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A common critique of the conventional analysis of composite endpoints is that all disease events are weighted equally, whereas their clinical relevance may differ substantially. We address this by introducing a framework for the weighted analysis of composite endpoints and interpretable test statistics, which are applicable to both binary and time\u2010to\u2010event data. To cope with the difficulty of selecting an exact set of weights, we propose a method for constructing simultaneous confidence intervals and tests that asymptotically preserve the family\u2010wise type I error in the strong sense across families of weights satisfying flexible inequality or order constraints based on the theory of \n<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/sim7147-math-0001.png\" xlink:title=\"urn:x-wiley:sim:media:sim7147:sim7147-math-0001\"\/>\u2010distributions. 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