Understanding MCP-MOD dose finding as a method based on linear regression

MCP-MOD is a testing and model selection approach for clinical dose finding studies. During testing, contrasts of dose group means are derived from candidate dose response models. A multiple-comparison procedure is applied that controls the alpha level for the family of null hypotheses associated with the contrasts. Provided at least one contrast is significant, a corresponding set of "good" candidate models is identified. The model generating the most significant contrast is typically selected. There have been numerous publications on the method. It was endorsed by the European Medicines Agency. The MCP-MOD procedure can be alternatively represented as a method based on simple linear regression, where "simple" refers to the inclusion of an intercept and a single predictor variable, which is a transformation of dose. It is shown that the contrasts are equal to least squares linear regression slope estimates after a rescaling of the predictor variables. The test for each contrast is the usual t statistic for a null slope parameter, except that a variance estimate with fewer degrees of freedom is used in the standard error. Selecting the model corresponding to the most significant contrast P value is equivalent to selecting the predictor variable yielding the smallest residual sum of squares. This criteria orders the models like a common goodness-of-fit test, but it does not assure a good fit. Common inferential methods applied to the selected model are subject to distortions that are often present following data-based model selection.