In a cluster randomized trial studying a primary outcome patients are sometimes exposed to competing events. These are risks that alter the probability of the primary outcome occurring. Traditional methods of estimating the cumulative incidence for an outcome and its associated confidence interval under competing risks do not account for the effect of clustering. This may cause incorrect estimation of confidence intervals because outcomes among patients from the same center are correlated. This thesis compared six nonparametric methods of confidence interval construction for cumulative incidence, four of which account for clustering effect, under competing risks via simulation study. Over the range of examined scenarios, if the clustering effect is mild (i.e. ICC = 0.01), estimators not accounting for clustering never have worse coverage than those that do. However, in cases with a large clustering effect (i.e. ICC = 0.05), using confidence interval estimators accounting for clustering should be considered
