Background: Intermediate outcome variables can often be used as auxiliary variables for the true outcome of interest in randomized clinical trials. For many cancers, time to recurrence is an informative marker in predicting a patient's overall survival outcome and could provide auxiliary information for the analysis of survival times.
Purpose: To investigate whether models linking recurrence and death combined with a multiple imputation procedure for censored observations can result in efficiency gains in the estimation of treatment effects and be used to shorten trial lengths.
Methods: Recurrence and death times are modeled using data from 12 trials in colorectal cancer. Multiple imputation is used as a strategy for handling missing values arising from censoring. The imputation procedure uses a cure model for time to recurrence and a time-dependent Weibull proportional hazards model for time to death. Recurrence times are imputed, and then death times are imputed conditionally on recurrence times. To illustrate these methods, trials are artificially censored 2 years after the last accrual, the imputation procedure implemented, and a log-rank test and Cox model used to analyze and compare these new data with the original data.
Results: The results show modest, but consistent gains in efficiency in the analysis using the auxiliary information in recurrence times. Comparison of analyses show the treatment effect estimates and log-rank test results from the 2-year censored imputed data to be in between the estimates from the original data and the artificially censored data, indicating that the procedure was able to recover some of the lost information due to censoring.
Limitations: The models used are all fully parametric, requiring distributional assumptions of the data.
Conclusions: The proposed models may be useful in improving the efficiency in estimation of treatment effects in cancer trials and shortening trial length.