OBJECTIVES: To show how the discrete modelling of continuously varying dose-response relationships in cost-effective analysis (CEA) influences incremental cost-effectiveness ratios (ICERs), cost-effectiveness acceptability curves (CEACs) and the expected value of perfect information (EVPI). In particular, to show that each of these metrics is contingent on the discrete comparisons chosen within a CEA. METHODS: The cost-effectiveness of a hypothetical intervention with a continuous dose-response relationship is simulated. The cost-effectiveness of a small number of possible dose levels is simulated first. The analysis is then repeated a number of times, progressively increasing the number of possible doses and resulting combinations of costs and effects. For each run of the analysis ICERs are calculated for each dose level, a probabilistic sensitivity analysis is simulated, and CEACs and the EVPI are plotted. RESULTS: As the number of potential cost and effect combinations increases, the ICERs for each dose level increase, the CEACs fall towards zero and the EVPI both rises and changes from having sharp inflection points to being a smooth, downward-sloping curve.  CONCLUSIONS: Many interventions demonstrate dose-response relationships, most of which are in principle continuous, even if doses are typically varied discretely. The continuously increasing intensity of interventions means the number of possible alternatives is infinite. The general conclusion from the analysis is that each of the metrics presented here are contingent on the discrete comparisons chosen within the analysis. The significance of this finding for CEACs depends on their interpretation, which varies in the literature. The significance for EVPI is that while it has previously been recognised that excluding relevant comparators can reduce the EVPI, including all theoretically relevant alternatives may be impossible. Further work may be required to understand this constraint on measuring the upper bound of the value of further research.