Partition testing in dose-response studies with multiple endpoints

Dose-response studies with multiple endpoints can be formulated as closed testing or partition testing problems. When the endpoints are primary and secondary, whether the order in which the doses are to be tested is pre-determined or sample determined lead to different partitioning of the parameter space corresponding to the null hypotheses to be tested. We use the case of two doses and two endpoints to illustrate how to apply the partitioning principle to construct multiple tests that control the appropriate error rate. Graphical representation can be useful in visualizing the decision process.