Quantifying Robustness to Unmeasured Confounding in Time-Varying Treatment Confounder Settings: An Extension of E-value Approach
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917299941801984 |
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| author | Sium, Md. Niamul Islam |
| author_facet | Sium, Md. Niamul Islam |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_24261 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantifying Robustness to Unmeasured Confounding in Time-Varying Treatment Confounder Settings: An Extension of E-value Approach Sium, Md. Niamul Islam Applications 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. |
| title | Quantifying Robustness to Unmeasured Confounding in Time-Varying Treatment Confounder Settings: An Extension of E-value Approach |
| topic | Applications |
| url | https://arxiv.org/abs/2602.24261 |