An Adaptive Two-Stage Dose-Response Design Method for Establishing Proof of Concept

Abstract

We propose an adaptive two-stage dose-response design where a prespecified adaptation rule is used to add and/or drop treatment arms between the stages. We extend the multiple comparison procedures-modeling (MCP-Mod) approach into a two-stage design. In each stage, we use the same set of candidate dose-response models and test for a dose-response relationship or proof of concept (PoC) via model-associated statistics. The stage-wise test results are then combined to establish “global” PoC using a conditional error function. Our simulation studies showed good and more robust power in our design method compared to conventional and fixed designs.

Key Words:

• Adding and/or dropping treatment arms
• Drug development
• Proof of concept
• Two-stage adaptive design
• xMCP-Mod

ACKNOWLEDGMENTS

Stewart J. Anderson was partially supported by an NIMH grant, ACISR: P30 MH090333, and NIH/NCI grant U10CA6965i. The authors thank the associate editor and two referees for their helpful comments and suggestions.

Notes

Note. For model significance, 1 indicates significant model in Stage 1 and 0 otherwise. For doses in Stage 2, 1 indicates doses to be used in Stage 2 and 0 otherwise. In this example, there are eight possible inputs, which can be enumerated as the number of rows in the left column, for the decision making on dose selection. There are four rows in the right column, which is the number of prespecified dose combinations, called adaptation choices 1, 2, 3, and 4.

The lexicographic order of vectors is defined as ordering them dimension by dimension. Vectors are ordered according to their first dimension; vectors with the same value in the first dimension are ordered according to the second dimension; and so forth. For example, (0, 5, 1) < (1, 1, 4) < (1, 2, 3).

We use g ⁻¹(a) as shorthand for the set {b ∈ B: g(b) = a} ⊆ B, that is, the set of all elements b of B that the function g(.) maps to a.

Note. d ∈ {d ₀, d ₁,…, d ₄}.