Identifying Therapeutic Window for the Ratio of Means under Heteroscedasticity

Abstract

In efficacy and safety studies, a vital research concern is to determine the therapeutic window of a pharmaceutical compound. The approach to finding minimum effective dose and maximum safe dose involves multiple comparisons. Generally, in such a problem, a family-wise error rate is inherited if multiplicity adjustment is not handled properly. This article without a need for multiplicity adjustment formulates a stepwise confidence interval method to identify a therapeutic window of a pharmaceutical compound when equality of variances cannot be assumed and when ratios of variances are known. This article employed Fieller’s method and obtained individual confidence intervals for the identification of the minimum effective dose and maximum safe dose. A simulation study was performed and the results show that the confidence interval method proposed in this article controls the family-wise error rate strongly. Power increases whenever the ratio of means increases and decreases against higher clinical relevance margins. The proposed procedure was applied to real data and provided optimum results. It was also observed that as both the ratio of means and the sample sizes increase, power increases accordingly.