Investigating the Use of the Difference Method for Sampling More Than Two Ordered Variables

OBJECTIVES: In a recent appraisal by the National Institute for Health and Care Excellence (HST28: birch bark extract for epidermolysis bullosa), health state utility values (HSUVs) were inappropriately sampled within probabilistic sensitivity analysis (PSA). Each sampled HSUV was capped at the value of the adjacent, less severe state if better utility was implied. Alternative methodology exists for retaining distributional properties of ordered variables (OVs) using the difference method (DM), though this method was created for only two OVs. In this study, we extend the DM to >2 OVs.

METHODS: An economic model was developed to replicate the model used in HST28. ‘Capped’ and ‘uncapped’ PSA methods were implemented, and then a ‘chained’ version of the DM was applied to each pair of ordered HSUVs. By chaining together each application of the DM, sampled values remained consistent. We assessed the consistency in the mean and variance of the input distributions with the sampled results using each method, and generated both probabilistic results and the expected value of perfect information (EVPI).

RESULTS: Summary statistics for HSUVs were largely maintained when using the chained DM, as well as the ordering of the sampled HSUVs. The chained DM approach maintained the published mean and variance across eight out of nine health states, whereas the capped approach only managed to maintain the summary statistics for one health state. The mean incremental cost-effectiveness ratio had over £4,000 difference, and the EVPI was reduced from £13,376 to £9,359 when using the chained DM.

CONCLUSIONS: The DM may be chained across more than two OVs. Using this approach, summary statistics of original inputs are maintained, and parameter uncertainty is not over-inflated. Further research is needed to establish how the chained DM affects sampled values themselves.