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

<b>These are peer-reviewed supplementary materials for the article '</b><b>Application of quantitative bias analysis </b><b>for unmeasured confounding in </b><b>cost–effectiveness modelling</b><b>' published in the</b><b> </b><b><i>Journal of Comparative Effectiveness Research</i></b><b>.</b><b>Appendix 1 – Simulation of survival data</b><b>Table 1: </b>Parameters used in the simulation of patient-level data<b>Appendix 2 – Model parameters and output</b><b>Table 2: </b>Sensitivity parameters and adjusted hazard ratios and corresponding confidence intervals after applying the Ding <i>et al.</i> (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<b>Table 3: </b>Sensitivity parameters, adjusted hazard ratios and corresponding confidence intervals after applying the Huang <i>et al.</i> (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<b>Table </b><b>4</b><b>:</b> Sensitivity parameters and adjusted hazard ratios and corresponding confidence intervals after applying the Ding<i> et al.</i> (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<b>Table </b><b>5</b><b>:</b> Sensitivity parameters and adjusted hazard ratios and corresponding confidence intervals after applying the Huang <i>et al. </i>(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<b>Table </b><b>6</b><b>:</b> Sensitivity parameters and adjusted hazard ratios and corresponding confidence intervals after applying the Ding <i>et al.</i> (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<b>Appendix 3 – Cost-effectiveness model</b><b>Figure 1: </b>Model Structure<b>Table 1: </b>Parameter value for baseline survival functions<b>Table 2: </b>HR values used in the model for different scenarios and methods<b>Table 3: </b>Summary of utility values used in the CEM<b>Appendix 4 – Supportive results</b><b>Table 1:</b> Proportion of iterations leading to potential misallocation of resources<b>Appendix 5 – R code</b>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.<br>本材料为发表于《Journal of Comparative Effectiveness Research》（比较效果研究期刊）的论文《未测量混杂因素的定量偏倚分析在成本效果建模中的应用》（Application of quantitative bias analysis for unmeasured confounding in cost–effectiveness modelling）的同行评议补充材料。 附录1 – 生存数据模拟 表1：患者层面数据模拟所用参数 附录2 – 模型参数与输出结果 表2：在对未测量混杂因素具备充分认知的场景下，应用Ding等人（2016）方法后得到的敏感性参数、校正后风险比（hazard ratio, HR）及其对应置信区间，其中RR_EU为暴露因素与未测量混杂因素间的相对风险（relative risk, RR），HR_UD为未测量混杂因素与结局间的风险比。 表3：在对未测量混杂因素认知不足的场景下，应用Huang等人（2020）方法后得到的敏感性参数、校正后风险比及其对应置信区间，其中Ω为未测量混杂因素的边缘概率，α_U为治疗模型中未测量混杂因素的回归系数，η为结局模型中未测量混杂因素的回归系数。 表4：在对未测量混杂因素认知不足的场景下，应用Ding等人（2016）方法后得到的敏感性参数、校正后风险比及其对应置信区间，其中为暴露因素与未测量混杂因素间的相对风险，为未测量混杂因素与结局间的风险比。 表5：在对未测量混杂因素认知有误的场景下，应用Huang等人（2020）方法后得到的敏感性参数、校正后风险比及其对应置信区间，其中Ω为未测量混杂因素的边缘概率，为治疗模型中未测量混杂因素的回归系数，为结局模型中未测量混杂因素的回归系数。 表6：在对未测量混杂因素认知有误的场景下，应用Ding等人（2016）方法后得到的敏感性参数、校正后风险比及其对应置信区间，其中为暴露因素与未测量混杂因素间的相对风险，为未测量混杂因素与结局间的风险比。 附录3 – 成本效果模型 图1：模型结构 表1：基线生存函数的参数取值 表2：模型中用于不同场景与方法的风险比（HR）取值 表3：成本效果建模（cost–effectiveness modelling, CEM）中所用效用值汇总 附录4 – 辅助结果 表1：导致潜在资源错配的迭代比例 附录5 – R语言代码 鉴于未测量混杂因素的潜在影响存在不确定性，卫生技术评估（health technology assessment, HTA）机构在评估新技术时常会排除非随机对照研究的证据。定量偏倚分析（quantitative bias analysis, QBA）方法可用于量化此类不确定性，但目前在HTA场景中尚未得到广泛应用，尤其在成本效果建模（CEM）领域。本研究展示了汇总层面与患者层面的QBA方法在模拟生存结局的非随机比较中，对未测量混杂因素进行量化与校正的应用。通过确定性与概率敏感性分析，并结合不同未测量混杂因素认知场景，将QBA结果应用于CEM中，证实了QBA在HTA中的潜在应用价值。