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 dataTable 1: Parameters used in the simulation of patient-level dataAppendix 2 – Model parameters and outputTable 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 RREU is the relative risk between the exposure and unmeasured confounder and HRUD is the hazard ratio between the unmeasured confounder and outcomeTable 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, αU is the coefficient of the unmeasured confounder in the treatment model and η is the coefficient of the unmeasured confounder in the outcome modelTable 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 outcomeTable 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 modelTable 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 outcomeAppendix 3 – Cost-effectiveness modelFigure 1: Model StructureTable 1: Parameter value for baseline survival functionsTable 2: HR values used in the model for different scenarios and methodsTable 3: Summary of utility values used in the CEMAppendix 4 – Supportive resultsTable 1: Proportion of iterations leading to potential misallocation of resourcesAppendix 5 – R codeDue 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.

此为发表于《比较疗效研究杂志》之文章《在成本效益建模中应用定量偏差分析以处理未测混杂因素》的同行评审补充材料。附录1 – 生存数据表的模拟数据表1：用于模拟患者层级数据的参数附录2 – 模型参数及输出数据表2：在充分了解未测混杂因素的场景下，应用Ding等（2016）方法后的敏感性参数、调整后的风险比及其对应的置信区间，其中RREU为暴露与未测混杂因素之间的相对风险，HRUD为未测混杂因素与结果之间的风险比数据表3：在了解未测混杂因素不足的场景下，应用Huang等（2020）方法后的敏感性参数、调整后的风险比及其对应的置信区间，其中Ω为未测混杂因素的概率边缘值，αU为治疗模型中未测混杂因素的系数，η为结果模型中未测混杂因素的系数数据表4：在了解未测混杂因素不足的场景下，应用Ding等（2016）方法后的敏感性参数、调整后的风险比及其对应的置信区间，其中为暴露与未测混杂因素之间的相对风险，为未测混杂因素与结果之间的风险比数据表5：在了解未测混杂因素错误的情况下，应用Huang等（2020）方法后的敏感性参数、调整后的风险比及其对应的置信区间，其中Ω为未测混杂因素的概率边缘值，为治疗模型中未测混杂因素的系数，为结果模型中未测混杂因素的系数数据表6：在了解未测混杂因素错误的情况下，应用Ding等（2016）方法后的敏感性参数、调整后的风险比及其对应的置信区间，其中为暴露与未测混杂因素之间的相对风险，为未测混杂因素与结果之间的风险比附录3 – 成本效益模型图1：模型结构表1：基线生存函数的参数值表2：在不同场景和方法中模型使用的HR值表3：成本效益模型中使用的效用值摘要附录4 – 支持性结果表1：导致资源潜在错配的迭代比例附录5 – R代码鉴于对未测混杂因素潜在影响的不确定性，健康技术评估（HTA）机构在考虑新技术时，往往忽视非随机研究的证据。定量偏差分析（QBA）方法提供了一种量化这种不确定性的手段，但尚未在HTA环境中得到广泛应用，特别是在成本效益建模（CEM）的背景下。本研究展示了将汇总和患者层级QBA方法应用于模拟的非随机生存结果比较中，以量化并调整未测混杂因素。通过确定性及概率敏感性分析，在未测混杂因素知识的不同场景下应用QBA输出，展示了QBA在HTA中的潜在价值。