Comparison Between Two Controlled Multiple Imputation Methods for Sensitivity Analyses of Time-to-Event Data With Possibly Informative Censoring

Controlled imputation methods provide general and flexible sensitivity analyses to address nonignorable missing data. For time-to-event data with possibly informative censoring, we compare two popular methods for imputing the censored event time conditional on the time of follow-up discontinuation. One is the delta-adjusted method that specifies that the hazard of having an event for subjects who discontinued before the time point is multiplicatively increased relative to the hazard for subjects who continued beyond the time point. The other is the reference-based method that specifies that the hazard for experimental subjects who discontinued lies between the hazard for experimental subjects who continued and the hazard for the reference control (e.g., placebo) subjects. We consider both piecewise constant and nonparametric baseline hazard functions, Bayesian and frequentist imputations, and Rubin's and bootstrap variances for the multiple imputation estimator. We show that both the reference-based and delta-adjusted sensitivity analyses control the one-sided Type I error rate (in the direction of a difference favoring the experimental treatment). In addition, when the bootstrap variance is used for inference, the reference-based sensitivity analysis has better power than the delta-adjusted sensitivity analysis for the same underlying treatment effect.