Model assisted Cox regression

Semiparametric random censorship (SRC) models (Dikta, 1998) [7], derive their rationale from their ability to utilize parametric ideas within the random censorship environment. An extension of this approach is developed for Cox regression, producing new estimators of the regression parameter and baseline cumulative hazard function. Under correct parametric specification, the proposed estimator of the regression parameter and the baseline cumulative hazard function are shown to be asymptotically as or more efficient than their standard Cox regression counterparts. Numerical studies are presented to showcase the efficacy of the proposed approach even under significant misspecification. Two real examples are provided. A further extension to the case of missing censoring indicators is also developed and an illustration with pseudo-real data is provided.