Estimation and Confidence Regions for Multi-Dimensional Effective Dose

The problem of finding confidence regions for multiple predictor variables corresponding to given expected values of a response variable has not been adequately resolved. Motivated by an example from a study on hyperbaric exposure using a logistic regression model, we develop a conceptual framework for the estimation of the multi‐dimensional effective dose for binary outcomes. The k ‐dimensional effective dose can be determined by conditioning on k – 1 components and solving for the last component as a conditional univariate effective dose. We consider various approaches for calculating confidence regions for the multi‐dimensional effective dose and compare them via a simulation study for a range of possible designs. We analyze data related to decompression sickness to illustrate our procedure. Our results provide a practical approach to finding confidence regions for predictor variables for a given response value. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)