondent is asked to compare vs (H, 10). Subsequently, the time spent in FH is modified in order to reach the indifference between the two alternatives. Once the indifference is established for some , it is concluded that and cTTO ends.

After the warm-up, the preferences for six EQ-5D-5L health states were elicited using cTTO. For each state, after cTTO has ended, TTO follow-up questions (TTOFUs) were asked. The specific TTOFUs depended on the outcome of cTTO, and only some TTOFUs relate to the aim of this paper (see Section Time trade-off follow-up questions for details). After the TTO part, as a debriefing, the respondents answered additional questions on religiosity and perceived difficulty of the interview.

Health states

The EQ-5D-5L descriptive system was used to define health states. Each health state is described using five dimensions: mobility, self-care, usual activities, pain/discomfort, and anxiety/depression. In each dimension, there are possible five levels of health issues denoted by digits from 1 (no problems) to 5 (extreme problems). Each health state can be presented as a five-tuple of digits for consecutive dimensions. Hence, 11111 represents no health problems (in the dimensions included in EQ-5D-5L), and 55555 represents the most severe health state in this descriptive system.

In the warm-up, health states 21111 and 55233 were used besides living in a wheelchair scenario, to to familiarize respondents with the EQ-5D-5L descriptive system and to demonstrate the possibility of providing WTD answers (not to bias the results upwards). In the actual part of the interview, three blocks of states were used. In each block, a mix of mild, moderate, and severe states were used, to span the whole range of severity. This diversity aimed to ensure that sufficient trading is observed in each respondent, as states preferentially equivalent to FH yield no useful information on discounting. A mix of problems across EQ-5D-5L dimensions was used to avoid results being driven by particular combinations of health problems. The severe states were included as the study also included other TTOFUs — beyond those used in the present paper — that were only asked for WTD states. The following states were used:

• block A: 11122, 21112, 22434, 21334, 52455, 55555;

• block B: 11212, 12121, 31514, 42321, 55225, 55555;

• block C: 11212, 11221, 32314, 32443, 24553, 55555.

Time trade-off follow-up questions

The specific TTOFUs asked depended on the outcome of cTTO. The detection of the discount function and direction was based on TTOFUs asked if respondent declared indifference , for some . Then H has an estimated utility . In this case, three TTOFUs — referred to as Q1–Q3 below — were asked (in other cases, TTOFUs were asked that were designed for the purpose of research questions beyond this paper):

• Q1: vs (H, 5), where initially , i.e., the durations are halved as compared to the alternatives that yielded indifference in cTTO;

• Q2: vs , where initially , i.e., a lead-time of 5 years in FH is added to both alternatives;

• Q3: vs (H, 15), where initially , i.e., a lag-time of 5 years in H is added to both alternatives.

Importantly, the considered alternatives either form constant profiles (they entail living in a single state, H or ), or — where mixed profiles are used (Q2 and Q3) — always precedes H. Hence, in the tasks used in this study, the ordering effects are avoided.

In each of Q1–Q3, T was varied until a new indifference point was found. The new indifference point was sought by changing T by six months in the direction depending on the answer (e.g., in Q1, if (H, 5) was preferred, then T was increased) and by three months if the direction needs to be changed, i.e., a finer granularity was used than usually in cTTO to also match the halving of the durations in Q1.

The rationale for using Q1–Q3 is as follows. Under the standard QALY model, the respondent should remain indifferent in Q1–Q3 for the initial value of T. This paper focuses on three discounting functions predominantly used in the literature: exponential, hyperbolic, or power. To make the paper more self-contained, I present how the three models are defined. Let us consider a subperiod of life that consists in living in H between years from now until years from now, and let us write down the contribution of this subperiod to the overall QALY for various discounting models.

• standard QALY model without discounting: ,

• discounting with parameter r: for and if , where , , represents no, positive, and negative time preference, respectively,

• hyperbolic discounting with parameter r: for and for , where and represents no and positive time preference, respectively,

• power discounting with parameter : , where , and , , and represents no, positive, and negative time preference, respectively.

Depending on the discounting function (exponential, hyperbolic, or power) and the direction of time preference (positive, negative, or lack thereof), the pattern of answers to the first question in TTOFU should differ (notice that hyperbolic discounting is in general impossible for negative time preference). The details are presented in Table 1, and the formal proof is delegated to the Supplementary Material. Conveniently, Q1 and Q2 combined point unambiguously to the specific discount function and direction, while Q3 alone unambiguously points to the direction of time preference. Table 1 demonstrates that concluding based on only one type of task may be limited if the true discount model is unknown. For instance, indifference in Q2 implies no time preference for power discounting but not for the exponential discounting.

Table 1.

The theoretically-expected responses for the three time trade-off follow-up questions (TTOFUs) depending on the direction of time preference (or absence thereof) and the discount function (exp. = exponential, hyp. = hyperbolic)

TTOFU	Time preference
	positive			none	negative
	Function type				Function type
	exp.	hyp.	power		exp.	power
Q1	H	H
Q2
Q3					H	H
% respondent-state observations matching a given pattern
all data	1.9	3.8	1.9	12.1	0	0.7
states with	2.1	4.3	2.1	6.4	0	0.8
states with	2.8	5.3	2.1	3.5	0	1.1
states with	1.0	2.4	1.7	20.4	0	0.3
% respondent-aggregated answers matching a given pattern
all data	2	1.4	0.7	21.8	0	0

It is indicated which alternative should be preferred in the starting question of each TTOFU: H = alternative only using disease state, = alternative only using full health; = alternative with varying health state; denotes that indifference is expected. The structure of actually observed patterns presented in the bottom rows for all data and for subsets of states

Even if the answer to the first task in each TTOFU suffices to determine the discounting function and time preference direction, the interview continued and the alternatives were modified in order to identify the indifference point in TTOFU. This was done to make sure that the initial answer was not erroneously given and then reverted in subsequent answers. The inference about the discounting function and direction is based on the indifference point reached.

Analysis

To provide information about the sample and the collected utilities, basic demographic characteristics of the respondents were calculated, and then the raw mean utility values elicited in the standard cTTO part of the interview were calculated for each health state. These utility values were juxtaposed with the QALY weights from the Polish EQ-5D-5L valuation study.

To assess the reliability of cTTO in capturing the preference and the quality of the data, the proportion of cTTO utility values at predefined levels of , , 0, 0.5, and 1 was verified. The utility taking the extreme values may indicate that, for , the respondent was not able to report their preference with cTTO because of censoring or, for , that the respondent did not accept to trade-off offered intervals to avoid health problems [25]. The case of may denote that the respondent considered the valued state to be severe enough to trade-off all life years in TTO but did not want to accept immediate death as a preferred alternative [26]. Because the situations when utility is close to 0 may reflect the respondent having ambiguous views on state H (treating it as severe but not willing to accept immediate death is preferred), the TTOFUs Q1–Q3 were only asked for cases. The cases and may indicate that the respondent used a satisficing strategy and accepted early close-enough answers, which signals diminished reliability of cTTO values [27].

To verify within-respondent consistency, the proportion of misordered utility values was checked within respondents in cases where two health states could be logically ordered (i.e., one state was objective better, i.e., it had all dimensions at lower or equal level values).

The proportion of answers corresponding to patterns presented in Table 1 was calculated for all individual respondents and states. Additionally, the proportion of answers separately to each of Q1–Q3 was calculated, to determine, among other things, the implied direction of time preference. Because for some mild states the respondents may be unwilling to trade any time in cTTO, e.g., in view of only being offered 6-month intervals to trade, and the states effectively treated as preferentially equivalent to FH yield no insight into time preference, the proportion of answers was also calculated for subset of states with elicited cTTO utilities falling below predefined thresholds.

To provide additional insight, individual-level analysis was performed in the following manner. For each respondent, it was determined if their answers to TTOFUs were consistent, i.e., in what proportion of states they provided the same answer for a given TTOFU (in theory, their answers should only depend on the discounting, and not on the health state). Subsequently, for each respondent the most prevalent answer was selected using the majority rule (indifference was selected in case of ties) and the proportion of patterns across Q1–Q3 was calculated for such aggregated results.

Results

Respondents characteristics

Of the total of 150 recruited respondents, 2 respondents were removed (technical issues & low credibility as assessed by the interviewer), so data from 148 respondents were ultimately included in the analysis. The respondents were between 19 and 83 years old, with the average age of 27.6 and standard deviation (SD) of 11.1. There were 78 (52.7%) females, 69 (46.6%) males and a single respondent (0.7%) of other sex. The respondents were overall in very good health: 48 (32.4%) reported perfect health according to EQ-5D-5L (i.e., 11111), while 80 more (54.1%) reported health problems at level 2 at most; only a single respondent reported a level 4 problem. The respondents reported the VAS score between 55 and 100 with the mean of 82.7 and .

Health state utility values

The elicitation results of the cTTO part are presented in Table 2. In this table, also the values from the official EQ-5D-5L Polish value set are presented [see 1, for details]. As it can be seen, the values elicited in the present study tend to be lower than in the value set, which may result from the present sample not being representative for the general population and instead it being younger and less religious than in the Polish valuation study: in the present sample, 81.8% of respondents were years old and were religious, compared with 30.2% and 90.1%, respectively.

Table 2.

The results of the composite time trade-off for individual health states. Polish value set based on Golicki et al. [1]

Health state (n)	Mean utility (SD)	Polish value set	% BTD (% )	%
						0	0.5	1
11122 (58)	0.864 (0.151)	0.952	100.0% (100.0%)	0%	0%	0%	3.4%	20.7%
11212 (45)	0.819 (0.321)	0.959	97.8% (97.8%)	2.2%	0%	0%	6.7%	26.7%
11221 (45)	0.813 (0.319)	0.947	97.8% (97.8%)	2.2%	0%	0%	2.2%	26.7%
12121 (45)	0.859 (0.149)	0.939	100.0% (100.0%)	0%	0%	0%	6.7%	15.6%
21112 (58)	0.831 (0.176)	0.957	100.0% (98.3%)	0%	0%	0%	5.2%	13.8%
21334 (58)	0.512 (0.416)	0.777	94.8% (89.7%)	3.4%	1.7%	3.4%	8.6%	3.4%
22211 (45)	0.801 (0.180)	0.921	100.0% (100.0%)	0%	0%	0%	2.2%	13.3%
22434 (58)	0.342 (0.411)	0.689	89.7% (74.1%)	1.7%	3.4%	12.1%	12.1%	0%
24553 (45)	−0.274 (0.555)	0.055	51.1% (22.2%)	22.2%	6.7%	20%	4.4%	0%
31514 (45)	0.211 (0.485)	0.653	84.4% (64.4%)	4.4%	4.4%	17.8%	6.7%	0%
32314 (45)	0.416 (0.474)	0.787	88.9% (80.0%)	4.4%	0%	2.2%	11.1%	4.4%
32443 (45)	0.054 (0.581)	0.548	68.9% (57.8%)	13.3%	2.2%	0%	2.2%	0%
42321 (45)	0.479 (0.487)	0.773	88.9% (82.2%)	2.2%	4.4%	2.2%	4.4%	2.2%
52455 (58)	−0.292 (0.599)	−0.249	48.3% (29.3%)	25.9%	5.2%	15.5%	5.2%	0%
55225 (45)	−0.186 (0.571)	0.137	62.2% (33.3%)	17.8%	4.4%	24.4%	6.7%	0%
55555 (148)	−0.519 (0.516)	−0.590	30.4% (12.8%)	35.8%	6.1%	10.1%	0.7%	0%
all pooled (888)	0.263 (0.674)	n.a.	75.9% (65.0%)	11.5%	2.8%	7.1%	5.1%	7.0%

n = number of observations, BTD = better than dead, NT = non-trading

For most of the states, there are only a few cases of utility values equal to or 0.5, which suggests no problems with respondents using satisficing strategy. For some states (notably those that simultaneously contain level 5 and levels 1 or 2 in their description), there are many cases with utility equal to 0: the respondents neither wanted to live in these states nor wanted to admit they are WTD. The TTOFUs reported in this paper were not asked for such states, so the results of this paper are not affected by the peak of utility values at 0.

Regarding the intra-respondent consistency, there were 1667 within-respondents pairs of health states that were logically ordered, i.e., one state had lower or equal levels of all dimensions. For such ordered pairs, the proportion of strict inconsistencies (i.e., objectively better state being assigned strictly lower utility) amounted to 1.6%, which suggests good data quality. The proportion of non-strict inconsistencies (i.e., objectively better state being assigned lower or equal utility, unless both utilities amounted to the censoring threshold of ) amounted to 6.5%.

Eliciting the discounting function and time preference direction

The structure of all individual responses patterns to Q1–Q3 is presented in Table 1. Notably, only very few observations match any of the patterns corresponding to one of the usual discount functions, i.e., 20.4% in total, while 12.1% (i.e., 59.3% of the matching patterns) corresponds to indifference-only pattern. For the hyperbolic function with negative time preference (which is not feasible in general, hence, is omitted in the table), the corresponding pattern was observed in 0.9% of the cases.

The two most frequently observed patterns (which do not correspond to any of the considered theoretical possibilities) were: , , (21.3% of all observations) and , , (17.7% of all observations). The triple indifference pattern presented in Table 1 (i.e., , , ) ranked third.

The results for individual TTOFUs Q1–Q3 are presented in Table 3. For Q2, the responses in majority, i.e., in 57.2% of the cases, imply negative time preference (i.e., the preference for ). Meanwhile, for Q3, the responses in majority, i.e., in 63.6%, imply positive time preference (i.e., the preference for ), and only in 10.7% the responses agree with negative time preference. The responses to Q1 are not informative regarding the direction of time preference: indifference was obtained as the single most frequent category of answers (47.8%) and indifference does not imply the linear time preference and may be associated with both positive and negative time preference for power discounting.

Table 3.

The structure of observed responses to individual time trade-off follow-up questions (TTOFUs)

TTOFU	alternative 1 (%)	(% indifference)	alternative 2 (%)
all data
Q1	H (23.1%)	(47.8%)	(29.1%)
Q2	(15.9%)	(26.9%)	(57.2%)
Q3	(63.6%)	(25.6%)	H (10.7%)
utility in the starting composite time trade-off
Q1	H (25.8%)	(42.7%)	(31.5%)
Q2	(17.9%)	(21.6%)	(60.6%)
Q3	(67.0%)	(21.0%)	H (12.0%)

See the caption of Table 1 for the explanation of alternatives

Regarding the consistency at the individual respondent level, for each of Q1–Q3 TTOFUs, two measures of consistency were defined. Strong consistency was defined as choosing the same alternative (e.g., always , always , always H, or always ) for all states for a given TTOFU. Weak consistency was defined as not choosing the opposite alternatives for a given TTOFU (e.g., never choosing both and H for Q1 in two different states). In Table 4, the proportion of strongly and weakly consistent respondents is shown split by the number of health states for which Q1–Q3 TTOFUs were asked. The split is useful as answering Q1–Q3 for more states provides more opportunity of demonstrating lack of consistency. To put these numbers in perspective, the lower half of Table 4 presents what values would be obtained if the respondents provided answers for all states independently and according only to the empirical probability distribution for a given TTOFU reported in Table 3.

Table 4.

The consistency of responses within individuals (see explanation in the main text)

# of states (# of respondents)	% weak consistency			% strong consistency
	Q1	Q2	Q3	Q1	Q2	Q3
Actual data
2 (17)	88.2%	88.2%	100.0%	58.8%	64.7%	70.6%
3 (35)	74.3%	74.3%	80.0%	20.0%	51.4%	51.4%
4 (52)	69.2%	59.6%	69.2%	21.2%	26.9%	32.7%
5 (23)	52.2%	52.2%	56.5%	13.0%	26.1%	21.7%
6 (19)	78.9%	57.9%	63.2%	21.1%	5.3%	15.8%
Simulated data, independent answers within each respondent
2	86.6%	81.8%	86.4%	36.7%	42.5%	48.2%
3	70.2%	65.4%	74.3%	14.6%	21.1%	27.5%
4	55.0%	52.9%	64.9%	6.2%	11.3%	16.8%
5	42.3%	43.4%	57.3%	2.8%	6.3%	10.5%
6	32.2%	36.0%	50.9%	1.3%	3.5%	6.6%

Majority rule approach was used to determine a single response pattern for each respondent in the following way. If more than half of the responses for a given individual in one type of TTOFU (e.g., Q1) indicated preference for one of the alternatives (e.g., or H for Q1), then this answer was taken as single aggregate answer for this respondent; otherwise (i.e., when none of the alternatives was preferred in the majority of cases), indifference was assumed as aggregate answer. Using this approach, for Q1, indifference was picked for 63.9% of respondents; for Q2, was picked for 52.4% of respondents; for Q3, was picked based on 63.3% of respondents. Notably, the combined pattern (indifference, FH, FH+H) does not match any of the theoretical possibilities presented in Table 1. Looking at all TTOFU questions combined in terms of patterns of responses, the pattern composed of these individually most prevalent answers (i.e., indifference, FH, FH+H) was the second most prevalent (20.4% of the respondents), second only to indifference-only (21.8%). In total, only 25.9% of respondents demonstrated a pattern that matched any theoretically plausible one.

Discussion

Contribution

In the paper, I have endeavoured to elicit the discount functions and direction with respect to future health states at the individual respondent level. This elicitation was done by designing and asking the respondents additional TTO questions, referred to as TTOFUs, after the regular cTTO elicitation task has ended for a given health state. From a methodological point of view, the paper shows that it is possible to detect these discount mechanisms by just three choice tasks. Additionally, to detect the discount mechanism with the proposed TTOFus, looking for a new indifference point is not needed, i.e., a single discrete answer suffices. The proposed method may be used in other studies to gain insight into the time preference of individual respondents.

Admittedly, the idea to simultaneously use different TTO-type tasks to study time preference was used previously [28, 29]. However, the present paper differs in some important aspects. In Dolan and Gudex [28], the time preference (the direction and the strength) was inferred based on the comparison of TTO results for profiles that either entailed living in state H before or after living in (compared with living in only). In consequence, the results are likely affected by the ordering effect. In Attema and Versteegh [29] (who reused the data from Versteegh et al. [30]), lead-time and lag-time, both in , were included. However, in that study these approaches were used in different groups of respondents which makes it impossible to infer the time preference at the individual level. Moreover, as it is shown in Table 1 of the present paper, the responses to lead-time tasks are individually not fully informative of time preference, as the conclusion also depends on the discounting model (e.g., adding lead-time preserves indifference also with non-zero time preference, if exponential model holds). Hence, it is important that a collection of tasks should also allow for an identification of the discounting model, as done here.

Based on the approach constructed in this paper, an important empirical conclusion follows. The obtained results show that respondents behaviour is mostly discordant with any of the theoretical models of discounting used in the health preference research. In the minority of cases where the behaviour is consistent with theoretical models, it trivially corresponds to no discounting. On the one hand, the observed discordance made it impossible to actually measure the discounting model and direction at the individual level for most of the respondents. On the other hand, this negative result makes the implications more pronounced: it remains unclear how discounting should be accounted for in health state valuation studies, as respondents’ behaviour appears more complex than standard models assume. Hence, further research is clearly warranted, and possible directions are suggested below.

Explanations

I see the following possible explanations of the above empirical findings, presented below in an order of increasing plausibility (admittedly, from the author’s subjective point of view). First, one may associate the findings with a simplified study protocol that may have hampered the data quality. There was no feedback module that is a standard part of the official EQ-5D-5L valuation studies using cTTO and the EQ-VT protocol and that would allow the respondents to reflect more on the validity of their answers [7, 31]. Additionally, the multitude of different choice tasks might have tired or confused the respondents. There was no test-retest check to verify the robustness of the answers. While this explanation cannot be entirely ruled out, the data quality analysis presented in the paper, e.g., the analysis of consistency among logically ordered states, does not indicate any major problems. Nevertheless, replicating the present study in another sample would be welcome.

Second, perhaps there are random deviations of respondents’ behaviour from the predictions of theoretical models or the respondents use other discount models altogether than the exponential, hyperbolic, or power model (see Lipman and Attema [32] for a systematic review of various models). The plausibility of this explanation seems diminished for the following reason. Admittedly, all parametric models necessarily are only simplifications of true behaviour, i.e., people do not perform calculations prescribed by the models and only behave as if they were performing them [33]; hence, it is not surprising that the models match behaviour only approximately. However, it seems not intuitive why the deviations were so large that only a minority of observations matches the theoretical possibilities. Regarding the respondents using other forms of discounting, it would be quite surprising for this other forms to predict altogether different patterns of responses than any of the three usually assumed in the literature. If the respondents actually use such a different model of discounting, then using one of the three standard models in the preference elicitation seems not recommended as it may distort the obtained health state utilities.

Third, perhaps depending on the specific task, different discounting models may be appropriate. That the discounting rate may depend on the task details (on the duration of the disease state specifically) was suggested in the literature [29]. The time preference changing with the task used may explain the observed differences in the literature: the high proportion of negative time preference in studies using direct method [13, 18, 19] or when lead-time and lag-time are used within respondents, hence, making the ordering focal [28], the negligible proportion of negative time preference when lead-time and lag-time are used between respondents [29], or the large aggregate positive time preference when DCE tasks are used [34, 35]. To explain the results obtained in the present paper, it would be required that not only the strength of the discounting varied with task but also the discounting model or perhaps even the direction of discounting. Qualitative studies involving think-aloud experiments could perhaps inform about the plausibility of this explanation (for instance, respondents may indicate that their answers are based on the ordering of subperiods). To see the impact of the ordering of states within non-constant profiles, it would be worth to replicate the present study with modified Q2 and Q3: i.e., adding lead-time in H and lag-time in .

Fourth, the results of the present study could be explained by respondents not using a QALY model, i.e., not based on a product of health-state utility and (possibly discounted) duration. For instance, assume that respondents compare the two offered alternatives based on their total value which is derived from two sources: HRQoL and longevity. Regarding the HRQoL part: if an alternative is a constant health state, then simply the value assigned to this state is used. However, for non-constant profiles, only the value of the health state specific to this alternative is used. For instance, if is compared with H, then the first alternative is evaluated using (which is specific to this alternative), while the second alternative is evaluated using health state H (which is a constant health state in this alternative). Regarding the longevity part, each alternative is evaluated using its relative longevity comparing to the other alternative. For instance, if lasts 10 years and H lasts 15 years, then the first alternative is evaluated at , and the second alternative is evaluated at . Finally, the two sources are added (possibly using weights) to form a single value. Eventually, the alternative with the greater value is picked. It is trivial to see that the above mechanism would produce the pattern of answers to TTOFUs resulting from the voting-based aggregation procedure. In Q1, halving the durations does not change the evaluation and would result in indifference. In Q2 and Q3, prolonging both alternatives by the same time (either adding lead-time in in Q2, or adding lag-time in H in Q3) would drive the duration ratio towards 1 and, which would increase the relative evaluation of the short-lasting alternative: of in Q2 and of in Q3. Crucially for this mechanism to work, HRQoL is not integrated over duration, but HRQoL and duration are considered separately and combined additively. This is somewhat similar to the duration-neglect phenomenon observed in medical contexts [36, 37]. Similar mechanisms were also considered in the health-preference research literature. For instance, in the predictive modelling competition reported in Jakubczyk et al. [17], the model with greatest prediction accuracy assumed that the value of each alternative is derived additively based on the HRQoL (irrespective of duration) and on longevity (logarithm of relative duration was used). In Jonker and Norman [38], the authors identified that a majority of respondents combines the information on HRQoL and longevity (however, non-discounted) in an additive way. The possibility that valuation tasks do not reflect QALY-type trade-offs is a hypothesis that merits future studies, both quantitative and qualitative.

Implications

There are two trivial conclusions from the present study. First, the respondents differ substantially in their behaviour. When the answers to each of TTOFUs were pooled within each respondent, many different patterns of responses were observed and the most prevalent pattern of responses was observed in only of respondents. This observation implies that when eliciting the time-preference for health states, it is important to use models that allow for respondent heterogeneity.

Second, the models of discounting that are typically used in the literature are not capable of explaining the behaviour even at the individual level. Whether this is because non-standard models would be needed (second explanation in the list above), or different tasks induce different discounting and perhaps ordering effects (third explanation), or because the QALY model does not describe the behaviour (fourth explanation) cannot be concluded based on the present study. Under the third explanation (task changing behaviour), some practical conclusions appear. For instance, when trying to remove the impact of discounting on the utility values elicited with one type of task, one should not use the discounting function estimated in a different task (say, use the direct method to correct the data collected with cTTO). Within cTTO itself, two types of task are used: one for better-than-dead and one for WTD states. The difference between them may result in different discounting behaviour. Hence, perhaps two discounting models should be used when modelling cTTO data. Another conclusion is that it is conceptually misleading to make inferences about discounting using only one type of task (e.g., just scaling the durations of both alternatives but not using lead-time or lag-time).

The fourth explanation (non-QALY model being used) obviously undermines the foundations of valuation studies. However, even if the QALY model is misspecified, it may still be treated as a convenient approximation of the true model for the following reasons related to how it is used in CUA. Because of its simplicity it may be seen as transparent in decision making. Additionally, because of how it is linking HRQoL and longevity, it may be seen as producing intuitive results: it is the absolute (and not relative) number of additional years of life that count; and there is benefit in reducing the time spent in the worsened health, even if not avoiding the worsened health entirely and not increasing the overall duration (while such an improvement would not be favoured by the non-QALY model presented above). If the QALY model is treated as a useful approximation of some true non-QALY model, then the utility values elicited under the QALY model also reflect the difference between both models. Including the discounting in this elicitation process, if the discounting is truly not part of the true preference model, may distort the utility values. In other words, what is taken as the effect of discounting on utility values (which we want to remove) may actually by the effect of the differences between the true non-QALY model and the QALY approximation (which should not be removed). As mentioned above, the replication of the present study possibly with other types of tasks and the qualitative studies could help to resolve which explanation of the findings is most plausible.

Limitations

Clichéd but true, the present study has several limitations, and some of them were already hinted above. Additionally, only a relatively small sample was used and the sample is not representative of any specific general population. While the representativeness seems not to be a crucial limitation in view of the methodological and exploratory character of the study, the sample size remains a limitation. As this study introduces a novel approach to measuring time preference, there were no hypotheses formulated, and there was no formal sample size calculation.

The limited size of the sample relates not only to the number of respondents but also to the limited number of health states and the fact that only states that were sufficiently better than dead were used to ask TTOFUs. As shown in Table 4, only a small proportion of respondents answered Q1–Q3 for 5 or 6 states, which limits the possibility of analysing the consistency of answers. It also merits mentioning that there was no randomization of the order in which Q1–Q3 were asked. In consequence, it is impossible to determine if there is any ordering effect.

As TTO is an expensive elicitation method as it requires interviews (rather than unsupervised surveys), it could be worth to conduct a similar study using DCE. Using DCE seems feasible, as only ordinal information is needed in TTOFUs to conclude about the form and direction of discounting. In the present study, because of the limited amount of data per respondent and of the limited consistency, it was impossible to estimate the parameters of the individual level discounting functions. Hence, the cardinality of TTO answers was not used in this paper.

I have to acknowledge that perhaps the complex behaviour of the respondents was provoked by non-trivial tasks used in the experiment, i.e., the non-constant health profiles used as alternatives. If this is the case, then the practical importance of the findings is somewhat reduced, as it does not relate to tasks that only use constant health profiles (for instance, DCE with duration).

Finally, it deserves to be emphasized that the results of the present study do not imply that respondents do not discount in TTO tasks. Rather, it seems that the discounting is more complicated than the standard models assume or that other phenomena than discounting also impact the responses.

Conclusions

The responses to the TTO tasks used in this study do not comply with the standard QALY model, i.e., the one with linear time preference. However, they also cannot be explained by the usual forms of discounting: exponential, power, or hyperbolic. In consequence, it is not entirely clear what range of phenomena is actually being captured by including the discounting in the modelling of the TTO data. In consequence, perhaps while attempting to remove the effect of time preference and to de-distort the utilities, some other form of distortion is introduced. Further studies are needed, both qualitative ones and quantitative ones using a variety of task types, to understand the respondents’ behaviour.

Supplementary Information

Below is the link to the electronic supplementary material.

Funding

The author reports receiving grants from the EuroQol Research Foundation for the present study and outside the submitted work. The author is a member of the EuroQol Group.

Availability of Data and Materials

The data used in this study are available upon reasonable request.

Declarations

Conflicts of Interest

Michał Jakubczyk reports receiving grants from the EuroQol Research Foundation for the present study and outside the submitted work. Michał Jakubczyk is a member of the EuroQol Group.

Ethical Approval

The ethical approval for the present study was obtained at the SGH Warsaw School of Economics, Poland.