Background: The E-value has become widely used for assessing robustness to unmeasured confounding in observational studies, but the original framework was developed for single time-point exposure-outcome settings. This study extends the E-value methodology to longitudinal set up with time-varying treatments and confounders, where treatment-confounder feedback occurs. Methods: A combined bias factor accounting for unmeasured confounding at multiple time points was extended, with three reporting scenarios presented: equal bias distribution across time points, confounding at a single time point, and a general case visualizing all possible confounder strength combinations. Results: In simulations with an observed risk ratio of 1.73, unmeasured confounders with 1.96-fold associations at each time point could nullify the effect under equal distribution-substantially lower than the single time-point E-value of 2.85. Re-analysis of a published insulin resistance and cardiovascular disease study yielded similar patterns, with time-varying E-values of 1.63 at each time point compared to the originally reported 2.09. Conclusions: Studies more like longitudinal set up may be more vulnerable to unmeasured confounding than single time-point E-values suggest. This extension provides accessible tools for transparent sensitivity analysis in time-varying settings while preserving the simplicity and minimal assumptions that make E-values widely applicable.
Sensitivity Analysis of Treatment Effect to Unmeasured Confounding in Observational Studies with Survival and Competing Risks Outcomes
当使用倾向得分和逆概率加权等方法时，在估计观察性数据的处理效应时，通常假设没有未测量的混杂因素。然而，在许多这样的研究中，由于数据库的限制，收集的混杂因素并不详尽，关键是要检查所得到的估计值对未测量的混杂因素的敏感程度。我们考虑生存和竞争风险数据的这个问题。由于此类数据模型的复杂性，我们采用了Carnegie et al.（2016）的模拟潜在混杂因素方法，该方法为未测量混杂因素的敏感性分析提供了通用工具。更具体地说，我们指定一个敏感性参数来量化未测量的混杂因素与治疗分配之间的关联，另一组参数来量化混杂因素与事件发生时间结局之间的关联。通过改变灵敏度参数的大小，我们使用随机EM和期望最大化算法来估计感兴趣的处理效应。我们证明了我们的方法在模拟数据上的性能，并将其应用于炎症性肠病（IBD）的比较有效性研究。
Using instrumental variables to disentangle treatment and placebo effects in blinded and unblinded randomized clinical trials influenced by unmeasured confounders
The Impact of Unmeasured Within- and Between-Cluster Confounding on the Bias of Effect Estimators from Fixed Effect, Mixed effect and Instrumental Variable Models
A Practical Introduction to Regression-based Causal Inference in Meteorology (II): Unmeasured confounders
University of Washington（华盛顿大学）；Applied Physics Laboratory, University of Washington（华盛顿大学应用物理实验室）；Climate Impacts Group, University of Washington（华盛顿大学气候影响研究组）；School of Meteorology, University of Oklahoma（俄克拉荷马大学气象学院）
Adjustment for Unmeasured Spatial Confounding in Settings of Continuous Exposure Conditional on the Binary Exposure Status: Conditional Generalized Propensity Score-Based Spatial Matching
Real Effect or Bias? Best Practices for Evaluating the Robustness of Real-World Evidence through Quantitative Sensitivity Analysis for Unmeasured Confounding
Identifying and Estimating Causal Direct Effects Under Unmeasured Confounding
McGill University（麦吉尔大学）；Research Institute of the McGill University Health Centre（麦吉尔大学健康中心研究所）；Harvard T.H. Chan School of Public Health（哈佛大学陈曾熙公共卫生学院）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；Fred Hutchinson Cancer Center（弗雷德·哈钦森癌症中心）；University of California, Berkeley（加州大学伯克利分校）
