Improved estimation of hazard function when failure information is missing not at random

Hazard function plays a crucial role in survival analysis. Its estimation has garnered a lot of attention when the survival time variable suffers from right-censoring. Most of the existing works focus on the cases that failure information is complete or missing at random (MAR). When the censoring information is missing not at random (MNAR), statistical inferences on hazard function are very challenging. In this study, estimation of hazard function is addressed under the MNAR mechanism of the failure information. Three estimators are proposed by employing the techniques of correcting biases and adjusting weighting probabilities. These estimators are validated to be consistent and asymptotically normal. Simulation studies and two real-data analyses are performed to assess the proposed methods.