"The instrumental variable (IV) method with a Cox proportional hazard (PH) model has been used to evaluate treatment effects in epidemiological studies involving survival data. The effectiveness of the IV methods in these circumstances has yet to be fully understood, though. The study aimed to evaluate the performance of IV methods using a Cox model. We evaluated the validity of treatment effects estimated by two-stage IV models using simulated scenarios with varying confounder strengths and baseline hazards. Our simulation demonstrated that when observed confounders were not taken into account in the IV models, and the confounder strength was moderate, the treatment effects based on the two-stage IV models were similar to the true value. However, the effect estimates diverged from the true value when observed confounders were taken into account in the IV models. In the case of a null treatment effect (i.e., hazard ratio=1), the estimates from the unadjusted and adjusted IV models (only two-stage) were close to the true value. The implication of our study findings is that the treatment effects obtained through IV analyses using the Cox PH model remain valid if the estimates are reported from unadjusted IV models with moderate confounding effects or if the treatment does not impact the outcome.

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For every simulation, we utilized a sample size of 10,000 and performed 1,000 replications.

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The true treatment effects (HR) of 3, 2, and 1 (null effect) were evaluated.

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The 95% confidence intervals (CI) were calculated as the range between the 2.5 and 97.5 percentiles of the 1000 estimates."