Shikhar Tyagi, Arvind Pandey, Bhupendra Singh, Vrijesh Tripathi
Implements estimation for the Cox (1972, 1975) <doi:10.1111/j.2517-6161.1972.tb00899.x> <doi:10.1093/biomet/62.2.269> proportional hazards model when the failure indicator (cause of failure) is missing not at random (MNAR), following the two adjusted imputation-based estimating equations of Liu and Liu (2026) <doi:10.1007/s11222-026-10857-1>. Also provided for comparison are the full-data partial-likelihood estimator of Andersen and Gill (1982) <doi:10.1214/aos/1176345976>, the complete-case estimator, and the missing-at-random imputation estimator of Liu and Wang (2010, Statistica Sinica, 20, 1125-1142). The probability models for the failure indicator and for the missingness mechanism are estimated jointly by maximum likelihood following Sun, Xie, and Liang (2013) <doi:10.1007/s11425-012-4492-x>, and a Nadaraya-Watson kernel-smoothed estimator of the missingness propensity is constructed following Qiu, Chen, and Zhou (2015) <doi:10.1016/j.spl.2014.12.006>. Both an asymptotic (sandwich-type) variance estimator and a nonparametric bootstrap variance estimator are provided. When failure indicators are fully observed the estimators reduce algebraically to the classical Cox partial-likelihood estimator.