An adaptive method for establishing a dose‐response relationship

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Abstract
A multistage sampling method is proposed in dose—response trials, where dose adaptions can be performed in the preplanned adaptive interim analyses. The overall test for proving a dose—response relationship is performed by Fisher'S product criterion for the p‐values from the separate tests of a dose effect in the disjoint samples at the different stages. Based on these p‐values decision boundaries for early stopping with the rejection of the global null hypothesis of no existing dose—response relationship are introduced. The power of the adaptive two‐stage procedure using a particular adaptation rule is compared with the power of the test for a linear trend under analysis of variance assumptions in extensive simulations. The bias in estimation is also quantified. This procedure could be used for establishing a dose—response relationship without including a placebo treatment.

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