In most randomized clinical trials (RCTs) with a right-censored time-to-event outcome, the hazard ratio is taken as an appropriate measure of the effectiveness of a new treatment compared with a standard-of-care or control treatment. However, it has long been known that the hazard ratio is valid only under the proportional hazards (PH) assumption. This assumption is formally checked only rarely. Some recent trials, particularly the IPASS trial in lung cancer and the ICON7 trial in ovarian cancer, have alerted researchers to the possibility of gross non-PH, raising the critical question of how such data should be analyzed. Here, we propose the use of the restricted mean survival time at a prespecified, fixed time point as a useful general measure to report the difference between two survival curves. We describe different methods of estimating it and we illustrate its application to three RCTs in cancer. The examples are graded from a trial in kidney cancer in which there is no evidence of non-PH, to IPASS, where the opposite is clearly the case. We propose a simple, general scheme for the analysis of data from such RCTs. Key elements of our approach are Andersen's method of ‘pseudo-observations,’ which is based on the Kaplan–Meier estimate of the survival function, and Royston and Parmar's class of flexible parametric survival models, which may be used for analyzing data in the presence or in the absence of PH of the treatment effect. Copyright © 2011 John Wiley & Sons, Ltd.