Abstract: Sample size determination for clinical trials with competing risks survival data is proposed in this dissertation for comparing two treatment groups. The procedure is based on a weighted log-rank test, which measures the difference between the weighted averages of the cause-specific hazard functions. To allow for simultaneous inference, our methodology retains the multivariate structure of the competing risk statistic, in which each component corresponds to a specific cause. But no assumption regarding the dependence of the competing risks is made. First we derive the asymptotic normality for the multivariate test statistic under the alternative. Then, the sample size determination procedure is obtained using the asymptotic preperties. This method allows for very general situations, including time-variant hazard ratio and arbitrary choice of survival and censoring distributions. Finally, the proposed method is illustrated on both simulated competing risks data and real data sets. Simulation studies are also conducted to compare our method with existing methods which ignore the competing risks by treating them as independent censoring.