<p>The Cox proportional hazards model is a widely used tool for analyzing survival data and evaluating covariate effects. However, standard estimation procedures typically rely on the assumption that failure indicators are fully observed or missing at random. Once the assumptions are violated, traditional estimators will become inconsistent and cause biased results. In this paper, we develop two imputation-based estimating equations for the Cox model when failure indicators are missing not at random. The asymptotic normality properties of the proposed estimators are established under some regularity conditions. Simulation studies and real data analyses demonstrate the robustness and efficiency of the proposed methods across various scenarios.</p>