Composite endpoints are widely used in clinical trials. The outcome of a clinical trial can affect many individuals and it is therefore of importance that the methods used are as effective and correct as possible. Improvements of the standard method of testing composite endpoints have been proposed and in this thesis, the alternative method using nonparametric combination methodology is compared to the standard method. Performing a simulation study, the power of three combining functions (Fisher, Tippett and the Logistic) are compared to the power of the standard method. The performances of the four methods are evaluated for different compositions of treatment effects, as well as for independent and dependent components. The results show that using the nonparametric combination methodology leads to higher power in both dependent and independent cases. The combining functions are suitable for different compositions of treatment effects, the Fisher combining function being the most versatile. The thesis is written with support from Statisticon AB.