Survival analysis encompasses investigation of time to event data. In most clinical studies, estimating the cumulative incidence function (or the probability of experiencing an event by a given time) is of primary interest. When the data consist of patients who experience an event and censored individuals, a nonparametric estimate of the cumulative incidence can be obtained using the Kaplan-Meier method. Under this approach, the censoring mechanism is assumed to be noninformative. In other words, the survival time of an individual (or the time at which a subject experiences an event) is assumed to be independent of a mechanism that would cause the patient to be censored. Often times, a patient may experience an event other than the one of interest which alters the probability of experiencing the event of interest. Such events are known as competing risk events. In this setting, it would often be of interest to calculate the cumulative incidence of a specific event of interest. Any subject who does not experience the event of interest can be treated as censored. However, a patient experiencing a competing risk event is censored in an informative manner. Hence, the Kaplan-Meier estimation procedure may not be directly applicable. The cumulative incidence function for an event of interest must be calculated by appropriately accounting for the presence of competing risk events. In this paper, we illustrate nonparametric estimation of the cumulative incidence function for an event of interest in the presence of competing risk events using two published data sets. We compare the resulting estimates with those obtained using the Kaplan-Meier approach to demonstrate the importance of appropriately estimating the cumulative incidence of an event of interest in the presence of competing risk events.