Sample Size for Linear and Quadratic Terms in a Dose-Response Relationship

Tables for sample size determination in parallel group dose-response clinical trials analyzed with second degree equations are presented in this paper. They were obtained by simulations and provide sample sizes to detect, with different power values, single degree of freedom F tests for a linear component (indicating a trend across doses) and a quadratic component (usually indicating a plateau, less frequently a nonmonotonic relationship or a steep change in slope).

In addition to a sample size for a linear pattern (response proportional to log dose), one nonmonotonic example and different patterns with plateaus are available. Selection of a pattern depends on previous pharmacological information. Sample sizes to detect quadratic components are usually larger than those for the linear component, except in the nonmonotonic case (rare but important to detect). Practical considerations for choosing the patterns in a given situation are described.