Joint model imputation to estimate the treatment effect on long-term survival using auxiliary events

Clinical trial duration may be a concern in clinical research, especially in cancer trials where the endpoint is overall survival. A surrogate endpoint can be used as an auxiliary variable to analyze the treatment effect earlier. At an early time point, the high number of censored observations can be compensated by the imputation of the unobserved deaths times. We propose to use predictions of the risk of death from a joint model for a recurrent event and a terminal event, which account for disease relapse information. Two imputation methods were compared: sampling from the estimated parametric distribution of the survival time and sampling using its nonparametric estimation. The treatment effect and its standard error were estimated via multiple imputations. The performances of the two methods were compared in terms of bias in the estimates, standard errors, and coverage probability. Both methods were then retrospectively applied to two randomized clinical trials studying the effect of adjuvant chemotherapy in breast cancer patients.