Confirmatory clinical trials often classify clinical response variables into primary and secondary endpoints. The presence of two or more primary endpoints in a clinical trial usually means that some adjustments of the observed p-values for multiplicity of tests may be required for the control of the type I error rate. In this paper, we discuss statistical concerns associated with some commonly used multiple endpoint adjustment procedures. We also present limited Monte Carlo simulation results to demonstrate the performance of selected p-value-based methods in protecting the type I error rate.