Retrospective analysis of sequential dose-finding designs

The continual reassessment method (CRM) is a dose-finding design using a dynamic sequential updating scheme. In common with other dynamic schemes the method estimates a current dose level corresponding to some target percentile for experimentation. The estimate is based on all included subjects. This continual reevaluation is made possible by the use of a simple model. As it stands, neither the CRM, nor any of the other dynamic schemes, allow for the correct estimation of some target percentile, based on retrospective data apart from the exceptional situation in which the simplified model exactly generates the observations. In this article we focus on the very specific issue of retrospective analysis of data generated by some arbitrary mechanism and subsequently analyzed via the continual reassessment method. We show how this can be done consistently. The proposed methodology is not restricted to that particular design and is applicable to any sequential updating scheme in which dose levels are associated with percentiles via model inversion.