Kaplan–Meier survival curve estimation is a commonly used non-parametric method to evaluate survival distributions for groups of patients in the clinical trial setting. However, this method does not permit covariate adjustment which may reduce bias and increase precision. The Cox proportional hazards model is a commonly used semi-parametric method for conducting adjusted inferences and may be used to estimate covariate-adjusted survival curves. However, this model relies on the proportional hazards assumption that is often difficult to validate. Research work has been carried out to introduce a non-parametric covariate-adjusted method to estimate survival rates for certain given time intervals. We extend the non-parametric covariate-adjusted method to develop a new model to estimate the survival rates for treatment groups at any time point when an event occurs. Simulation studies are conducted to investigate the model's performance. This model is illustrated with an oncology clinical trial example. Copyright © 2011 John Wiley & Sons, Ltd.