TABLE 1.

Algorithm of multiple imputation

Step MI-1.	Create m complete data sets by filling in missing times to event with imputed values generated from an imputation model. Specifically, to create the jth imputed data set, generate $T_i^{*(j)}$ from the imputation model for each missing Ti.
Step MI-2.	Apply a full-sample estimator of Δτ to each imputed data set. Denote the point estimator applied to the jth imputed data set by ${\widehat{\Delta }}_{\tau }^{(j)}$. Denote the variance estimator applied to the jth imputed data set by ${\widehat{V}}^{(j)}$.
Step MI-3.	Use Rubin’s combining rule to summarize the results from the multiple imputed data sets. The MI estimator of Δτ is ${\widehat{\Delta }}_{\tau ,\text{mi}}=m^{-1}{\sum }_{j=1}^m{\widehat{\Delta }}_{\tau }^{(j)}$, and Rubin’s variance estimator is ${\widehat{V}}_{\text{mi}}\left({\widehat{\Delta }}_{\tau ,\text{mi}}\right)=\frac{m+1}{(m-1)m}{\sum }_{j=1}^m{\left({\widehat{\Delta }}_{\tau }^{(j)}-{\widehat{\Delta }}_{\tau ,\text{mi}}\right)}^2+\frac{1}{m}{\sum }_{j=1}^m{\widehat{V}}^{(j)}$.