How Estimators Change When Adapted From the Missing Covariate Problem to the Right‐Censored Covariate Problem

Summary Coarsened data, where the true value of a variable is not fully observed, arise frequently. One common form is right‐censoring—where the true value exceeds an observed lower bound—familiar from survival analysis as a feature of outcomes but less commonly recognized as a feature of covariates. Right‐censored covariates resemble missing covariates, making the missing data literature a natural source of estimators. The two problems are not equivalent, however: A missing covariate is completely unknown, whereas a right‐censored covariate is bounded below. How estimators must be adapted from one problem to the other has not received systematic treatment. Through the framework of ‐estimation, we establish how estimators developed for the missing covariate problem change when adapted to the right‐censored covariate problem and show that adaptation has unexpected consequences: Augmented estimators can lose double robustness, weight specifications natural for missingness can introduce bias and efficiency gains can disappear. We develop two new augmented estimators for the right‐censored covariate problem and provide improved versions of all augmented estimators with closed‐form expressions and guaranteed efficiency gains. Simulation studies and an application to cognitive health in Huntington disease confirm these findings. The framework clarifies how estimators change when adapted and guides analysts in choosing among them.