Multiply imputing informatively censored time-to-event data

Time-to-event data, such as overall survival in a cancer clinical trial, are commonly right-censored, and this censoring is commonly assumed to be non-informative. While non-informative censoring is plausible when censoring is due to end of study, it is less plausible when censoring is due to loss to follow-up. Sensitivity analyses for departures from the non-informative censoring assumption can be performed using multiple imputation under the Cox model [1]. These have been implemented in R [2] but are not commonly used. We propose a new implementation in Stata. Our existing -stsurvimpute- command (on SSC) imputes right-censored data under non-informative censoring, using a flexible parametric survival model fitted by -stpm2-. We extend this to allow a sensitivity parameter gamma, representing the log of the hazard ratio in censored individuals versus comparable uncensored individuals (the informative censoring hazard ratio, ICHR). The sensitivity parameter can vary between individuals, and imputed data can be re-censored at the end-of-study time. Because the -mi- suite does not allow imputed variables to be -stset-, we create an imputed data set in -ice- format and analyse it using -mim-. In practice, sensitivity analysis computes the treatment effect for a range of scientifically plausible values of gamma. We illustrate the approach using a cancer clinical trial.