Comparing Practical Approaches for Regression Models With Censored Covariates


August 2022


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The accelerated failure time (AFT) model is a useful linear model to estimate the effect of some covariates on the failure time. Estimating the AFT model coefficients is challenging when there are missing values in the covariate due to the limit of detection (LOD) or when there are randomly censored covariates. Removing the subjects with the missing observations in the complete-case (CC) analysis is the usual approach due to the simplicity and consistency of the estimator. In small sample studies with a high missing proportion in more than one covariate, dropping observations in the CC analysis may result in a non-convergence issue. When the covariates are subject to the LOD, the missingness in the data is due to the inability to measure the values beyond the LODs. The missing indicator (MDI) approach could be a good alternative to the CC analysis. For small samples, the MDI is justified in simulation studies for the AFT model with covariates subject to the lower, upper, and interval LOD. In the linear and Cox models, the MDI outperforms other approaches too. When the covariates are randomly censored, imputing the censored values could be useful in parametric and semi-parametric AFT models. For the parametric AFT model, we proposed a parametric imputation approach that takes advantage of the available information in the censored covariate. The parametric imputation approach outperforms the CC analysis under the correct parametric assumptions. In the absence of a correct parametric assumption and under the semi-parametric AFT model, the MDI approach could be a good alternative to the CC analysis that preserves the sample size. In application to the NCCTG lung cancer data, the bias of the MDI estimator is less than that of the CC estimator when some covariates are subject to artificial LOD.