title: Estimation and confidence regions for multi-dimensional effective dose.
abstract: 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.
authors.affiliation: Department of Statistics and Applied Probability, National University of Singapore, 117546, Singapore. stalj@nus.edu.sg
authors.forename: Jialiang
authors.initials: J
authors.lastname: Li
authors.forename: Erik V
authors.initials: EV
authors.lastname: Nordheim
authors.forename: Chunming
authors.initials: C
authors.lastname: Zhang
authors.forename: Charles E
authors.initials: CE
authors.lastname: Lehner
mesh_terms: D000818:Animals; D003198:Computer Simulation; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D003665:Decompression Sickness / Q000517:prevention & control; D004242:Diving / Q000293:injuries / Q000502:physiology; D016015:Logistic Models; D008954:Models, Biological; D012756:Sheep