Consider a typical two-treatment randomized clinical trial involving a time-to-event endpoint, with randomization stratified by a categorical prognostic factor (for example gender). At the design stage, it is often assumed that the treatment hazard ratio (HR) is constant across the strata, and the data are commonly analyzed using the stratified Cox proportional hazards model. We caution that this ubiquitous approach is needlessly risky because departures from the assumption of the HR being the same for all the strata can result in a notably biased and/or less powerful analysis. An alternative approach is proposed in which first the [log] HR is estimated separately for each stratum using an unstratified Cox model, and then the stratum-specific estimates are combined for overall inference using either sample size or ‘minimum risk’ stratum weights. The advantages of the proposed two-step analysis versus the common one-step stratified Cox model analysis are illustrated using simulations that were conducted to support the design of a vaccine clinical trial. Copyright © 2012 John Wiley & Sons, Ltd.