This article presents a multiple imputation method for sensitivity analyses of time-to-event data with possibly informative censoring. The imputed time for censored values is drawn from the failure time distribution conditional on the time of follow-up discontinuation. A variety of specifications regarding the post-discontinuation tendency of having events can be incorporated in the imputation through a hazard ratio parameter for discontinuation versus continuation of follow-up. Multiple-imputed data sets are analyzed with the primary analysis method, and the results are then combined using the methods of Rubin. An illustrative example is provided.