Cost-utility analysis when not everyone wants the treatment: modelling split-choice bias

Not all clinically eligible patients will necessarily accept a new treatment. Cost-utility analysis recognizes this by multiplying the mean incremental expected utility (EU) by the participation rate to obtain the utility gain per head. However, the mean EU gain over all patients in a defined clinical category is traditionally used as a proxy for the mean EU gain over the subpopulation of acceptors. Even for clinically identical patients, this may lead to a biased assessment of total benefit because a patient motivated to accept the new treatment is likely to value its effects more favorably than a patient who declines. An analysis that ignores this tendency will be biased toward an underestimate of true benefits of a health technology (HT). The extent of this bios is described within a quality-adjusted life year-based utility model for a population of clinically indistinguishable patients who differ with respect to the values that they place on the possible health outcomes of an HT The size of the bias is sensitive to the proportion of patients who accept the treatment, under both deterministic and probabilistic models of individual decision making. In all cases in which decision making is correlated with personal utility gain, the bias rises steeply as the proportion of acceptors declines.