Perform methods of multiple imputation for time to event data
See Nonparametric comparison of two survival functions with dependent censoring via nonparametric multiple imputation. Hsu and Taylor Statistics in Medicine (2009) 28:462-475 for Hsu's method
See Relaxing the independent censoring assumption in the Cox proportional hazards model using multiple imputation. Jackson et al., Statistics in Medicine (2014) 33:4681-4694 for Jackson's method