11.6. Summary

This chapter reviews most important issues arising in the analysis of dose-ranging trials. The following topics are discussed in the chapter.

• Assessment of the dose-related trend. Dose-response analysis begins with an overall assessment of dose-related trends in the response variable. The chapter reviews contrast-based, isotonic (Bartholomew and Williams tests) and non-parametric (Jonckheere test) approaches to testing dose-response trends.

• Estimation of the shape of the dose-response function. The next step after the assessment of the overall drug effect is the characterization of the underlying dose-response relationship. This is achieved by modeling dose-response functions and estimation of their parameters The chapter introduces two dose-response models (linear and sigmoid) that are widely used in dose-ranging trials.

• Determination of the optimal dose. The last step in dose-response analysis is the determination of the therapeutic window defined by the minimum effective and maximum tolerated doses. Two popular approaches to the estimation of the minimum effective dose (MED) are considered in the chapter. The first one, based on the principle of closed testing, relies of a sequential application of contrast tests to determine the smallest dose that is significantly different from placebo. The closed testing procedures control the overall Type I error rate only if the underlying dose-response function is monotone. An alternative approach which relies on the partitioning principle can be safely used even when the assumption of monotonicity is not met.

Statistical methods introduced in this chapter are illustrated using examples from cross-over and parallel group clinical trials.