In data analysis, when a variety of clinical endpoints are combined into a composite endpoint for evaluating the effect of treatment, several approaches for analysis are mainly based on prioritized clinical endpoints. By standard analysis framework of a composite endpoint, a subject is characterized as a winner or loser based on the outcome of the first prioritized endpoint. If that outcome is unknown, then the subject is characterized as a winner or loser depending on the outcome of the second prioritized endpoint, and so on. Yet, a subject can be categorized as winner or loser without ordering the endpoints. In this work, we construct a composite score using the generalized Wilcoxon testing procedure by combining all endpoints together and making comparisons within all available between-treatment pairs. Within each pair, the subject who performs better on every single component of the composite endpoint is assigned a better score. We propose a parametric significance and bootstrap testing procedures to evaluate the effect of treatment. We perform an extensive simulation study to assess the operating characteristics of the proposed methods.