  Analysts are often confronted with censoring, wherein some variables are not
observed at their true value, but rather at a value that is known to fall above
or below that truth. While much attention has been given to the analysis of
censored outcomes, contemporary focus has shifted to censored covariates, as
well. Missing data is often overcome using multiple imputation, which leverages
the entire dataset by replacing missing values with informed placeholders, and
this method can be modified for censored data by also incorporating partial
information from censored values. One such modification involves replacing
censored covariates with their conditional means given other fully observed
information, such as the censored value or additional covariates. So-called
conditional mean imputation approaches were proposed for censored covariates in
Atem et al. [2017], Atem et al.[2019a], and Atem et al. [2019b]. These methods
are robust to additional parametric assumptions on the censored covariate and
utilize all available data, which is appealing. As we worked to implement these
methods, however, we discovered that these three manuscripts provide
nonequivalent formulas and, in fact, none is the correct formula for the
conditional mean. Herein, we derive the correct form of the conditional mean
and demonstrate the impact of the incorrect formulas on the imputed values and
statistical inference. Under several settings considered, using an incorrect
formula is seen to seriously bias parameter estimation in simple linear
regression. Lastly, we provide user-friendly R software, the imputeCensoRd
package, to enable future researchers to tackle censored covariates in their
data.
