Closure procedures for monotone bi-factorial dose-response designs.

Two goals of multiple-dose factorial trials are (i) demonstrating improved effectiveness of a fixed combination over each of its components as well as (ii) identifying a safe and effective dose range. The authors address both goals though with focus on the second by closure procedures that guarantee strong control of the familywise error rate. Two different families of null hypotheses are investigated for bi-factorial dose-response designs that are monotone with respect to the matrix partial order. One is suitable to find the minimum effective dose(s) and the other one is large enough to identify the highest effective dose step(s). Likelihood ratio tests and appropriate multiple contrast tests are applied to an unbalanced clinical trial example taken from Hung (2000, Statistics in Medicine 19, 2079-2087). Full computer code written in the R language is available from the Internet.