Risk-stratified imputation in survival analysis

Background Censoring that is dependent on covariates associated with survival can arise in randomized trials due to changes in recruitment and eligibility criteria to minimize withdrawals, potentially leading to biased treatment effect estimates. Imputation approaches have been proposed to address censoring in survival analysis; while these approaches may provide unbiased estimates of treatment effects, imputation of a large number of outcomes may over- or underestimate the associated variance based on the imputation pool selected. Purpose We propose an improved method, risk-stratified imputation, as an alternative to address withdrawal related to the risk of events in the context of time-toevent analyses. Methods Our algorithm performs imputation from a pool of replacement subjects with similar values of both treatment and covariate(s) of interest, that is, from a riskstratified sample. This stratification prior to imputation addresses the requirement of time-to-event analysis that censored observations are representative of all other observations in the risk group with similar exposure variables. We compared our risk-stratified imputation to case deletion and bootstrap imputation in a simulated dataset in which the covariate of interest (study withdrawal) was related to treatment. A motivating example from a recent clinical trial is also presented to demonstrate the utility of our method. Results In our simulations, risk-stratified imputation gives estimates of treatment effect comparable to bootstrap and auxiliary variable imputation while avoiding inaccuracies of the latter two in estimating the associated variance. Similar results were obtained in analysis of clinical trial data. Limitations Risk-stratified imputation has little advantage over other imputation methods when covariates of interest are not related to treatment. Risk-stratified imputation is intended for categorical covariates and may be sensitive to the width of the matching window if continuous covariates are used. Conclusions The use of the risk-stratified imputation should facilitate the analysis of many clinical trials, in which one group has a higher withdrawal rate that is related to treatment.