Ajit C. Tamhane, Brent R. Logan (Northwestern University, USA)
Multiple test procedures for identifying the minimum effective and maximum safe doses simultaneously
The therapeutic window is a range of doses of a drug that are both effective and safe. Since generally the efficacy increases with the dose level while the safety decreases, the determination of the therapeutic window reduces to finding the minimum effective and maximum safe doses (MINED and MAXSD). This problem is addressed in the present paper. A bivariate normal model is assumed for the efficacy and safety endpoints. The MINED is defined as the lowest dose that exceeds the mean efficacy of the zero dose by a specified threshold. Similarly the MAXSD is defined as the highest dose that does not exceed the mean toxicity of the zero dose by a specified threshold. Single-step and step-down multiple test procedures are proposed to identify the MINED and MAXSD. These procedures control the type I familywise error probability of declaring any ineffective dose as effective or any unsafe dose as safe at a preassigned level . The critical points of the exact normal theory procedures depend on the correlation coefficient between the efficacy and safety variables. This difficulty can be side-stepped by using the Bonferroni approximation to the exact critical values which amounts to treating the efficacy and safety testing as two separate families, each with type I familywise error probability controlled at level . This approximation is shown to be not very conservative. Another way to avoid this difficulty as well as to relax the assumption of bivariate normality is to use the bootstrap versions of the exact normal theory procedures. The different Bonferroni normal theory and the bootstrap procedures are compared in a simulation study. A real data example is provided to illustrate the procedures.