Supplementary materials: Comparing the performance of two-stage residual inclusion methods when using physician’s prescribing preference as an instrumental variable: unmeasured confounding and noncollapsibility

These are peer-reviewed supplementary materials for the article 'Supplementary materials: Comparing the performance of two-stage residual inclusion methods when using physician’s prescribing preference as an instrumental variable: unmeasured confounding and noncollapsibility' published in the Journal of Comparative Effectiveness Research.Figure S1. Results from prior 1 prescription as IVFigure S2. Results from prior 2 prescriptions as IVFigure S3. Results from prior 3 prescriptions as IVFigure S4. Results from prior 4 prescriptions as IVR CodeAim: The first objective is to compare the performance of two-stage residual inclusion (2SRI), two-stage least square (2SLS) with the multivariable generalized linear model (GLM) in terms of the reducing unmeasured confounding bias. The second objective is to demonstrate the ability of 2SRI and 2SPS in alleviating unmeasured confounding when noncollapsibility exists. Materials & methods: This study comprises a simulation study and an empirical example from a real-world UK population health dataset (Clinical Practice Research Datalink). The instrumental variable (IV) used is based on physicians’ prescribing preferences (defined by prescribing history). Results: The percent bias of 2SRI in terms of treatment effect estimates to be lower than GLM and 2SPS and was less than 15% in most scenarios. Further, 2SRI was found to be robust to mild noncollapsibility with the percent bias less than 50%. As the level of unmeasured confounding increased, the ability to alleviate the noncollapsibility decreased. Strong IVs tended to be more robust to noncollapsibility than weak IVs. Conclusion: 2SRI tends to be less biased than GLM and 2SPS in terms of estimating treatment effect. It can be robust to noncollapsibility in the case of the mild unmeasured confounding effect.

本数据集为发表于《比较疗效研究杂志》的论文《补充材料：比较使用医师处方偏好作为工具变量的两阶段残差包含方法性能：未测量混杂因素和非可折叠性》的同行评审补充材料。图S1. 以先前1次处方作为工具变量的结果；图S2. 以先前2次处方作为工具变量的结果；图S3. 以先前3次处方作为工具变量的结果；图S4. 以先前4次处方作为工具变量的结果；R代码。研究目标：首先，旨在比较两阶段残差包含（2SRI）、两阶段最小二乘（2SLS）与多变量广义线性模型（GLM）在减少未测量混杂偏差方面的性能。其次，旨在展示2SRI和2SPS在存在非可折叠性时减轻未测量混杂因素的能力。研究方法：本研究包括一项模拟研究和一项来自真实世界英国人口健康数据集（临床实践研究数据链）的经验示例。所使用的工具变量（IV）基于医师的处方偏好（由处方历史定义）。结果：在治疗效应估计方面，2SRI的百分比偏差低于GLM和2SPS，并且在大多数情况下低于15%。此外，2SRI被发现对轻微的非可折叠性具有鲁棒性，百分比偏差低于50%。随着未测量混杂程度的增加，减轻非可折叠性的能力下降。强工具变量相对于弱工具变量往往对非可折叠性具有更强的鲁棒性。结论：在估计治疗效应方面，2SRI相较于GLM和2SPS，往往具有较低的偏差。在轻微的未测量混杂效应存在的情况下，2SRI能够对非可折叠性表现出鲁棒性。