Multiple Endpoints Formulations and Properties of Procedures
Arthur Cohen and Harold B. Sackrowitz
A discussion concerning multiple endpoint problems is considered and various properties of procedures are noted. Among the formulations are the following:
the global testing problem and ensuing simultaneous confidence intervals vector risk approach 2^k action problem (assuming k endpoints). This latter formulation with losses corresponding to the number of mistakes appears realistic.
Properties to be discussed include monotonicity and cone order monotonicity of procedures, familywise error rate, admissibility, risk evaluations, likelihood procedures and order-sensitivity, and Bayesian considerations.
The problem of testing treatments vs. control for normal data is used as a prototypical situation for which the multiple endpoint approach applies.