| Reverse survival regression (Section 3) |
Overview: estimate the survival function of the censored covariate given the outcome and the fully observed covariates Types of censoring currently addressed: random (right) Benefits: (a) takes advantage of existing methods for censored outcomes and (b) has higher power to detect an association between the original censored covariate and the outcome compared with multiple imputation and thresholding Drawbacks: changes parameter interpretation
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| Naive analysis (Section 4.1) |
Overview: analyze the dataset treating the observed covariates as the true values, i.e., ignore censoring Types of censoring currently addressed: limit of detection (left/right), random (left/right) Benefits: none (never recommended) Drawbacks: (a) no theoretical underpinnings and (b) increased bias and type I error rates
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| Substitution (Section 4.2) |
Overview: replace censored covariate values with some function of the censored value and analyze the revised dataset Types of censoring currently addressed: limit of detection (left) Benefits: none (never recommended) Drawbacks: (a) no theoretical underpinnings and (b) increased bias
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| Complete case analysis (Section 5) |
Overview: analyze the uncensored data Types of censoring currently addressed: all Benefits: (a) is computationally simple and easy to implement, (b) can provide consistent initial values for iterative methods, and (c) is a straightforward reference to gauge performance of more advanced methods Drawbacks: (a) has reduced efficiency due to deleting data and (b) consistent estimation is not guaranteed
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| Inverse probability weighting (IPW) (Section 6.1) |
Overview: estimate the subject-specific probabilities that the covariate is uncensored, use these probabilities to reweight uncensored observations, and analyze the reweighted dataset Types of censoring currently addressed: random (right) Benefits: (a) is computationally simple and easy to implement, (b) can be consistent when complete case analysis is not, (c) there is no need to specify a distribution for the censored covariate given the fully observed data Drawbacks: (a) has reduced efficiency (similar to the complete case analysis) and (b) is sensitive to large weights
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| Augmented inverse probability weighting (AIPW) (Section 6.2) |
Overview: for the weights, estimate the subject-specific probabilities that the covariate is uncensored; for the augmentation term, specify a distribution for the censored covariate given the fully observed data Types of censoring currently addressed: random (interval) Benefits: (a) can be doubly robust, i.e., the distribution of the weights or of the censored covariate given the fully observed data may be misspecified and (b) has increased efficiency over IPW Drawbacks: (a) the current implementation of AIPW only addresses right-censored outcomes and relies on a random visit times assumption, and (b) is not as computationally simple or easy to implement as IPW
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| Imputation (Section 7) |
Overview: impute the censored covariates (once or multiple times), analyze the imputed dataset(s), and pool multiple estimates (if multiple imputation is used) Types of censoring currently addressed: limit of detection (left/right), random (right) Benefits: (a) includes all observations in the analysis and (b) is computationally simple once imputed values have been obtained Drawbacks: (a) is sensitive to misspecification of the imputation model, (b) single imputation underestimates standard errors, and (c) calculating the imputed values can be computationally complex and intensive
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| Parametric maximum likelihood estimation (MLE) (Section 8) |
Overview: specify a parametric model for the outcome given the covariates, specify a parametric model for the censored covariate given the fully observed data, and construct and maximize the likelihood Types of censoring currently addressed: limit of detection (left), random (right) Benefits: (a) includes all observations in the analysis and (b) is optimally efficient under correct specification Drawbacks: (a) is sensitive to model misspecification and (b) maximizing the likelihood can be computationally intensive
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| Semiparametric MLE (Section 8) |
Overview: specify a parametric model for the outcome given the covariates, nonparametrically or semiparametrically estimate a model for the censored covariate given the fully observed data, and construct and maximize the likelihood Types of censoring currently addressed: limit of detection (left), random (interval) Benefits: (a) includes all observations in the analysis and (b) is more robust to model misspecification than parametric MLE Drawbacks: (a) some current methods rely on proportional hazards assumption, (b) method can be less efficient than parametric MLE, and (c) maximizing the likelihood can be computationally intensive
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| Bayesian methods (Section 9) |
Overview: specify prior distributions for all unknown model components (including censored covariate and parameters), and estimate parameters based on their posterior distribution Types of censoring currently addressed: any Benefits: (a) are a flexible modeling approach, (b) incorporate prior knowledge on model parameters, and (c) capture all variability in the data Drawbacks: (a) may be computationally intensive and (b) are sensitive to the choice of the prior distributions
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| Threshold method (Section 10) |
Overview: replace the continuous, censored covariate with a dichotomous, uncensored covariate, and analyze the revised dataset Types of censoring currently addressed: random (right) Benefits: is computationally simple and easy to implement Drawbacks: efficiency loss from dichotomization
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