When the data from long-term clinical trials are reviewed continually over time for evidence of adverse or beneficial treatment effects, the classical significance tests are not appropriate. A simulation procedure is described which provides, for different mortality rates and different patterns of patient enrollment, the correct critical regions corresponding to specified frequencies of looks at the data over the course of the study. The power of the test and the robustness of the critical regions for differences in pattern of enrollment, length of study, mortality model and sample size are discussed. An application is made to a drug trial in coronary heart disease.