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Abstract:
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We propose two multiple imputation approaches, namely, the seimparametric direct imputation (SDI) method and the semiparametric two-step importance sampling imputation (STISI) method, to handle regression with censored covariate. The SDI directly imputes the missing covariate from a semiparametric accelerated failure time (AFT) model conditional on fully observed covariates and the response, which is valid when the AFT model and substantive model are compatible. The STISI imputes the missing covariate from a semiparametric AFT model conditional only on fully observed covariates with acceptance probability derived from the substantive model. This two-step procedure automatically ensures compatibility and takes the full advantage of semiparametric assumption in the imputation. Extensive simulations demonstrate that the SDI method yields consistent estimates and appropriate coverage rates when the imputation model in SDI is compatible with the substantive model. While the STISI method yields valid estimates in all scenarios and outperforms some existing methods that are commonly used in practice. Both methods are illustrated by analyzing the urine arsenic data for patients from NHANES
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