Estimating uncertainty ranges for costs by the bootstrap procedure combined with probabilistic sensitivity analysis

When an economic evaluation incorporates patient-level data, there are two types of uncertainty over the results: uncertainty due to variation in the sampled data, and uncertainty over the choice of modelling parameters and assumptions. Previously statistical methods have been used to estimate the extent of the former, and sensitivity analysis to estimate the extent of the latter. Ideally interval estimates for economic variables should reflect both types of uncertainty. This paper describes a method for combining bootstrapping with probabilistic sensitivity analysis to estimate a total 'uncertainty range' for incremental costs. The approach is illustrated using cost data from a randomized controlled trial of endoscopy for Helicobactor pylori negative young dyspeptic patients. The trial failed to demonstrate any clinical benefit from endoscopy, which was on average pound 395 more costly. The combined 95% uncertainty range for incremental costs (-pound 236 to pound 931) was wider than 95% intervals estimated by either probabilistic sensitivity analysis (pound 43 to pound 592) or the non-parametric bootstrap method (-pound 95 to pound 667) alone. The method can easily be extended to the calculation of uncertainty ranges for incremental cost-effectiveness ratios.