# Supplementary materials: Application of quantitative bias analysis for unmeasured confounding in cost–effectiveness modelling

**These are peer-reviewed supplementary materials for the article '****Application of quantitative bias analysis ****for unmeasured confounding in ****cost–effectiveness modelling****' published in the**** ***Journal of Comparative Effectiveness Research***.**

__Appendix 1 – Simulation of survival data__

**Table 1:**Parameters used in the simulation of patient-level data

__Appendix 2 – Model parameters and output__

**Table 2:**Sensitivity parameters and adjusted hazard ratios and corresponding confidence intervals after applying the Ding*et al.*(2016) method under the scenario with good knowledge of the unmeasured confounder where RR_{EU}is the relative risk between the exposure and unmeasured confounder and HR_{UD}is the hazard ratio between the unmeasured confounder and outcome**Table 3:**Sensitivity parameters, adjusted hazard ratios and corresponding confidence intervals after applying the Huang*et al.*(2020) method under the scenario with poor knowledge of the unmeasured confounder where Ω is the marginal probability of the unmeasured confounder, α_{U}is the coefficient of the unmeasured confounder in the treatment model and η is the coefficient of the unmeasured confounder in the outcome model**Table****4****:**Sensitivity parameters and adjusted hazard ratios and corresponding confidence intervals after applying the Ding*et al.*(2016) method under the scenario with poor knowledge of the unmeasured confounder where is the relative risk between the exposure and unmeasured confounder and is the hazard ratio between the unmeasured confounder and outcome**Table****5****:**Sensitivity parameters and adjusted hazard ratios and corresponding confidence intervals after applying the Huang*et al.*(2020) method under the scenario with incorrect knowledge of the unmeasured confounder where Ω is the marginal probability of the unmeasured confounder, is the coefficient of the unmeasured confounder in the treatment model and is the coefficient of the unmeasured confounder in the outcome model**Table****6****:**Sensitivity parameters and adjusted hazard ratios and corresponding confidence intervals after applying the Ding*et al.*(2016) method under the scenario with incorrect knowledge of the unmeasured confounder where is the relative risk between the exposure and unmeasured confounder and is the hazard ratio between the unmeasured confounder and outcome

__Appendix 3 – Cost-effectiveness model__

**Figure 1:**Model Structure**Table 1:**Parameter value for baseline survival functions**Table 2:**HR values used in the model for different scenarios and methods**Table 3:**Summary of utility values used in the CEM

__Appendix 4 – Supportive results__

**Table 1:**Proportion of iterations leading to potential misallocation of resources

__Appendix 5 – R code__

Due to uncertainty regarding the potential impact of unmeasured confounding, health technology assessment (HTA) agencies often disregard evidence from nonrandomized studies when considering new technologies. Quantitative bias analysis (QBA) methods provide a means to quantify this uncertainty but have not been widely used in the HTA setting, particularly in the context of cost–effectiveness modelling (CEM). This study demonstrated the application of an aggregate and patient-level QBA approach to quantify and adjust for unmeasured confounding in a simulated nonrandomized comparison of survival outcomes. Application of the QBA output within a CEM through deterministic and probabilistic sensitivity analyses and under different scenarios of knowledge of an unmeasured confounder demonstrates the potential value of QBA in HTA.