As the costs of medical care increase, more studies are evaluating cost in addition to effectiveness of treatments. Cost‐effectiveness analyses in randomized clinical trials have typically been conducted only at the end of follow‐up. However, cost‐effectiveness may change over time. We therefore propose a nonparametric estimator to assess the incremental cost‐effectiveness ratio over time. We also derive the asymptotic variance of our estimator and present formulation of Fieller‐based simultaneous confidence bands. Simulation studies demonstrate the performance of our point estimators, variance estimators, and confidence bands. We also illustrate our methods using data from a randomized clinical trial, the second Multicenter Automatic Defibrillator Implantation Trial. This trial studied the effects of implantable cardioverter‐defibrillators on patients at high risk for cardiac arrhythmia. Results show that our estimator performs well in large samples, indicating promising future directions in the field of cost‐effectiveness. Copyright © 2015 John Wiley & Sons, Ltd.