Double-Semiparametric Method for Missing Covariates in Cox Regression Models

The problem of nuisance covariate model specification is considered in Cox regression where the maximum semiparametric likelihood method is used to handle the missing covariates. A component of the covariates is modeled nonparametrically to achieve robustness against covariate model misspecification and to reduce the number of possibly intractable integrations involved in the parametric modeling of the covariates. The statistical properties of the proposed method are examined. It is found that in some important situations, the maximum semiparametric likelihood can be applied without making any additional parametric model assumptions on covariates. The proposed method can yield a more efficient estimator than the nonparametric imputation methods and does not require specification of the missingness mechanism when compared with the inverse probability weighting method. A real data example is analyzed to demonstrate use of the proposed method.