This paper considers a regression imputation method for estimating the regression coefficients in the Cox model when some failure indicators are missing at random, and the conditional probability of the censoring indicator is assumed to be of a parametric form. To avoid problems with missspecification of the parametric form, two augmented inverse probability weighted estimators are defined, and their asymptotic properties are established. Simulation studies were conducted to demonstrate the

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... ormance of the proposed estimators, and a data set from a stage II breast cancer trial is used to illustrate our methods.