Quantifying Robustness to Unmeasured Confounding in Time-Varying Treatment Confounder Settings: An Extension of E-value Approach

TL;DR

This paper extends the E-value method to assess robustness against unmeasured confounding in longitudinal studies with time-varying treatments, revealing greater vulnerability than single time-point analyses suggest.

Contribution

It introduces a new bias factor for multiple time points and provides practical tools for sensitivity analysis in complex longitudinal settings.

Findings

Unmeasured confounders with 1.96-fold associations can nullify effects in simulations.

Time-varying E-values are lower than single time-point E-values, indicating higher vulnerability.

Re-analysis shows similar patterns, confirming the method's applicability.

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.