On closed test procedures for dose‐response analysis

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Abstract
This paper concerns the testing of a dose-response effect in medical studies. We consider two situations. The first is when the drug effect on a parameter of interest is likely to increase (or decrease) with increasing doses. We propose a procedure based on the closure principle of Peritz combined with an application of a closed testing procedure of Marcus et al. to a test proposed by Tukey et al. The second situation is the analysis of a drug effect where one might observe a reversal at higher doses. For this situation, we propose simultaneous examination of contrasts among the doses at each of several stages of the testing scheme. We calculate critical values for this procedure incorporating the correlation structure among the contrasts. Both procedures strongly control the family-wise error rate at the pre-determined α level. They also provide information about the shape of the dose response lacking in other commonly used procedures for testing against an ordered alternative hypothesis. We illustrate the procedures on two datasets.