Person Trade-Off

Person Trade-Off in Health State Valuation and Priority Setting

The person trade-off places a respondent in the role of a decision maker who must choose between two health programmes, and asks for the number of people helped by one programme that would make it as worthwhile as helping a fixed number of people with the other. The answer is a judgement about the value of outcomes for other people, which is why Nord presented the technique as a way of valuing health care programmes for resource allocation, and why the person trade-off sits apart from methods that ask people to value their own health. For a health economist the method matters in two places. The disability weights of the 1996 revision of the Global Burden of Disease (GBD) 1990 study were set by small groups of health professionals using two forms of the person trade-off, and the later literature on equity weights uses the method to test whether the public values a health gain differently depending on how ill the patient was before treatment. An equivalence number turns into a relative value by simple division, but the result depends on how the question is framed.

How the person trade-off question is put

Nord described the technique as asking people how many outcomes of one kind they consider equivalent in social value to a given number of outcomes of another kind. In practice the respondent sees two programmes that cannot both be funded. One helps a fixed number of people in a reference way, often by saving their lives or curing a reference condition, and the other helps people with the condition being valued.

The respondent then states the number of people in the second group at which the two programmes are equally worth funding, or the number is varied until the respondent is indifferent. Two framings are common. A cure framing compares saving a number of lives with curing a number of people of a non-fatal condition. A life extension framing compares extending the lives of healthy people with extending, by the same amount, the lives of people who will live on with the condition.

The viewpoint is what separates the person trade-off from other valuation tasks. Dolan and Green note that values from the standard gamble and time trade-off reflect individual preferences, while social preferences may depend on other factors such as the severity of the patient's condition before treatment. The person trade-off asks the respondent to weigh benefits to other people, so the answer can carry concerns about fairness as well as about the size of the health gain.

Converting an equivalence number into a relative value

A person trade-off answer states that two programmes have equal total value. If values add across people, the total value of each programme is the number of people helped multiplied by the value of each person's gain, and setting the two totals equal gives the relative value of the gains.

$$N_R \times g_R = N_X \times g_X$$

where $N_R$ is the number of people helped by the reference programme, $g_R$ is the value of each person's gain under the reference programme, $N_X$ is the number of people helped by the programme being valued at which the respondent is indifferent, and $g_X$ is the value of each person's gain under that programme.

$$\frac{g_X}{g_R} = \frac{N_R}{N_X}$$

where the left side is the value of one gain of the second kind relative to one gain of the reference kind, and $N_R$ and $N_X$ are as defined above.

When the reference programme saves lives that continue in full health and the second programme restores people with condition $h$ to full health for the same length of time, the reference gain counts as 1 and the cure gain equals 1 minus the value of state $h$.

$$v_h = 1-\frac{N_R}{N_X}$$

where $v_h$ is the value of state $h$ on a scale with full health at 1 and dead at 0, and the fraction $N_R / N_X$ is the loss associated with the state, the quantity a burden of disease study would record as a disability weight. In the life extension framing the gain of the second kind is a year lived in state $h$, so the value of the state is $N_R / N_X$ directly.

Three assumptions sit inside this arithmetic. The value of a programme is taken to rise in proportion to the number of people helped, the durations of the two gains are taken to be equal or are adjusted for explicitly, and the respondent is assumed to judge only the health outcomes described. A respondent who refuses to trade at all breaks the first assumption. A respondent who gives extra priority to the more severely ill breaks the third, because the number then mixes the size of the health gain with a judgement about who receives the gain, and no longer measures a health state value alone.

Worked example converting person trade-off answers into weights and a funding choice

All numbers in this example are illustrative and do not come from any published study. Both programmes affect people for 10 remaining years, there is no discounting, and a cured person returns to full health. Programme L saves 100 people who would otherwise die now, and each lives 10 years in full health. Programme C cures people of a chronic non-fatal condition X that would otherwise last 10 years.

1. Cure framing. A respondent judges that curing 400 people of condition X is as worthwhile as saving the 100 lives. The relative value of a cure is 100 ÷ 400 = 0.25, so the implied disability weight is 0.25 and the implied value of condition X is 0.75, the remainder when 0.25 is subtracted from 1.

2. Checking the totals. Programme L yields 100 × 1 × 10 = 1,000 value-weighted life years, and 400 cures yield 400 × 0.25 × 10 = 1,000. The two totals match, which is what the respondent's indifference means under the arithmetic above.

3. Life extension framing. The same respondent is asked how many people living with condition X would need a one-year life extension to match a one-year extension for 100 healthy people, and answers 125. A year in condition X is then worth 100 ÷ 125 = 0.8, giving a disability weight of 0.2. The two framings disagree by 0.05 on the same condition.

4. Comparison with a patient time trade-off. Suppose patients with condition X give the state a time trade-off value of 0.90. A cure then gains 0.10 × 10 = 1 QALY and a life saved gains 1 × 10 = 10 QALYs. On QALY arithmetic the number of cures that matches 100 lives saved is 100 × 10 = 1,000, since each cure adds 1 QALY. The respondent asked for only 400, giving each cure 0.25 ÷ 0.10 = 2.5 times the weight that the patient values imply. That gap cannot show whether the respondent rates condition X as worse than patients do or applies a distributive weight, and any such weight here favours the less severely ill group, not the people facing death.

5. A funding choice. A budget of GBP 2,000,000 is available. Saving a life costs GBP 20,000 and a cure costs GBP 4,000, so the budget buys 2,000,000 ÷ 20,000 = 100 lives saved or 2,000,000 ÷ 4,000 = 500 cures. The totals under each set of values are shown below.

The QALY count built on patient values favours saving lives, the cure framing of the person trade-off favours the cure programme, and the life extension framing leaves the two programmes level. The person trade-off answers therefore depart from patient-based values, but the size of the departure depends on which question was asked. An analysis using such weights would need to report the framing and show how the choice changes when the other framing is used.

Expert panels and the person trade-off in the Global Burden of Disease

The person trade-off entered burden of disease work through the disability-adjusted life year. The World Health Organization (WHO) methods document for its global health estimates covering 2000 to 2019 records that Murray argued that health state values should reflect societal judgements.

Following that argument, the 1996 version of GBD 1990 used two forms of the person trade-off to assess social preferences for health states. WHO describes the weighting exercises as asking small groups of health professionals to make a composite judgement on the severity distribution of each condition and the social preference for time spent at each severity level. The resulting weights scaled time lived with each condition in years lived with disability.

The GBD 2010 study re-estimated disability weights with its main emphasis on surveys of the general population. Salomon and colleagues ran household surveys in Bangladesh, Indonesia, Peru and Tanzania, face to face, and in the USA by telephone, with 13,902 respondents, alongside an open-access web survey with 16,328 respondents. The main task was a paired comparison, in which respondents considered two hypothetical people with different health states and said which was healthier. The web survey added population health equivalence questions that compared the overall health benefits of different life-saving or disease-prevention programmes, and these answers anchored the paired comparison results on the scale from 0 to 1 for 220 health states.

Social value, severity and equity weights

Nord concluded that, despite its practical problems, the technique deserves greater attention in cost-utility analysis. Conventional QALY counting values a programme by the sum of individual health gains, whereas the person trade-off asks directly about the social value of outcomes for different groups of people. Green's review records that the person trade-off has been proposed for eliciting social preferences both to value interventions and to weight other criteria, such as the severity of a patient's condition before treatment.

That second use links the method to equity-weighted analysis. If answers depart systematically from QALY arithmetic based on patient values, as in step 4 of the worked example, the departure mixes any difference between public and patient values for the health states with any distributive weight the respondent applies. Only with the health state values held fixed can such a ratio be read as a severity weight, and the ratio in the worked example favours the less severe condition, so it would not support a priority for the severely ill. The evidence is mixed. Dolan and Green found that people's preferences over treatments for themselves differ from their preferences when they think about the treatment of others, but their qualitative data suggested that health gain is an important determinant of social value, counter to studies suggesting that concern about pre-treatment severity is as important or more so.

Whose values to ask for is a further choice. Ubel and colleagues revisited an earlier proposal to use patients' values to estimate the effect of a condition on health-related utility and the general public's person trade-off answers to estimate the societal value of those changes. They argued that this still lets the public misvalue the benefit of health care interventions through bias or misunderstanding, and proposed a procedure that combines patient and public values to correct the problem in part.

How the person trade-off differs from the time trade-off and standard gamble

All three methods are forms of health state valuation, but they ask different people to trade different things. The time trade-off and standard gamble ask a respondent to give up years of their own life or accept their own risk of death, while the person trade-off asks for a choice between groups of other people.

Pinto Prades compared the person trade-off with the standard gamble and a visual analogue scale in a pilot study with 30 economics undergraduates. Judged against their stated preferences about setting priorities between hypothetical patients, the person trade-off performed better than the other two methods, and one of three person trade-off framings appeared to predict those preferences. The criterion was itself a set of stated priorities, so the finding says nothing about whether such values should replace health state utility values in a QALY calculation.

Practical demands, framing effects and consistency

Nord judged the person trade-off theoretically appealing for resource allocation but quite demanding in practice. Fairly large groups of respondents are needed to keep random measurement error at an acceptable level, and answers are open to framing effects, including how the arguments for each programme are presented and which numbers are used as starting points. Nord suggested a multistep procedure in which respondents weigh the relevant arguments and then revisit their first answers.

Later reviews found the evidence thin. Green concluded that the technique has limited empirical support, that applications had been largely experimental, that its reliability was unproven and that its ability to reflect people's actual preferences was unclear, while still seeing potential for assessing the societal value of health care.

Consistency across questions is a separate test. If one cure of condition A is judged equal to two cures of condition B, and one cure of B equal to three cures of condition C, multiplying the ratios implies that one cure of A should equal six cures of C. Dolan and Tsuchiya, studying preferences over age weighting, found that very few person trade-off responses satisfied cardinal transitivity, although it appeared to hold on average once respondents who failed the ordinal condition were excluded. They recommended that future person trade-off studies check for ordinal transitivity.

Common misreadings of person trade-off values

Most errors come from treating a person trade-off number as if it were an individual utility. A weight elicited for one purpose, such as testing views on severity, is easily reused in a model built for another.

• Treating the result as a patient utility. A person trade-off value reports how a respondent weighs outcomes for other people, which can include concerns about severity and fairness, so it is not interchangeable with a time trade-off or standard gamble value in the same model.
• Ignoring the framing. Cure and life extension questions about the same condition can give different weights, as the worked example shows, and a study should report which form was used.
• Assuming linear aggregation. A respondent who refuses to trade, or who gives priority to the worst off at any ratio, gives a number that does not convert cleanly into a state value.
• Equating GBD 2010 weights with person trade-off weights. The GBD 2010 weights rest mainly on paired comparisons from population surveys and differ in method from the expert weights of 1996.

Sources

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• Dolan P, Tsuchiya A. The person trade-off method and the transitivity principle: an example from preferences over age weighting. Health Economics. 2003;12(6):505-510. doi:10.1002/hec.731
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• Pinto Prades JL. Is the person trade-off a valid method for allocating health care resources? Health Economics. 1997;6(1):71-81. doi:10.1002/(SICI)1099-1050(199701)6:1<71::AID-HEC239>3.0.CO;2-Z
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