The TTO method and procedural invariance

HEALTH ECONOMICS

Health Econ. 12: 655–668 (2003)

Published online 3 December 2002 in Wiley InterScience (www.interscience.wiley.com). DOI:10.1002/hec.768

OUTCOME VALUATION

TheTTOmethod and procedural invarianceAnne Spencer*Department of Economics, Queen Mary, University of London, UK

Summary

In a pilot study we investigate whether the inferences we draw about people’s preferences towards health caretreatments are altered if we vary the procedure that is used to elicit these preferences. In a conventional time trade-off (TTO) question, respondents express their preferences towards treatment by comparing a period of ill-health witha shorter period in a higher quality of life. In our less conventional TTO question, we vary the procedure by askingrespondents their preferences towards treatment by comparing a period of ill-health with a longer period in a lowerquality of life. The quantitative data are equivocal about whether preferences for treatment differ between theconventional and unconventional questions. The qualitative data support the notion of contrasting issues in thequestions that involve prolonging time in a lower quality of life and appear to account for a failure to findquantitative differences in all of the questions. Copyright # 2002 John Wiley & Sons, Ltd.

JEL classification: 131

Keywords time trade-off; procedural invariance

Introduction

In health economics, survey methods have beendeveloped over the last thirty years to elicitpeople’s preferences for undergoing differenthealth care treatments. One of these methods isthe time trade-off (TTO) method [1]. The TTOmethod applies the principle of opportunity cost todifferent types of treatment by asking respondentsto consider a trade-off between time and quality oflife. In the conventional TTO method, respondentsexpress their preferences towards treatment bycomparing a period of ill-health with a shorterperiod in a higher quality of life.

The assumptions required for the TTO methodto be a valid measure of preferences underexpected utility theory, a theory of decisionmaking under risk, are outlined by Pliskin et al.

[2,3]. This set of assumptions allows for a unifiedconcept of utility to represent preferences in bothriskless and risky health care decisions [4,5]. A keyfeature of this utility is that procedural invarianceholds and that preferences will be equivalent if themethod used to elicit them is changed slightly, forinstance, to one of prolonging life in a lowerquality of life [6].

Concern over whether procedural invarianceholds in practice has already been expressed forpreference elicitation methods that involve a trade-off between quality or longevity of life on the onehand and either risk or money on the other [7]. Inthe standard gamble (SG) method that involvesrisk, it has been shown that procedural invariancesystematically breaks down if the question is askedin terms of a treatment’s risk or longevity of life[8]. In the contingent valuation (CV) method thatinvolves money, the difference between asking the

Copyright # 2002 John Wiley & Sons, Ltd.Received 3 July 2001

Accepted 23 July 2002

*Correspondence to: Department of Economics, Queen Mary, University of London, Mile End Road, London, E1 4NS. UK.E-mail: [email protected]

question in terms of a person’s willingness-to-payor willingness-to-accept money is well documented[9,10]. In the SG and CV methods this has led tothe development and application of alternatives toexpected utility theory to explain the systematicfailures of procedural invariance. We add to thisdebate by exploring whether procedural invarianceholds in the TTO method.

The aim of this paper is to test the equivalenceof preferences elicited under the TTO method. Asecondary aim of the paper is to consider the issuesthat respondents may be using to make theirdecisions. We ask a conventional TTO questionand a less conventional TTO question. In our lessconventional TTO question, respondents expressthese preferences by comparing a period of ill-health with a longer period in a lower quality oflife. Procedural invariance states that if errors aresmall, preferences elicited from TTO questionsthat offer a longer period in a lower quality of lifeshould be equivalent to preferences elicited fromTTO questions that offer a shorter period in ahigher quality of life. This is interesting for tworeasons. Firstly, the possibility of prolonging timein a lower quality of life already occurs in thetreatment for certain cancers. Jansen et al. [11] areinterested in using such questions in applied workbut as far as we are aware such questions have notbeen used. Secondly, if this method elicits quitedifferent preferences, it raises concerns over theassumptions typically made in the conventionalTTO method.

The paper uses a combined qualitative andquantitative approach to reveal the issues con-sidered by respondents in their answers. Thereappears to be renewed interest in linking qualita-tive and quantitative approaches in the field ofvalue elicitation to help understand the issuesdriving respondents’ answers. However, there havebeen relatively few joint qualitative and quantita-tive studies of value elicitation procedures [12–15].A qualitative and quantitative approach is parti-cularly applicable in this paper given the pilotnature of this work.

Throughout, conventional values refer to valuesimplied by the conventional TTO question andunconventional values, refer to values implied byour question. The remainder of the paper is set outas follows. The Methods section overviews thequestionnaire used in our paper and our test. InTheoretical predictions, we consider other recentexplanations that have been offered to explaindifferences in the TTO values. Data collection and

analysis describes the qualitative and quantitativedata and Results overviews our findings. Finally,Discussion considers the implications of our testfor the TTO method.

Methods

The questionnaire

The study used the EuroQol classification system,which describes states of health along five dimen-sions: mobility, self-care, usual activities, pain andanxiety. Each dimension had three levels ofseverity: no problems, some problems and severeproblems, denoted by 1, 2 and 3, respectively, andcolour-coded black, blue and red in the study.Level 3 pain was described as moderate pain ordiscomfort with periods of severe pain or dis-comfort rather than extreme pain or discomfortused in the EuroQol work. The description of level3 pain was changed to ensure that worse thandeath states were not included in the study.Respondents were asked to tick one statementfrom each dimension that best described theircurrent state of health. This helped to familiariserespondents with the EuroQol dimensions. Re-spondents were then presented with six cards: fiveEuroQol states (11111, 12221, 21211, 21222 and22232) and immediate death [16,17]. Each statewas colour-coded: 11111 was given the colourwhite, 12221 the colour grey, 21211 the colouryellow, 21222 the colour green, 22232 the colourpink and death the colour black (following theexample of Carthy et al. [18]). These are referred tohere by letters: 11111 is referred to as N, 12221 asW , 21211 as X , 21222 as Y , 22232 as Z and deathas D. The state 12221 was used in a practicequestion to allow respondents to become familiarwith the methods but the actual values were notused in the study.

The respondents were asked to imagine thateach state lasted for ten years without change, tobe followed immediately by death. They wereasked to rank the cards from the best state to theworst and then to place the cards on a visualanalogue scale, putting the best state at 100 andthe worst state at 0. This was followed by twelveTTO questions, then seven SG questions. Theresearch question posed in this paper involves theTTO questions only and the SG questions arereported elsewhere [19]. To elicit the preferences

Copyright # 2002 John Wiley & Sons, Ltd. Health Econ. 12: 655–668 (2003)

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we used the TTO boards and interview protocoldeveloped by the measurement and valuation ofhealth (MVH) study [14]. These boards andinterview protocols were modified slightly toinclude the colours depicting each health stateand to allow for the new types of TTO questionspresented here. The respondents were asked fourconventional TTO questions that valued healthstates against normal health and death (questions1 to 4). They were then asked eight more TTOquestions. We concentrate here on the two TTOquestions that involved prolonging time in a lowerquality of life (questions 9 to 10). The remainder ofthe TTO questions tested whether the TTO valuewould be affected by comparing the health stateagainst normal health and a more-severe state (butnot death) and are reported elsewhere [19].

TTO questions

The conventional TTO questions are illustratedusing question 4 in Figure 1. A respondent wasasked to imagine living in health state Z for tenyears or undergoing a combination of t4 years innormal health (N) but dying (D) 10� t4, yearsearlier (where the subscript on the time, t, indicatesthe question number). In effect, they were asked toconsider a shorter period in a higher quality of life.

The time in normal health t4 was varied until therespondent was indifferent between the two alter-natives. At this point the two alternatives shouldbe equivalent. The majority of applied work usingthe TTO method then assumes that respondentsdo not have preferences towards the timing of ill-health (or a zero rate of time preference) [5]. It istherefore possible to express this equivalence bythe following equality where V ð:Þ represents theTTO value assigned to the health state:

10� V ðZÞ ¼ t4 � V ðNÞ þ ð10� t4Þ � V ðDÞ ð1Þ

If the value for V ðNÞ ¼ 1 and V ðDÞ ¼ 0 thisexpression can be rearranged to give

V ðZÞ ¼ t4=10 ð2Þ

Question 4 is summarised in row 4 of Table 1,where ten years in health state Z (column 1) iscompared against normal health and death (col-umn 2), and is used to derive a conventional valuefor Z (column 3).

We considered two different types of unconven-tional question for this study. The first typeinvolved asking a respondent to imagine living innormal health for t4 years or undergoing atreatment that involved prolonging time in healthstate Z. Procedural invariance holds if the valuederived from this unconventional question equal-led the value derived from the conventionalquestion in question 4. Early piloting of thequestionnaire suggested that respondents foundthis type of unconventional question unrealistic.Respondents argued that if they were in normalhealth, they would not want to consider analternative that offered a lower quality of life.Hence, it was very hard to get respondents toengage in the notion of a trade-off of time, anessential feature of the TTO method. The secondtype of unconventional question that was used inour study overcame this problem by asking arespondent to imagine living in health state X orY , rather than normal health.

The two unconventional TTO questions used inour study are questions 9 and 10. In thesequestions, respondents were asked to imagineliving in a given health state for two years followedby death, or prolonging life in a lower quality oflife. The time in the initial health state was set attwo years, since it was anticipated that theresponses to these questions would lie within theten year period based on conventional TTOquestions. Setting time at two years required usto impose an additional assumption, commonlyapplied to the TTO method, that utility is linear induration. If utility is linear, the value of a healthstate is not affected by the duration in that healthstate [5]. Together with procedural invariance, thisassumption suggests that if errors are small,the conventional value equals the unconven-tional value. Questions 9 and 10 are illustratedin Figure 2.

For example, in question 9, the question beginsby comparing two years in health state Y and twoyears in health state Z and respondents are askedwhich they prefer. When the time is the same, all

Figure 1. An example of a conventional TTO question,

question 4

TheTTOMethod and Procedural Invariance 657


respondents prefer to spend time in the higherquality of life, Y . The time in the lower quality oflife, t9 is then increased until the respondent isindifferent between the two alternatives (thequestionnaire and protocol are available uponrequest from the author). At this point ofindifference between the two alternatives thefollowing equality holds, assuming that respon-dents have a zero rate of time preference:

2� V ðY Þ ¼ t9 � V ðZÞ ð3Þ

If V ðY Þ is say, V ðY Þ ¼ t3=10 (from question 3) thisleads to:

V ðZÞ ¼2� t3

10� t9ð4Þ

Question 9 is summarised in row 5 in Table 1,where two years in health state Y (column 1) iscompared against a longer period in Z (column 2),and is used to derive an unconventional value forZ (column 3). The null hypotheses to be tested inour paper is that the conventional value equals theunconventional value, and so in Table 1 theconventional V(Z)=unconventional V ðZÞ andconventional V(Y)=unconventional V ðY Þ.

Theoretical predictions

Recent research has suggested that a respondent’spreferences are influenced by issues that are nottypically reflected in the assumptions made in theTTO method. These issues are of interest to thestudy since they have the potential to createdifferences between the conventional and uncon-ventional TTO values. In this section, we reviewthe impact these issues have on the conventionaland unconventional values.

Table 2 summarises four issues that are pre-dicted to create differences between the conven-tional and unconventional TTO responses: (1)maximal endurable time, (2) strong preference forlongevity of life, (3) loss aversion and (4) timepreference. In the following discussion we outlinethe links between these four issues and theconventional and unconventional values. We findthat the first two issues would serve to increase theunconventional value whilst the last two wouldserve to decrease the unconventional value. Table 2summarises the extent to which these issues resultin an unconventional value that is: ‘+’ higherthan, ‘=’ equal to or ‘�’ lower than the conven-tional value. If the four issues in Table 2 cancel oneanother out in our study, then the conventionalvalue will equal the unconventional value.

A respondent may learn to cope and adapt toa new health state [20], termed positive adaptationby Ross and Simonson [21], or they may be-come increasingly disgruntled, termed negative

Table 1. Questions used to test procedural invariance

(1) (2) (3)Question Health state Comparison health states Abbreviation

1 10W N þD Conventional V ðW Þ2 10X N þD Conventional V ðX Þ3 10Y N þD Conventional V ðY Þ4 10Z N þD Conventional V ðZÞ9 2Y þ 8D Z þD Unconventional V ðZÞ10 2X þ 8D Y þD Unconventional VðY Þ

Figure 2. Questions 9 and 10

Table 2. Summary of predicted impacts

Predicted impacts

Maximal endurable time +Strong preference for longevity of life +Loss aversion �Time preference �

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adaptation. Dolan [22] speculated that healthymembers of the public dwell more on the negativeadaptation, whilst patients dwell more on thepositive adaptation. As respondents were recruitedfrom the general public and mature students it islikely, therefore, that negative adaptation will bemore pronounced in the present study. If thehealth state is particularly severe a respondent maydoubt their ability to cope with continuing ill-health, termed maximal endurable time by Suther-land et al. [23]. Sutherland et al. suggested thatconcerns over endurance might be particularlyimportant if the health state is followed by deathrather than normal health. Question 9 involvedprolonging time in a more severe state Z, whilstquestion 10 involved prolonging time in a lesssevere state Y . We would, therefore, expect themaximal endurance to arise more in question 9than question 10. To illustrate the impact this hasupon the conventional and unconventional values,consider the conventional and unconventionalvalues in questions 4 and 9, respectively. Let te4and te9 denote the responses unaffected by theissues in Table 2 and tme

9 and tme9 denote the

responses under maximal endurance. For theunconventional value, a respondent’s fear thatthey cannot endure a severe health state maydiscourage them from increasing time in the worsestate and then tme

9 5te9 and the unconventionalvalue will increase. However for the conventionalvalue, the same respondent’s concern for the severehealth state will encourage them to sacrifice moretime to return to normal health and then tme

4 5te4,and the conventional value will decrease. Overallthen, maximal endurable time leads to an un-conventional value that is higher than the conven-tional value.

Anomalies between the conventional and un-conventional values may arise if respondents givestrong weight to quality or longevity of life. Arespondent’s concerns over the quality or long-evity of life can become more important if thetreatment is assessed against a scale that includesquality or longevity of life, termed scale compat-ibility [24]. Bleichrodt [25] used scale compatibilityto argue that respondents may give strong weightto the longevity of life in the TTO method, sincethe method varies time to elicit preferences. Forinstance, in questions that involve prolonging life,they may seek to increase the longevity of life evenif this puts them in a more severe health state.They would, therefore, be willing to take anytreatment which offered a marginal increase in

time. Let tl4 and tl9 denote the responses under scalecompatibility in questions 4 and 9, respectively. Ifa respondent prefers any treatment which extendslife then tl95te9. However, the same respondentmay be unwilling to give up time in the elicitationof the conventional value, tl44te4. The conventionaland unconventional values in this case, therefore,will both increase. It is likely that this effect will begreater for the unconventional value, given thatthe unconventional value has two instances wheretime has been set by a respondent (in Equation (4),t3 and t9) and so this could amplify the scalecompatibility effect. A strong preference for thelongevity of life can be linked to the Robinson et al.[15] idea that there exists a threshold of tolerancebelow which health must decline before a respon-dent considers sacrificing time. If a respondent isunwilling to sacrifice time, the conventional andunconventional values both equal 1. Overall then,a strong preference towards the longevity of life,arising from scale compatibility or a threshold oftolerance, leads to an unconventional value that isequal to or higher than the conventional value.

Bleichrodt [25] and Spencer [19,26] consider theimpact on the conventional TTO value if arespondent evaluates the question as gains andlosses relative to a reference point. Central to theseexplanations is the assumption that a respondent ismore sensitive to losses than to gains, termed lossaversion [27]. In addition, both Bleichrodt andSpencer assume that the reference point is theinitial health state that is considered in eachquestion. In the conventional value derived inquestion 4, the reference point is Z, and in theunconventional value derived in 9, is Y . Let tloss4and tloss9 denote the responses under loss aversionin questions 4 and 9, respectively. In the conven-tional value, the gains in health status are valuedless than the loss in longevity of life and so arespondent compensates by demanding a longertime in normal health, tloss4 > te4. The conventionalvalue will increase. Whilst in the unconventionalvalue, the loss in health state is valued more thanthe gain in health, and so they demand a longertime in Z to compensate, tloss9 > te9, and theunconventional value will decrease. As a result ofthese two issues, the unconventional value is lowerthan the conventional value.

Finally, the TTO responses may be affected by arespondent’s attitude towards time. Like themajority of TTO applications, the present studyassumes that a respondent does not have prefer-ences towards the timing of ill-health [5]. It is as



though a respondent gives equal weight to all timeperiods. If a respondent instead prefers to con-sume health in the short-term rather than in thelong-term they will assign a higher weight to theshort-term. A value that correctly adjusts for arespondent’s time preference hereafter is termed adiscounted value. The paper by Dolan and Jones-Lee [28] can be used to show that the unconven-tional value is lower than the conventional value,given that the unconventional value includes twoinstances where the values underestimate theimpact of discounting (see appendix).

In the conventional TTO value, Bleichrodt [25]noted that the assumption that there is nopreference towards the timing of ill-health mightcancel out the impacts of scale compatibility andloss aversion. Maximal endurable time also has thesame ability to cancel out the impacts of scalecompatibility and loss aversion in the conventionalTTO value. This issue is predicted to gainimportance in our study for questions that involvesevere states or cases where there is prolongedexposure to ill-health.

Data collection and analysis

Respondents were recruited from members of thegeneral public and from mature students begin-ning a course in the Department of HealthSciences at the University of York. Respondentswere invited to take part in a 90-min interview inthe Department of Economics at York Universityfor a payment of £15. All interviews were tape-recorded. In total, 30 respondents were inter-viewed, 12 males and 18 females (see Table 3).

In the quantitative data, the Wilcoxon signedranks test was used [29]. The test calculates theextent to which the conventional and unconven-tional values differ for each respondent. It thenranks the absolute value of these differences for allrespondents (i.e. considering only the size and notdirection of difference) from smallest to largest andcalculates the sum of the ranks for all positivedifferences and all negative differences. The nullhypothesis is that the median of these differences iszero and that the conventional and unconven-tional values are the same. The alternativehypothesis is that there is a systematic differencebetween the responses. If the alternative hypoth-esis was to hold, there would be a clustering of thepositive and negative differences in the ranking.

In the qualitative data the respondent wasencouraged to think aloud using a verbal protocolanalysis approach developed by Ericsson andSimons [30].

Early piloting of the questionnaire suggestedthat the questions might not have been well suitedto such concurrent data collection. In particular,the questions were broken down into a number ofrepetitive stages before the final answer wasreached and the natural reaction of respondentswas to give a conventional answer withoutelaboration.

To overcome the problem, it was felt necessaryto ask respondents an additional question at theend of the task:

What types of things were you thinking about whenyou answered this question?

We avoided ‘why’ questions because Patton [31]argues these can be answered on many differentlevels. Patton classifies four broad types of probes:detail orientated, elaboration, clarification andcontrast probes. The study used elaborationprobes, which encourage the respondent to con-tinue talking using body language by a gentlenodding of the head or verbal ‘uh-huh’ as well asquestions which asked a respondent to say a littlemore about a particular issue. The study also madeuse of clarification probes to check that theinterviewer had understood the respondent [31].The interviewer verbalised a respondent’s non-verbal cues, such as eye or hand movements whichwere used to emphasise a point. The interviewswere transcribed and analysed using the softwarepackage HyperResearch# that aids the manage-ment and analysis of non-numerical data. Thisanalysis began by summarising excerpts using therespondents own terminology and key phrases.These were categorised as specific codes. This wasfollowed by an attempt to link the specific codes toform general codes which help to characteriseparticular themes. Finally, themes that seemed tocontradict the TTO assumptions were identified.The qualitative analysis seemed best applied to

Table 3. The sample

(1) (2) (3)21–39 40–59 Total

Male 9 3 12Female 8 10 18Total 17 13 30

A. Spencer660


hypothesis generation rather than hypothesistesting as it challenged existing concepts andhelped to understand the material more fully. Atthe beginning of the analysis, there was no pre-defined coding schedule but only a series ofquestions that the researcher intended to address.In the process of transcribing a coding system wasdeveloped. Specific codes recorded the questionnumber and any additional interview probes.Some respondents wanted to engage in debatewith the interviewer and it was felt necessary tochallenge a respondent’s answer if they were notinterating towards their point of indifference. Thisoccurred particularly in the TTO question thatinvolved prolonging time in the lower quality oflife as some respondents began to answer thequestion by stating their maximum endurance inthat state, or suggested the point at which onetreatment would be strictly preferred.

Results

Quantitative results

The median conventional values for health statesX , Y and Z are 0.9, 0.65 and 0.45 (see Table 4) andthe Wilcoxon signed ranks test showed thatrespondents found the states statistically different(P ¼ 0:0002 or less). We can compare the conven-tional TTO values derived here against thoseestimated from a larger study to check the extentto which our results are consistent with earlierstudies. The MVH study asked 3395 members ofthe general public to value a subset of EuroQolstates using the TTO method and this subset ofstates were used to infer the values for the fullrange of EuroQol states [30]. For health states X ,

Y and Z the estimated mean values in the MVHstudy were 0.81, 0.62 and �0.02 and the estimatedmedian values were 0.94, 0.65 and 0.028. Thesevalues are very similar to those derived in thisstudy and that are shown in Table 4 except forHealth state Z. Health state Z is valued higher inthe present study since level 3 pain was describedas moderate pain or discomfort with periods ofsevere pain or discomfort rather than extreme painor discomfort used in the EuroQol work. Forequivalent health state descriptions, therefore, theconventional TTO method used in our study isconsistent with earlier TTO studies.

The median unconventional value for healthstate Z is 0.4 and for health state Y is 0.425 (seeTable 4). The Wilcoxon signed ranks test showedthe unconventional values for Y were significantlylower than the conventional values (in question 10)whilst the differences between the unconventionaland conventional values for Z were not statisti-cally different, and responses were evenly spreadbetween higher and lower unconventional values(in question 9, column 1 rows 1 and 2 in Table 5).In summary, the quantitative results were mixed:the unconventional values for Y were significantlylower in question 10 than conventional values, butthe unconventional values for Z in question 9 werenot statistically different to the conventionalvalues. The null hypotheses, that the conventionalvalues equal the unconventional values, are there-fore rejected in only one of the two tests.

Qualitative results

In the qualitative analysis responses appeared tofall into five themes listed in Table 6 for questions9 and 10, respectively. The first column of Table 6

Table 4. The summary statistics

(1) (2) (3) (4) (5)Question Abbreviation na Mean Median Standard deviation

1 Conventional V ðW Þ 30 0.802 0.950 0.2482 Conventional V ðX Þ 30 0.856 0.900 0.1633 Conventional V ðY Þ 29 0.635 0.650 0.2174 Conventional V ðZÞ 28 0.457 0.450 0.2079 Unconventional VðZÞ 28 0.479 0.400 0.22810 Unconventional V ðY Þ 29 0.502 0.425 0.257

aRespondents were excluded from the analysis it they felt that the health states were worse than death. Two respondents felt thathealth state Z was worse than death and one respondent felt that health state Y was worse than death.



refers to the number of respondents in questions 9and 10 who were willing to trade quality of life(based on specific codes Q9 trade-off and Q10trade-off). For example, in question 9 that askedrespondents to consider prolonging time in themore severe health state (health state Z), 13 of the28 respondents expressed a willingness to tradequality for longevity of life. This willingness totrade rose to 21 respondents in question 10 thatconsidered prolonging time in the more moderatehealth state (health state Y ). An example of thiskind of response is as follows:

Respondent: For several reasons, in pink (Z) you arein a greater degree of ill-health so you’re not able todo the things as you would be able to do if you werein a lesser degree of ill-health, i.e. in green (Y). Sotherefore, you may need that small duration of timeto achieve the same things as you would be able toachieve in a lesser state of ill-health, i.e. being ingreen (Y). Are you with me? What you can actuallydo here, you may be able to do in a lesser time thanyou could do there. [Interview 22, Q9 trade-off.]

The main reasons for their willingness to tradequality of life for longevity of life related to theimpression that two years was too short (specificcodes: Q9 time is short, Q10 time is short, Q9 thator death, Q9 yes alive, Q10 want extra life, Q10 stillalive) and that they would need more time toachieve the same life goals (specific codes: Q9something to achieve, Q10 a bit more). Respondentsthat were willing to trade accounted for themajority of the cases where the unconventional

values for a health state were lower than theconventional values.

Of those respondents who were willing totrade quality of life for longevity of life,some respondents felt that they would need moretime in Z to compensate (specific codes: Q9increase by a lot, Q9 need longer Z). This supportsthe notion that respondents sought longer periodsof time to compensate for the reduction in thequality of life and is consistent with loss aversion.In addition, they felt that they might accommo-date to the health state (specific code: Q10accommodate) or could cope with the state (specificcode: Q10 cope) which is consistent with positiveadaptation to the health state. Other respondentsfelt that they wanted longer to live but disliked themore severe health state Z (specific codes: Q9 tryhold on, Q9 only just cope, Q9 hang on, Q9 knockdeaths door, Q10 adding poor quality, Q10 notstand depression, Q10 plod, Q10 max endurance Y ).One respondent in question 9 and 10 demandedmore time in the lower quality of life, but it is notclear that this was perceived as a form ofcompensation and so this is reported separatelyin column 5, Table 6.

The second most popular response related toan unwillingness to prolong time in a lower qualityof life (based on specific codes: Q9 not prolongand Q10 not prolong). In the case of ques-tions that involved prolonging time in the moresevere health state Z, 11 of the 28 respondentswere unwilling to prolong time in Z (column 2,Table 6). An example of the unwillingness

Table 5. The Wilcoxon signed ranks test

(1) (2)Question 9 Question 10unconventional V ðZÞversus conventional V ðZÞ

unconventional V ðY Þ versusconventional V ðY Þ

No. of cases where unconventional value5conventional value

14 20

No. of cases where unconventional value>conventional value

13 7

No. of cases where unconventional value=conventional value

1 2

Total 28 29

Wilcoxon Z �0.745 �2.4992-tailed P 0.456 0.010

Accept Reject

A. Spencer662


Table

6.Theconventionalandunconventionalvalues

forhealthstates

(1)

(2)

(3)

(4)

(5)

Loss

aversion:

Maxim

alendurable

time:

Strongpreference

forlongevity

oflife:

Willingto

trade-offquality

forlongevity

oflife

Unwillingto

prolongtimein

alower

quality

oflife

and

Increase

longevityoflife

irrespectiveofquality

oflife

Health

statesperceived

tobe

thesame

Dem

anding

more

timein

lower

quality

oflife

Question9

Unconventional5

conventional

13

00

n/a

1Unconventional>

conventional

010

3n/a

0Unconventional=

conventional

01

0n/a

0n¼

28

13

11

3n/a

1

Question10

Unconventional5

conventional

20

00

00

Unconventional>

conventional

13

11

1Unconventional=

conventional

00

20

0n¼

29

21

33

11

n/a=notapplicable.



to prolong in a lower quality in Z is given asfollows:

Respondent: I wouldn’t really want it, it’s a . . .because its only two years anyway, but my sort ofpersonal feeling looking at it right now is, that’s itwould be two years in pink (Z) or 20 years in pink (Z)there’s not a great deal that’s going to be accom-plished, if I’m able to I’ll see the kids grow up andthat, so a definite choice that I would want to live,but I think that my own state of mind that I would gocrazy in the end, so I’ll stick with choice B. [Interview12, Q9 not prolong.]

The main reasons for respondents’ unwillingnessto prolong time in a lower quality of life centredaround the impression that this state represented avery severe state of health (specific codes: Q9absolute writhing, Q9 go crazy, Q9 suffer, Q9 seenpeople suffer, Q10 two major categories, Q10 cantake so much, Q10 prolong pain). However, allthese respondents had considered health state Z tobe better than death in the conventional TTOquestions. Some respondents saw immediate deathas an option to a lingering death in a lower qualityof life (specific codes: Q9 believe in euthanasia andQ9 go quickly) whilst others just stated that theywould receive no benefit from increasing time in alower quality of life (specific codes: Q9 no pointand Q9 not worth living). These explanations areconsistent with maximal endurable time.

There was an indication that more of therespondents would have been unwilling to prolongthe time in the lower quality of life if thealternative with which they were initially presentedwas for longer than two years (two respondents,specific codes: Q9 time is short and Q10 time isshort). An example of this kind of response is asfollows:

Respondent: Two years isn’t long, but I’m not toobad am I, I don’t know because it’s a hardcomparison to make because I don’t want to be inpink (Z) at all, so the thought of being in pink (Z) forany length of time, fills me with dread but thethought of being in green (Y ) for two years is equallyas bad because it’s only two years, so the instinct is tofavour pink (Z) because it’s for longer. . .. [Interview14, Q9 time is short.]

Some respondents were willing to increase thelongevity of life irrespective of quality of life(based on specific codes: Q9 prolong because likelife and Q10 prolong because like life). In the caseof questions that involved prolonging time inhealth state Z, three of the 28 respondents were

willing to prolong time irrespective of the qualityof life (column 3, Table 6). An example of this kindof response is as follows:

Respondent: No, I would always go for choice A,length of life rather than quality of life. [Interview 8,Q9 prolong life because like life.]

The main reasons for increasing longevity of lifeirrespective of quality of life seemed to relate to thedesire for longer lives (Q10 time is short, but canenvisage this). It is possible that scale compatiblityencouraged these responses to give more weight tothe longevity of life than quality of life. In question9, this led to an unconventional value that washigher than the conventional value. There is alsoevidence of a threshold of tolerance, below which ahealth state had to fall before they were willing tosacrifice longevity of life. Two respondents wereunwilling to trade longevity for improvements inquality of life for health states X and Y and theconventional and unconventional values equalled lfor these states.

These two types of responses, an unwillingnessto prolong time in a lower quality of life (linked tomaximal endurable time) and a willingness toincrease longevity irrespective of quality of life,account for the majority of cases where theunconventional values were higher than the con-ventional values. For example, in question 9, 10 ofthe 11 respondents who were unwilling to prolongtime in the lower quality of life gave an unconven-tional value that was higher than the conventional.This effect is greater for health state Z in question9 than health state Y in question 10 and is likely toaccount for our failure to find statistical differencesbetween the conventional and unconventionalvalues for Z. Finally, in question 10, one of therespondents felt that the two states were verysimilar (column 4, Table 6).

Discussion

In this section, we consider the issues raised by thequalitative results, and the extent to which theyexplain the quantitative results. We also outlinethe weakness of our test design and suggest wherefurther research is needed. Finally we look at theimplications that this study has the for the TTOmethod.

We are unable to conclusively reject proceduralinvariance, with only one of the two tests detectinga statistical difference. The qualitative data help to

A. Spencer664


shed light on the issues that people consider intheir responses and suggest three main issues canaccount for the quantitative results.

* Firstly, a willingness to trade-off quality forlongevity of life led to an unconventional valuethat was lower than the conventional value. Thedriving force for such responses appeared to berelated to loss aversion, where respondentsdemanded a larger increase in the time spentin the more severe state to compensate for thedecrease in the quality of life. It is also possiblethat people’s preferences for the timing of ill-health led to an unconventional value that waslower than the conventional. We are unable totest for these effects separately here but in alater section of the discussion we argue thatdiscounting is unlikely to be the main drivingforce in this study.

* Secondly, an unwillingness to prolong time in alower quality of life led to an unconventionalvalue that was higher than the conventionalvalue. The main driving force for such re-sponses appeared to be related to maximalendurance and was stronger when respondentswere asked to prolong time in the more severestate Z. More than a third of the sample wereunwilling to prolong time in a more severehealth state Z in question 9 compared to only atenth for prolonging time in health state Y inquestion 10. The concern over the severity of Z,therefore, appears to have undermined ourability to detect statistically significant differ-ences in one of the two tests. Hence, thequantitative results found lower unconventionalvalues in only one of the two tests considered.

* Thirdly, a willingness to increase longevity oflife irrespective of quality of life led to anunconventional value that was equal to orhigher than the conventional value. The maindriving force for such responses appeared to berelated to scale compatibility and threshold oftolerance.

There are two reasons to question whether timepreferences alone are able to explain our findings.Firstly, Dolan and Jones-Lee [28] show that thedistortions related to time preferences are largerfor health states that are valued around 0.5. Thehealth states that are involved in question 9 are

valued closer to 0.5 than those in question 10, andso we would anticipate more of an impact in theformer than the latter questions. The contraryresult is found in our study. It is of course possiblethat in question 9 the concerns over the maximalendurance undermined the impact of time prefer-ences. Secondly, there is a general conclusion thatalthough summary measures suggest people haveno preference over the timing of ill-health, there islarger variation in preferences between people[33,34]. It is therefore, quite possible that incor-porating people’s preferences towards time willlead to both higher and lower unconventionalvalues compared to the conventional values, andso may fail to explain our findings. Nevertheless, itis an important variable to consider in futurestudies to determine whether time preferences leadto differences between the conventional andunconventional values.

The study also allows us to consider the extentto which the different issues cancel one anotherout. Both a strong preference for longevity oflife and maximal endurable time have thepotential to cancel out the impact of loss aversion.However, maximal endurable time appears to playa greater role in the one test that resultedin equivalent conventional and unconventionalvalues.

A design weakness of the test is that arespondent’s willingness to trade quality andlongevity of life may have been affected by theshort duration of the states in the TTO questionsinvolving two years followed by death. Short timeperiods have been shown to affect people’s will-ingness to trade in conventional TTO questions.McNeil [35] found that, for states lasting underfive years, patients with laryngeal cancer wereunwilling to trade longevity for quality of life.However, unlike the questions here, the conven-tional TTO questions used by McNeil involved areduction in the longevity of life. The qualitativedata allow us to reflect upon whether the shortduration affected those questions that increaselongevity. Some respondents explicitly stated thatthey would be more unwilling to prolong the timein the lower quality of life if the alternativetreatment was for longer than two years. Thisunwillingness to trade is likely to be related toconcerns over the maximal endurable time and sothis issue could begin to dominate in longer timespans, leading to an unconventional value thatis higher than the conventional value. We recom-mend further work to replicate the questions



for different time periods and health states, to seethe extent to which concerns over maximalendurable time cancel out concerns over lossaversion.

What are the implications of this study forthe TTO method? Firstly, the study brings intoquestion the assumptions that are typically made.To improve the method’s descriptive ability,we recommend that it is expanded to incorporaterespondents’ loss of quality of life and concernover maximal endurance or longevity of life.For example, the TTO method could applynon-expected utility theories that model the impactof loss aversion. In addition, the impact ofmaximal endurable time and preference for long-evity of life could be considered in the interpreta-tion of results. Secondly, the study raises concernsover how best to aggregate individual responses.The equivocal quantitative results appear to maska variety of individual responses associated withloss aversion, maximal endurable time and astrong preference for longevity of life. The factthat these issues can cancel out at an aggregatelevel suggests that, in some instances, the summarystatistics may fail to closely approximate indivi-dual values [5]. There is a trend towards subgroupanalyses of preferences within populations [36]. Ifpolicy makers want to reflect more broadly thepreferences of individual members, future workshould consider more carefully the implications ofsubgroup analyses and how these views should beaggregated.

Acknowledgements

The author would like to thank Graham Loomes, KarlClaxton, Judith Covey, Nick Pidgeon, Bjorn Lindgren,Carl Hampus Lyttkens and two referees for theirvaluable comments. In addition, the author is gratefulto the Swedish Medical Research Council and theSwedish Social Research Council for funding a visitingresearch fellowship to pilot the approach, via researchgrants to Bjorn Lindgren, Lund University. The authoris also grateful to the ESRC award R00023 4987 forfinancial support for the UK study. Any errors are theresponsibility of the author alone.

Appendix A

Dolan and Jones-Lee [28] showed that theconventional value is lower than the discountedvalue. We use their approach to compare how the

conventional and unconventional values are af-fected by discounting.

Question 9 compares 2 years in Y and death ort9 years in Z and death. Question 9 thereforecompares 2 years in Y and dying (t9 � 2) yearsearlier or t9 years in health state Z. Let arespondent’s rate of time preference be representedby a discount weight, r, and let 05r51. Thediscounted value for Z is then calculated fromquestion 9 by equation (1).

X1

0

rt � V ðY Þ ¼Xt9�1

0

rt � V ðZÞ ðA1Þ

where t952. The geometric progression formula isgiven as

Xn�1

0

a� rt ¼a� ð1� rnÞ

1� r

using this in Equation (A1) gives:

1� r2

1� r� V ðY Þ ¼

1� rt9

1� r� V ðZÞ

Rearranging it follows that the discounted valuefor Z is:

V ðZÞ ¼1� r2

1� rt9� V ðY Þ ðA2Þ

The unconventional value for Z assumes nodiscounting and is given as

V ðZÞ ¼2

t9� V ðY Þ ðA3Þ

To compare the unconventional value in Equation(A3) against the discounted value in Equation (A2)it is important to note that since 05r51 it followsimmediately that

1� r2

1� rt9>2

t9ðA4Þ

Therefore, the unconventional value for Z,V ðZÞ ¼ ð2=t9Þ � V ðY Þ, is lower than the dis-counted value for Z, V ðZÞ ¼ ½ð1� r2Þ=ð1� rt9 Þ� �V ðY Þ

The extent to which the unconventional value islower than the discounted value is reinforced byany underestimation of the conventional value Ywhich forms part of the unconventional formulafor Z in Equation (A3) [28]. Overall then, thisreinforcement results in an unconventional valuefor Z that is lower than the conventional valuefor Z.

A. Spencer666


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Documents

The TTO method and procedural invariance