Sample restrictions and the elicitation of a constant willingness to pay per quality adjusted life year

It is well established that the underlying theoretical assumptions needed to obtain a constant proportional trade-off between a quality adjusted life year (QALY) and willingness to pay (WTP) are restrictive and often empirically violated. In this paper, we set out to investigate whether the proportionality conditions (in terms of scope insensitivity and severity independence) can be satisfied when data is restricted to include only respondents who pass certain consistency criteria. We hypothesize that the more we restrict the data, the better the compliance with the requirement of constant proportional trade-off between WTP and QALY. We revisit the Danish data from the European Value of a QALY survey eliciting individual WTP for a QALY (WTP-Q). Using a "chained approach" respondents were first asked to value a specified health state using the standard gamble (SG) or the time-trade-off (TTO) approach and subsequently asked their WTP for QALY gains of 0.05 and 0.1 (tailored according to the respondent's SG/TTO valuation). Analyzing the impact of the different exclusion criteria on the two proportionality conditions, we find strong evidence against a constant WTP-Q. Restricting our data to include only respondents who pass the most stringent consistency criteria does not impact on the performance of the proportionality conditions for WTP-Q.