Lack of multiplicative transitivity in person trade-off responses

The person trade-off (PTO) is a technique for eliciting preferences for resource allocation across patient groups. In principle PTO responses should satisfy a requirement of multiplicative transitivity, i.e. that if people consider treatment of 1 in state A to be equivalent to treating 10 in state B, and 1 in state B to be equivalent to 10 in state C, then they should find 1 in state A equivalent to 100 in state C. Earlier studies addressing labelled diseases (specific diagnoses), have shown multiplicative intransitivity of the PTO responses. Our purpose was to test multiplicative transitivity in the case of health states described with the EuroQol instrument only and to find a possible framing effect such as the number of persons in the reference intervention.

Forty-four master degree students were asked to fill in a questionnaire addressing four chronic health states. Their task consisted in (1). ranking the states by severity, (2). valuing each of them by the means of the time trade-off, and (3). doing the PTO for all the 10 possible pairwise combinations of the four chronic states plus a fatal one. In a subsequent questionnaire the number of persons in the reference intervention in the PTO was increased from 10 to 100. Multiplicative transitivity was studied in subjects who demonstrated a willingness to trade off and consistency in ranking individual values.

None of the 39 subjects included satisfied a minimum multiplicative transitivity requirement in PTO responses. Internal consistency was not improved when the PTO involved health states close to each other in terms of severity, nor when the prevention of death was not the reference intervention. For the 22 subjects having answered both types of questionnaire, increasing the number of persons in the reference intervention did not improve multiplicative transitivity.

The PTO holds promise as a useful method for determining social preferences for priority setting, inasmuch as it captures distributive concerns that individual utility techniques such as the time trade-off do not address. But the lack of multiplicative transitivity in PTO responses is unsatisfactory, and ways to reduce this problem need to be explored.