🤖 AI Summary
This study addresses the limitation of existing E-value methods, which are restricted to single-time-point exposure–outcome relationships and cannot adequately assess the robustness of causal estimates in longitudinal settings with time-varying treatments and confounders. The authors extend the E-value framework to accommodate time-varying confounding by introducing a multi-time-point joint bias factor and propose three sensitivity analysis scenarios: equal-strength distribution, single-time-point dominance, and full-combination visualization, integrated with hazard ratio correction for quantifying causal effect robustness. Simulations reveal that an observed hazard ratio of 1.73 can be nullified by unmeasured confounding associated with the exposure and outcome by as little as 1.96-fold at each time point (single-time-point E-value = 2.85). In a reanalysis of insulin resistance and cardiovascular disease, the time-varying E-value dropped to 1.63 from 2.09, indicating greater sensitivity to unmeasured confounding in longitudinal studies while preserving methodological simplicity and minimal assumptions.
📝 Abstract
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.