Sensitivity and scenario analyses
Deterministic one-way sensitivity analyses (OWSA) were conducted for each model parameter across ranges equal to the 95% confidence intervals. These were mostly calculated using a standard error of ±20% of the mean value for each parameter. Exceptions were health state utilities for which the values were sourced from the literature (for the healthy weight and overweight health states) and calculated (for the remaining health states), and the mortality hazard ratio for which the standard error was calculated. Results were plotted on a Tornado diagram to identify key drivers of cost effectiveness.A probabilistic sensitivity analysis was conducted using 10.000 iterations to characterise overall uncertainty in the cost-effectiveness results, with values for each parameter simultaneously drawn from their individual uncertainty distribution. Results were plotted on an incremental cost-effectiveness plane scatter plot to visualise uncertainty and a cost-effectiveness acceptability curve was generated to show the probability of ESG being cost effective over a range of willingness-to-pay thresholds (£0–50,000/QALY). A full list of model parameters including uncertainties and distributions is provided in the supplementary materials.Scenario analyses were conducted to explore structural uncertainty related to important model assumptions/inputs including use of alternative long-term BMI extrapolations. Additional scenario analyses included use of general population mortality rates without adjustment to account for the impact of BMI on mortality risk (all BMI-specific mortality HRs set to 1), use of an alternative mapping algorithm from Ara and Brazier, 2008 [A threshold analysis was conducted to estimate how high total ESG device/procedure costs would need to be for the ICER to exceed the £20,000/QALY willingness-to-pay threshold.